Question,Tag,label The expression large frac x y x y 2 is equal to The maximum of x and y The minimum of x and y 1 None of the above ,Absolute Value,0 If x is real and mid x 2 2x 3 mid 11 then possible values of mid x 3 x 2 x mid include 2 4 2 14 4 52 14 52 ,Absolute Value,0 If mid 4X 7 mid 5 then the values of 2 mid X mid mid X mid is quad 2 left dfrac 1 3 right left dfrac 1 2 right 3 left dfrac 3 2 right 9 left dfrac 2 3 right 9 ,Absolute Value,0 An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above ,Abstract Data Type,1 The number of full and half adders required to add 16 bit numbers is 8 half adders 8 full adders 1 half adder 15 full adders 16 half adders 0 full adders 4 half adders 12 full adders ,Adder,2 Fill in the blanks In the two bit full adder subtractor unit shown in below figure when the switch is in position 2 ___________ using _________ arithmetic ,Adder,2 Consider the ALU shown below If the operands are in 2 u2019s complement representation which of the following operations can be performed by suitably setting the control lines K and C_0 only and u2013 denote addition and subtraction respectively A B and A u2013 B but not A 1 A B and A 1 but not A u2013 B A B but not A u2013 B or A 1 A B and A u2013 B and A 1 ,Adder,2 Consider an eight bit ripple carry adder for computing the sum of A and B where A and B are integers represented in 2 s complement form If the decimal value of A is one the decimal value of B that leads to the longest latency for the sum to stabilize is ___________,Adder,2 An N bit carry lookahead adder where N is a multiple of 4 employs ICs 74181 4 bit ALU and 74182 4 bit carry lookahead generator The minimum addition time using the best architecture for this adder is proportional to N proportional to log N a constant None of the above ,Adder,2 A 4 bit carry look ahead adder which adds two 4 bit numbers is designed using AND OR NOT NAND NOR gates only Assuming that all the inputs are available in both complemented and uncomplemented forms and the delay of each gate is one time unit what is the overall propagation delay of the adder Assume that the carry network has been implemented using two level AND OR logic 4 time units 6 time units 10 time units 12 time units ,Adder,2 Consider a carry look ahead adder for adding two n bit integers built using gates of fan in at most two The time to perform addition using this adder is Theta 1 Theta log n Theta sqrt n Theta n ,Adder,2 Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable ,Aliasing,3 The maximum gate delay for any output to appear in an array multiplier for multiplying two n bit numbers is O n 2 O n O log n O 1 ,Array Multiplier,4 Consider an array multiplier for multiplying two n bit numbers If each gate in the circuit has a unit delay the total delay of the multiplier is Theta 1 Theta log n Theta n Theta n 2 ,Array Multiplier,4 The procedure given below is required to find and replace certain characters inside an input character string supplied in array A The characters to be replaced are supplied in array oldc while their respective replacement characters are supplied in array newc Array A has a fixed length of five characters while arrays oldc and newc contain three characters each However the procedure is flawed void find_and_replace char A char oldc char newc for int i 0 i lt 5 i for int j 0 j lt 3 j if A i oldc j A i newc j The procedure is tested with the following four test cases oldc u201cabc u201d newc u201cdab u201d oldc u201ccde u201d newc u201cbcd u201d oldc u201cbca u201d newc u201ccda u201d oldc u201cabc u201d newc u201cbac u201d The tester now tests the program on all input strings of length five consisting of characters u2018 a u2019 u2018 b u2019 u2018 c u2019 u2018 d u2019 and u2018 e u2019 with duplicates allowed If the tester carries out this testing with the four test cases given above how many test cases will be able to capture the flaw Only one Only two Only three All four ,Arrays,5 The procedure given below is required to find and replace certain characters inside an input character string supplied in array A The characters to be replaced are supplied in array oldc while their respective replacement characters are supplied in array newc Array A has a fixed length of five characters while arrays oldc and newc contain three characters each However the procedure is flawed void find_and_replace char A char oldc char newc for int i 0 i lt 5 i for int j 0 j lt 3 j if A i oldc j A i newc j The procedure is tested with the following four test cases oldc u201cabc u201d newc u201cdab u201d oldc u201ccde u201d newc u201cbcd u201d oldc u201cbca u201d newc u201ccda u201d oldc u201cabc u201d newc u201cbac u201d If array A is made to hold the string u201c abcde u201d which of the above four test cases will be successful in exposing the flaw in this procedure None 2 only 3 and 4 only 4 only ,Arrays,5 Suppose you are given arrays p 1 N and q 1 N both uninitialized that is each location may contain an arbitrary value and a variable count initialized to 0 Consider the following procedures set and is _set set i count count 1 q count i p i count is_set i if p i u2264 0 or p i gt count return false if q p i u2260 i return false return true Suppose we make the following sequence of calls set 7 set 3 set 9 After these sequence of calls what is the value of count and what do q 1 q 2 q 3 p 7 p 3 and p 9 contain Complete the following statement The first count elements of __________contain values i such that set _________________ has been called Show that if set i has not been called for some i then regardless of what p i contains is _set i will return false ,Arrays,5 Let A be a two dimensional array declared as follows A array 1 u2026 10 1 u2026 15 of integer Assuming that each integer takes one memory location the array is stored in row major order and the first element of the array is stored at location 100 what is the address of the element A i j 15i j 84 15j i 84 10i j 89 10j i 89 ,Arrays,5 In a compact single dimensional array representation for lower triangular matrices i e all the elements above the diagonal are zero of size n imes n non zero elements i e elements of lower triangle of each row are stored one after another starting from the first row the index of the i j th element of the lower triangular matrix in this new representation is i j i j 1 j 1 frac i i 1 2 i frac j j 1 2 ,Arrays,5 Consider the C function given below Assume that the array listA contains n gt 0 elements sorted in ascending order int ProcessArray int listA int x int n int i j k i 0 j n 1 do k i j 2 if x lt listA k j k 1 if listA k lt x i k 1 while i lt j if listA k x return k else return 1 Which one of the following statements about the function ProcessArray is CORRECT It will run into an infinite loop when x is not in listA It is an implementation of binary search It will always find the maximum element in listA It will return u2212 1 even when x is present in listA ,Arrays,5 Consider an array A 1 n It consists of a permutation of numbers 1 n Now compute another array B 1 n as follows B A i i for all i Which of the following is true B will be a sorted array B is a permutation of array A Doing the same transformation twice will not give the same array B is not a permutation of array A None of the above ,Arrays,5 An n imes n array v is defined as follows v left i j right i j for all i j i leq n 1 leq j leq n The sum of the elements of the array v is 0 n 1 n 2 3n 2 n 2 frac left n 1 right 2 ,Arrays,5 An array A contains n integers in non decreasing order A 1 leq A 2 leq cdots leq A n Describe using Pascal like pseudo code a linear time algorithm to find i j such that A i A j a given integer M if such i j exist ,Arrays,5 An array A contains n geq 1 positive integers in the locations A 1 A 2 dots A n The following program fragment prints the length of a shortest sequence of consecutive elements of A A i A i 1 dots A j such that the sum of their values is geq M a given positive number It prints u2018 n 1 u2019 if no such sequence exists Complete the program by filling in the boxes In each case use the simplest possible expression Write only the line number and the contents of the box begin i 1 j 1 sum u25fb min n finish false while not finish do if u25fb then if j n then finish true else begin j j 1 sum u25fb end else begin if j i lt min then min j i sum sum u2013A i i i 1 end writeln min 1 end ,Arrays,5 A Young tableau is a 2D array of integers increasing from left to right and from top to bottom Any unfilled entries are marked with infty and hence there cannot be any entry to the right of or below a infty The following Young tableau consists of unique entries 1 2 5 14 3 4 6 23 10 12 18 25 31 infty infty infty When an element is removed from a Young tableau other elements should be moved into its place so that the resulting table is still a Young tableau unfilled entries may be filled with a infty The minimum number of entries other than 1 to be shifted to remove 1 from the given Young tableau is _____ ,Arrays,5 A program P reads in 500 integers in the range 0 100 representing the scores of 500 students It then prints the frequency of each score above 50 What would be the best way for P to store the frequencies An array of 50 numbers An array of 100 numbers An array of 500 numbers A dynamically allocated array of 550 numbers ,Arrays,5 The order of an internal node in a B tree index is the maximum number of children it can have Suppose that a child pointer takes 6 bytes the search field value takes 14 bytes and the block size is 512 bytes What is the order of the internal node 24 25 26 27 ,B Tree,6 The order of a leaf node in a B tree is the maximum number of value data record pointer pairs it can hold Given that the block size is 1K bytes data record pointer is 7 bytes long the value field is 9 bytes long and a block pointer is 6 bytes long what is the order of the leaf node 63 64 67 68 ,B Tree,6 In a database file structure the search key field is 9 bytes long the block size is 512 bytes a record pointer is 7 bytes and a block pointer is 6 bytes The largest possible order of a non leaf node in a B tree implementing this file structure is 23 24 34 44 ,B Tree,6 Consider the B tree in the adjoining figure where each node has at most two keys and three links Now the key K 50 is deleted from the B tree resulting after the two insertions made earlier Consider the following statements about the B tree resulting after this deletion The height of the tree remains the same The node k20 disregarding the links is present in the tree The root node remains unchanged disregarding the links 1 Which one of the following options is true Statements i and ii are true Statements ii and iii are true Statements iii and i are true All the statements are false ,B Tree,6 Consider the B tree in the adjoining figure where each node has at most two keys and three links Keys K 15 and then K 25 are inserted into this tree in that order Exactly how many of the following nodes disregarding the links will be present in the tree after the two insertions 1 2 3 4 ,B Tree,6 Consider a table T in a relational database with a key field K A B tree of order p is used as an access structure on K where p denotes the maximum number of tree pointers in a B tree index node Assume that K is 10 bytes long disk block size is 512 bytes each data pointer PD is 8 bytes long and each block pointer PB is 5 bytes long In order for each B tree node to fit in a single disk block the maximum value of p is 20 22 23 32 ,B Tree,6 Consider a B tree with degree m that is the number of children c of any internal note except the root is such that m leq c leq 2m 1 Derive the maximum and minimum number of records in the leaf nodes for such a B tree with height h h geq 1 Assume that the root of a tree is at height 0 ,B Tree,6 A B Tree used as an index for a large database table has four levels including the root node If a new key is inserted in this index then the maximum number of nodes that could be newly created in the process are 5 4 3 2 ,B Tree,6 A B tree index is to be built on the Name attribute of the relation STUDENT Assume that all the student names are of length 8 bytes disk blocks are of size 512 bytes and index pointers are of size 4 bytes Given the scenario what would be the best choice of the degree i e number of pointers per node of the B tree 16 42 43 44 ,B Tree,6 Which of the following is correct B trees are for storing data on disk and B trees are for main memory Range queries are faster on B trees B trees are for primary indexes and B trees are for secondary indexes The height of a B tree is independent of the number of records ,B Tree,6 The following table refers to search items for a key in B trees and B trees B u2212tree B u2212tree Successful search Unsuccessful search Successful search Unsuccessful search X1 X2 X3 X4 A successful search means that the key exists in the database and unsuccessful means that it is not present in the database Each of the entries X_1 X_2 X_3 and X_4 can have a value of either Constant or Variable Constant means that the search time is the same independent of the specific key value where variable means that it is dependent on the specific key value chosen for the search Give the correct values for the entries X_1 X_2 X_3 and X_4 for example X_1 ext Constant X_2 ext Constant X_3 ext Constant X_4 ext Constant Relation R A B has the following view defined on it CREATE VIEW V AS SELECT R1 A R2 B FROM R AS R1 R as R2 WHERE R1 B R2 A The current contents of relation R are shown below What are the contents of the view V A B 1 2 2 4 6 6 9 2 3 4 5 7 8 10 The tuples 2 11 and 11 6 are now inserted into R What are the additional tuples that are inserted in V ,B Tree,6 Consider B tree of order d shown in figure A B tree of order d contains between d and 2d keys in each node Draw the resulting B tree after 100 is inserted in the figure below For a B tree of order d with n leaf nodes the number of nodes accessed during a search is O ,B Tree,6 B trees are preferred to binary trees in databases because Disk capacities are greater than memory capacities Disk access is much slower than memory access Disk data transfer rates are much less than memory data transfer rates Disks are more reliable than memory ,B Tree,6 A B tree of order d is a tree in which each internal node has between d and 2 d key values An internal node with M key values has M 1 children The root if it is an internal node has between 1 and 2d key values The distance of a node from the root is the length of the path from the root to the node All leaves are at the same distance from the root The height of the tree is the distance of a leaf from the root What is the total number of key values in the internal nodes of a B tree with l leaves l geq 2 What is the maximum number of internal nodes in a B tree of order 4 with 52 leaves What is the minimum number of leaves in a B tree of order d and height h h geq 1 ,B Tree,6 Suppose a fair six sided die is rolled once If the value on the die is 1 2 or 3 the die is rolled a second time What is the probability that the sum total of values that turn up is at least 6 dfrac 10 21 dfrac 5 12 dfrac 2 3 dfrac 1 6 ,Bayes Theorem,7 Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1 blue ball A ball is selected as follows i select a box ii choose a ball from the selected box such that each ball in the box is equally likely to be chosen The probabilities of selecting boxes P and Q are dfrac 1 3 and dfrac 2 3 respectively Given that a ball selected in the above process is a red ball the probability that it came from the box P is dfrac 4 19 dfrac 5 19 dfrac 2 9 dfrac 19 30 ,Bayes Theorem,7 An automobile plant contracted to buy shock absorbers from two suppliers X and Y X supplies 60 and Y supplies 40 of the shock absorbers All shock absorbers are subjected to a quality test The ones that pass the quality test are considered reliable Of X u2019s shock absorbers 96 are reliable Of Y u2019s shock absorbers 72 are reliable The probability that a randomly chosen shock absorber which is found to be reliable is made by Y is A 0 288 B 0 334 C 0 667 D 0 720,Bayes Theorem,7 The number of possible commutative binary operations that can be defined on a set of n elements for a given n is ___________ ,Binary Operation,8 The binary operator u2260 is defined by the following truth table p q p u2260 q 0 0 0 0 1 1 1 0 1 1 1 0 Which one of the following is true about the binary operator u2260 Both commutative and associative Commutative but not associative Not commutative but associative Neither commutative nor associative ,Binary Operation,8 On the set N of non negative integers the binary operation ______ is associative and non commutative ,Binary Operation,8 Let be the binary operator defined as X Y X Y where X and Y are Boolean variables Consider the following two statements S1 P Q R P Q R S2 Q R R Q Which are the following is are true for the Boolean variables P Q and R Only S1 is true Only S2 is true Both S1 and S2 are true Neither S1 nor S2 are true ,Binary Operation,8 For the set N of natural numbers and a binary operation f N x N u2192 N an element z u220a N is called an identity for f if f a z a f z a for all a u220a N Which of the following binary operations have an identity f x y x y 3 f x y max x y f x y xy I and II only II and III only I and III only None of these ,Binary Operation,8 Consider the set a b c with binary operators and defined as follows a b c a b a c b a b c c a c b a b c a a b c b b c a c c c b For example a c c c a a c b c and b c a Given the following set of equations a x a y c b x c y c The number of solution s i e pair s x y that satisfy the equations is 0 1 2 3 ,Binary Operation,8 A logical binary relation odot is defined as follows A B A odot B True True True True False True False True False False False True Let sim be the unary negation NOT operator with higher precedence then odot Which one of the following is equivalent to A wedge B sim A odot B sim A odot sim B sim sim A odot sim B sim sim A odot B ,Binary Operation,8 A binary operation oplus on a set of integers is defined as x oplus y x 2 y 2 Which one of the following statements is TRUE about oplus A Commutative but not associative B Both commutative and associative C Associative but not commutative D Neither commutative nor associative,Binary Operation,8 When searching for the key value 60 in a binary search tree nodes containing the key values 10 20 40 50 70 80 90 are traversed not necessarily in the order given How many different orders are possible in which these key values can occur on the search path from the root to the node containing the value 60 35 64 128 5040 ,Binary Search Tree,9 The numbers 1 2 dots n are inserted in a binary search tree in some order In the resulting tree the right subtree of the root contains p nodes The first number to be inserted in the tree must be p p 1 n p n p 1 ,Binary Search Tree,9 The following numbers are inserted into an empty binary search tree in the given order 10 1 3 5 15 12 16 What is the height of the binary search tree the height is the maximum distance of a leaf node from the root 2 3 4 6 ,Binary Search Tree,9 Suppose the numbers 7 5 1 8 3 6 0 9 4 2 are inserted in that order into an initially empty binary search tree The binary search tree uses the usual ordering on natural numbers What is the in order traversal sequence of the resultant tree 7 5 1 0 3 2 4 6 8 9 0 2 4 3 1 6 5 9 8 7 0 1 2 3 4 5 6 7 8 9 9 8 6 4 2 3 0 1 5 7 ,Binary Search Tree,9 Suppose that we have numbers between 1 and 100 in a binary search tree and want to search for the number 55 Which of the following sequences CANNOT be the sequence of nodes examined 10 75 64 43 60 57 55 90 12 68 34 62 45 55 9 85 47 68 43 57 55 79 14 72 56 16 53 55 ,Binary Search Tree,9 Let T n be the number of different binary search trees on n distinct elements Then T n sum_ k 1 n T k 1 T x where x is n k 1 n k n k 1 n k 2 ,Binary Search Tree,9 A program takes as input a balanced binary search tree with n leaf nodes and computes the value of a function g x for each node x If the cost of computing g x is Large min left substack ext number of leaf nodes ext in left subtree of x substack ext number of leaf nodes ext in right subtree of x right Then the worst case time complexity of the program is Theta n Theta n log n Theta n 2 Theta n 2 log n ,Binary Search Tree,9 A data structure is required for storing a set of integers such that each of the following operations can be done in O log n time where n is the number of elements in the set Deletion of the smallest element Insertion of an element if it is not already present in the set Which of the following data structures can be used for this purpose A heap can be used but not a balanced binary search tree A balanced binary search tree can be used but not a heap Both balanced binary search tree and heap can be used Neither balanced search tree nor heap can be used ,Binary Search Tree,9 A binary search tree is used to locate the number 43 Which of the following probe sequences are possible and which are not Explain a 61 52 14 17 40 43 b 2 3 50 40 60 43 c 10 65 31 48 37 43 d 81 61 52 14 41 43 e 17 77 27 66 18 43 ,Binary Search Tree,9 A binary search tree is generated by inserting in order the following integers 50 15 62 5 20 58 91 3 8 37 60 24 The number of nodes in the left subtree and right subtree of the root respectively is 4 7 7 4 8 3 3 8 ,Binary Search Tree,9 A binary search tree contains the numbers 1 2 3 4 5 6 7 8 When the tree is traversed in pre order and the values in each node printed out the sequence of values obtained is 5 3 1 2 4 6 8 7 If the tree is traversed in post order the sequence obtained would be 8 7 6 5 4 3 2 1 1 2 3 4 8 7 6 5 2 1 4 3 6 7 8 5 2 1 4 3 7 8 6 5 ,Binary Search Tree,9 A Binary Search Tree BST stores values in the range 37 to 573 Consider the following sequence of keys 81 537 102 439 285 376 305 52 97 121 195 242 381 472 142 248 520 386 345 270 307 550 149 507 395 463 402 270 Suppose the BST has been unsuccessfully searched for key 273 Which all of the above sequences list nodes in the order in which we could have encountered them in the search II and III only I and III only III and IV only III only ,Binary Search Tree,9 Insert the following keys one by one into a binary search tree in the order specified 15 32 20 9 3 25 12 1 Show the final binary search tree after the insertions Draw the binary search tree after deleting 15 from it Complete the statements S1 S2 and S3 in the following function so that the function computes the depth of a binary tree rooted at t ypedef struct tnode int key struct tnode left right Tree int depth Tree t int x y it t NULL return 0 x depth t gt left S1 ___________ S2 if x gt y return __________ S3 else return _______ ,Binary Search Tree,9 What is the number of binary trees with 3 nodes which when traversed in post order give the sequence A B C Draw all these binary trees ,Binary Tree,10 State whether the following statements are TRUE or FALSE It is possible to construct a binary tree uniquely whose pre order and post order traversals are given ,Binary Tree,10 State whether the following statements are TRUE or FALSE If the number of leaves in a tree is not a power of 2 then the tree is not a binary tree ,Binary Tree,10 Prove by the principal of mathematical induction that for any binary tree in which every non leaf node has 2 descendants the number of leaves in the tree is one more than the number of non leaf nodes ,Binary Tree,10 In the balanced binary tree in the below figure how many nodes will become unbalanced when a node is inserted as a child of the node u201cg u201d 1 3 7 8 ,Binary Tree,10 If the binary tree in figure is traversed in inorder then the order in which the nodes will be visited is ______ ,Binary Tree,10 Construct a binary tree whose preorder traversal is K L N M P R Q S T and inorder traversal is N L K P R M S Q T ,Binary Tree,10 Consider the binary tree in the figure below Outline a procedure in Pseudo code to delete an arbitrary node from such a binary tree with n nodes that preserves the structures What is the worst case time complexity of your procedure ,Binary Tree,10 Consider the binary tree in the figure below Give different steps for deleting the node with key 5 so that the structure is preserved ,Binary Tree,10 A rooted tree with 12 nodes has its nodes numbered 1 to 12 in pre order When the tree is traversed in post order the nodes are visited in the order 3 5 4 2 7 8 6 10 11 12 9 1 Reconstruct the original tree from this information that is find the parent of each node and show the tree diagrammatically ,Binary Tree,10 A binary tree T has n leaf nodes The number of nodes of degree 2 in T is log_2 n n 1 n 2 n ,Binary Tree,10 A binary search tree contains the value 1 2 3 4 5 6 7 8 The tree is traversed in pre order and the values are printed out Which of the following sequences is a valid output 5 3 1 2 4 7 8 6 5 3 1 2 6 4 8 7 5 3 2 4 1 6 7 8 5 3 1 2 4 7 6 8 ,Binary Tree,10 Which of the following sequences denotes the post order traversal sequence of the below tree f e g c d b a g c b d a f e g c d b f e a f e d g c b a ,Binary Tree,10 The weighted external path length of the binary tree in figure is ______ ,Binary Tree,10 Consider the binary tree in the figure below a What structure is represented by the binary tree ,Binary Tree,10 When a coin is tossed the probability of getting a Head is p 0 lt p lt 1 Let N be the random variable denoting the number of tosses till the first Head appears including the toss where the Head appears Assuming that successive tosses are independent the expected value of N is dfrac 1 p dfrac 1 1 p dfrac 1 p 2 dfrac 1 1 p 2 ,Binomial Distribution,11 For each element in a set of size 2n an unbiased coin is tossed The 2n coin tosses are independent An element is chosen if the corresponding coin toss was a head The probability that exactly n elements are chosen is frac 2n mathrm C _n 4 n frac 2n mathrm C _n 2 n frac 1 2n mathrm C _n frac 1 2 ,Binomial Distribution,11 An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same Assuming that the trials are independent the expected number of tosses is 3 4 5 6 ,Binomial Distribution,11 A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail respectively The probability that two such randomly generated strings are not identical is frac 1 2 n 1 frac 1 n frac 1 n 1 frac 1 2 n ,Binomial Distribution,11 The total number of Boolean functions which can be realised with four variables is 4 17 256 65 536 ,Boolean Algebra,12 The simultaneous equations on the Boolean variables x y z and w x y z 1 xy 0 xz w 1 xy bar z bar w 0 have the following solution for x y z and w respectively 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 ,Boolean Algebra,12 Let x_ 1 u2295 x_ 2 u2295 x_ 3 u2295 x_ 4 0 where x_ 1 x_ 2 x_ 3 x_ 4 are Boolean variables and u2295 is the XOR operator Which one of the following must always be TRUE x_ 1 x_ 2 x_ 3 x_ 4 0 x_ 1 x_ 3 x_ 2 0 bar x _ 1 u2295 bar x _ 3 bar x _ 2 u2295 bar x _ 4 x_ 1 x_ 2 x_ 3 x_ 4 0 ,Boolean Algebra,12 For x in 0 1 let lnot x denote the negation of x that is lnot x begin cases 1 amp mbox iff x 0 0 amp mbox iff x 1 end cases If x in 0 1 n then lnot x denotes the component wise negation of x that is lnot x _i biggl lnot x_i mid i in 1 n biggr Consider a circuit C computing a function f 0 1 n o 0 1 using AND land OR lor and NOT lnot gates Let D be the circuit obtained from C by replacing each AND gate by an OR gate and replacing each OR gate by an AND Suppose D computes the function g Which of the following is true for all inputs x g x lnot f x g x f x land f lnot x g x f x lor f lnot x g x lnot f lnot x None of the above ,Boolean Algebra,12 What values of A B C and D satisfy the following simultaneous Boolean equations overline A AB 0 AB AC AB A overline C CD overline C D A 1 B 0 C 0 D 1 A 1 B 1 C 0 D 0 A 1 B 0 C 1 D 1 A 1 B 0 C 0 D 0 ,Boolean Expressions,13 The truth table X Y X Y 0 0 0 0 1 0 1 0 1 1 1 1 represents the Boolean function X X Y X oplus Y Y ,Boolean Expressions,13 The function AB C A BC ABC A B C AB C is equivalent to AC AB A C AB AC A C A B AC AB A B AC AB ,Boolean Expressions,13 The Boolean expression A oplus B oplus A is equivalent to AB bar A bar B bar A B A bar B B bar A ,Boolean Expressions,13 Let f w x y z sum left 0 4 5 7 8 9 13 15 right Which of the following expressions are NOT equivalent to f P x y z w xy wy z xz Q w y z wx y xz R w y z wx y xyz xy z S x y z wx y w y P only Q and S R and S S only ,Boolean Expressions,13 Let f A B A B Simplified expression for function f f x y y z is x z xyz xy z None of the above ,Boolean Expressions,13 Let be defined as x y bar x y Let z x y Value of z x is bar x y x 0 1 ,Boolean Expressions,13 If P Q R are Boolean variables then P bar Q P bar Q P R bar P bar R bar Q simplifies to P bar Q P bar R P bar Q R P bar R Q ,Boolean Expressions,13 Find values of Boolean variables A B C which satisfy the following equations A B 1 AC BC A C 1 AB 0 ,Boolean Expressions,13 Define the connective for the Boolean variables X and Y as X Y XY X Y Let Z X Y Consider the following expressions P Q and R P X Y Z Q Y X Z R X Y Z 1 Which of the following is TRUE Only P and Q are valid Only Q and R are valid Only P and R are valid All P Q R are valid ,Boolean Expressions,13 Consider the following state diagram and its realization by a JK flip flop The combinational circuit generates J and K in terms of x y and Q The Boolean expressions for J and K are overline x oplus y and overline x oplus y overline x oplus y and x oplus y x oplus y and overline x oplus y x oplus y and x oplus y ,Boolean Expressions,13 A Boolean function x u2019y u2019 xy x u2019y is equivalent to x y x y x y x y ,Boolean Expressions,13 Let be a Boolean operation defined as A B AB overline A overline B If C A B then evaluate and fill in the blanks A A ____ C A ____ Solve the following boolean equations for the values of A B and C AB overline A C 1 AC B 0 ,Boolean Expressions,13 Consider the Boolean operator with the following properties x 0 x x 1 overline x x x 0 and x overline x 1 Then x y is equivalent to x overline y overline x y x overline y overline x overline y overline x y xy xy overline x overline y ,Boolean Expressions,13 Choose the correct alternatives more than one may be correct and write the corresponding letters only The operation which is commutative but not associative is AND OR EX OR NAND ,Boolean Operations,14 When multiplicand Y is multiplied by multiplier X x_ n 1 x_ n 2 dots x_0 using bit pair recoding in Booth s algorithm partial products are generated according to the following table Row xi 1 xi xi 1 Partial Product 1 0 0 0 0 2 0 0 1 Y 3 0 1 0 Y 4 0 1 1 2Y 5 1 0 0 6 1 0 1 Y 7 1 1 0 Y 8 1 1 1 The partial products for rows 5 and 8 are 2Y and Y 2Y and 2Y 2Y and 0 0 and Y ,Booth Recoding,15 Using Booth s Algorithm for multiplication the multiplier 57 will be recoded as 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 ,Booths Algorithm,16 The two numbers given below are multiplied using the Booth s algorithm Multiplicand 0101 1010 1110 1110 Multiplier 0111 0111 1011 1101 How many additions Subtractions are required for the multiplication of the above two numbers 6 8 10 12 ,Booths Algorithm,16 Booth u2019s algorithm for integer multiplication gives worst performance when the multiplier pattern is 101010 u2026 1010 100000 u2026 0001 111111 u2026 1111 011111 u2026 1110 ,Booths Algorithm,16 Booth s coding in 8 bits for the decimal number 57 is 0 100 1000 0 100 100 1 0 1 100 10 1 00 10 100 1 ,Booths Algorithm,16 The maximum number of superkeys for the relation schema R E F G H with E as the key is _____ ,Candidate Keys,17 Given an instance of the STUDENTS relation as shown as below StudentID StudentName StudentEmail StudentAge CPI 2345 Shankar Shankar math X 9 4 1287 Swati swati ee 19 9 5 7853 Shankar Shankar cse 19 9 4 9876 Swati swati mech 18 9 3 8765 Ganesh ganesh civil 19 8 7 For StudentName StudentAge to be a key for this instance the value X should NOT be equal to______ ,Candidate Keys,17 Consider a relational table with a single record for each registered student with the following attributes ext Registration_Num Unique registration number for each registered student ext UID Unique identity number unique at the national level for each citizen ext BankAccount_Num Unique account number at the bank A student can have multiple accounts or joint accounts This attribute stores the primary account number ext Name Name of the student ext Hostel_Room Room number of the hostel Which of the following options is INCORRECT A ext BankAccount_Num is a candidate key B ext Registration_Num can be a primary key C ext UID is a candidate key if all students are from the same country D If S is a super key such that S cap ext UID is ext NULL then S cup ext UID is also a superkey,Candidate Keys,17 An instance of a relational scheme R A B C has distinct values for attribute A Can you conclude that A is a candidate key for R ,Candidate Keys,17 A prime attribute of a relation scheme R is an attribute that appears in all candidate keys of R in some candidate key of R in a foreign key of R only in the primary key of R ,Candidate Keys,17 The total number of prime implicants of the function f w x y z sum 0 2 4 5 6 10 is __________,Canonical Normal Form,18 The minterm expansion of f P Q R PQ Q bar R P bar R is m_2 m_4 m_6 m_7 m_0 m_1 m_3 m_5 m_0 m_1 m_6 m_7 m_2 m_3 m_4 m_5 ,Canonical Normal Form,18 Given the function F P QR where F is a function in three Boolean variables P Q and R and P P consider the following statements S1 F sum 4 5 6 S2 F sum 0 1 2 3 7 S3 F Pi 4 5 6 S4 F Pi 0 1 2 3 7 Which of the following is true S1 False S2 True S3 True S4 False S1 True S2 False S3 False S4 True S1 False S2 False S3 True S4 True S1 True S2 True S3 False S4 False ,Canonical Normal Form,18 Given f_1 f_3 and f in canonical sum of products form in decimal for the circuit f_1 Sigma m 4 5 6 7 8 f_3 Sigma m 1 6 15 f Sigma m 1 6 8 15 hen f_2 is Sigma m 4 6 Sigma m 4 8 Sigma m 6 8 Sigma m 4 6 8 ,Canonical Normal Form,18 Find the minimum product of sums of the following expression f ABC bar A bar B bar C ,Canonical Normal Form,18 Consider the following logic circuit whose inputs are functions f_1 f_2 f_3 and output is f Given that f_1 x y z Sigma 0 1 3 5 f_2 x y z Sigma 6 7 and f x y z Sigma 1 4 5 f_3 is Sigma 1 4 5 Sigma 6 7 Sigma 0 1 3 5 None of the above ,Canonical Normal Form,18 A Boolean expression is an expression made out of propositional letters such as p q r and operators wedge vee and eg e g p wedge eg q vee eg r An expression is said to be in sum of product form also called disjunctive normal form if all eg occur just before letters and no vee occurs in scope of wedge e g p wedge eg q vee eg p wedge q The expression is said to be in product of sum form also called conjunctive normal form if all negations occur just before letters and no wedge occurs in the scope of vee e g p vee eg q wedge eg p vee q Which of the following is not correct Every Boolean expression is equivalent to an expression is sum of product form Every Boolean expression is equivalent to an expression in product of sum form Every Boolean expression is equivalent to an expression without vee operator Every Boolean expression is equivalent to an expression without wedge operator Every Boolean expression is equivalent to an expression without eg operator ,Canonical Normal Form,18 In a look ahead carry generator the carry generate function G_i and the carry propagate function P_i for inputs A_i and B_i are given by P_i A_i oplus B_i ext and G_i A_iB_i The expressions for the sum bit S_i and the carry bit C_ i 1 of the look ahead carry adder are given by S_i P_i oplus C_i ext and C_ i 1 G_i P_iC_i ext where C_0 ext is the input carry Consider a two level logic implementation of the look ahead carry generator Assume that all P_i and G_i are available for the carry generator circuit and that the AND and OR gates can have any number of inputs The number of AND gates and OR gates needed to implement the look ahead carry generator for a 4 bit adder with S_3 S_2 S_1 S_0 and C_4 as its outputs are respectively 6 3 10 4 6 4 10 5 ,Carry Generator,19 Given two three bit numbers a_ 2 a_ 1 a_ 0 and b_ 2 b_ 1 b_ 0 and c the carry in the function that represents the carry generate function when these two numbers are added is a_ 2 b_ 2 a_ 2 a_ 1 b_ 1 a_ 2 a_ 1 a_ 0 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 1 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 b_ 0 a_ 0 b_ 2 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 b_ 1 b_ 0 a_ 2 a_ 1 b_ 1 b_ 0 a_ 1 a_ 0 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 a_ 1 a_ 0 b_ 2 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 oplus b_ 2 a_ 1 b_ 1 a_ 1 oplus b_ 1 a_ 0 b_ 0 a_ 2 b_ 2 overline a_ 2 a_ 1 b_ 1 overline a_ 2 a_ 1 a_ 0 b_ 0 overline a_ 2 a_ 0 overline b_ 1 b_ 0 a_ 1 overline b_ 2 b_ 1 overline a_ 1 a_ 0 overline b_ 2 b_ 0 a_ 0 overline b_ 2 b_ 1 b_ 0 ,Carry Generator,19 The logic expression for the output of the circuit shown in figure below is overline AC overline BC CD A overline C B overline C CD ABC overline C overline D overline A overline B overline B overline C CD ,Circuit Output,20 The following arrangement of master slave flip flops has the initial state of P Q as 0 1 respectively After a clock cycle the output state P Q is respectively 1 0 1 1 0 0 0 1 ,Circuit Output,20 Multiple choices can be correct Mark all of them For the initial state of 000 the function performed by the arrangement of the J K flip flops in figure is Shift Register Mod 3 Counter Mod 6 Counter Mod 2 Counter None of the above ,Circuit Output,20 Find the contents of the flip flop Q_2 Q_1 and Q_0 in the circuit of figure after giving four clock pulses to the clock terminal Assume Q_2Q_1Q_0 000 initially ,Circuit Output,20 Consider the partial implementation of a 2 bit counter using T flip flops following the sequence 0 2 3 1 0 as shown below To complete the circuit the input X should be Q_2 c Q_2 Q_1 left Q_1 Q_2 right c Q_1 oplus Q_2 ,Circuit Output,20 Consider the following multiplexer where 10 11 12 13 are four data input lines selected by two address line combinations A1A0 00 01 10 11 respectively and f is the output of the multiplexor EN is the Enable input The function f x y z implemented by the above circuit is xyz xy z x y None of the above ,Circuit Output,20 Consider the following circuit with initial state Q_0 Q_1 0 The D Flip flops are positive edged triggered and have set up times 20 nanosecond and hold times 0 Consider the following timing diagrams of X and C The clock period of C geq 40 nanosecond Which one is the correct plot of Y ,Circuit Output,20 Consider the following circuit involving a positive edge triggered D FF Consider the following timing diagram Let A_ i represents the logic level on the line a in the i th clock period Let A represent the compliment of A The correct output sequence on Y over the clock periods 1 through 5 is A_ 0 A_ 1 A_ 1 A_ 3 A_ 4 A_ 0 A_ 1 A_ 2 A_ 3 A_ 4 A_ 1 A_ 2 A_ 2 A_ 3 A_ 4 A_ 1 A_ 2 A_ 3 A_ 4 A_ 5 ,Circuit Output,20 Consider the following circuit The flip flops are positive edge triggered D FFs Each state is designated as a two bit string Q_0Q_1 Let the initial state be 00 The state transition sequence is ,Circuit Output,20 Consider the circuit shown below In a certain steady state the line Y is at 1 What are the possible values of A B and C in this state A 0 B 0 C 1 A 0 B 1 C 1 A 1 B 0 C 1 A 1 B 1 C 1 ,Circuit Output,20 Consider the circuit in figure f implements overline A overline B C overline A B overline C ABC A B C A oplus B oplus C AB BC CA ,Circuit Output,20 Consider the circuit in Fig 2 21 which has a four bit binary number b_3b_2b_1b_0 as input and a five bit binary number d_4d_3d_2d_1d_0 as output Binary to Hex conversion Binary to BCD conversion Binary to grey code conversion Binary to radix 12 conversion ,Circuit Output,20 Consider a logic circuit shown in figure below The functions f_1 f_2 ext and f in canonical sum of products form in decimal notation are f_1 w x y z sum 8 9 10 f_2 w x y z sum 7 8 12 13 14 15 f w x y z sum 8 9 The function f_3 is sum 9 10 sum 9 sum 1 8 9 sum 8 10 15 ,Circuit Output,20 Analyse the circuit in Fig below and complete the following table a b Q_n 0 0 0 1 1 0 1 1 ,Circuit Output,20 A two way switch has three terminals a b and c In ON position logic value 1 a is connected to b and in OFF position a is connected to c Two of these two way switches S1 and S2 are connected to a bulb as shown below Which of the following expressions if true will always result in the lighting of the bulb S1 overline S2 S1 S2 overline S1 oplus S2 S1 oplus S2 ,Circuit Output,20 At what time between 6 a m and 7 a m will the minute hand and hour hand of a clock make an angle closest to 60 u00b0 6 22 a m 6 27 a m 6 38 a m 6 45 a m ,Clock Time,21 Let L_1 L_2 be any two context free languages and R be any regular language Then which of the following is are CORRECT L_1 cup L_2 is context free overline L_1 is context free L_1 R is context free L_1 cap L_2 is context free I II and IV only I and III only II and IV only I only ,Closure Property,22 Let L be a context free language and M a regular language Then the language L u2229 M is always regular never regular always a deterministic context free language always a context free language ,Closure Property,22 Context free languages and regular languages are both closed under the operation s of Union Intersection Concatenation Complementation ,Closure Property,22 Consider the following types of languages L_ 1 Regular L_ 2 Context free L_ 3 Recursive L_ 4 Recursively enumerable Which of the following is are TRUE bar L_ 3 cup L_ 4 is recursively enumerable bar L_ 2 cup L_ 3 is recursive L _ 1 cap L_ 2 is context free L_ 1 cup bar L_ 2 is context free I only I and III only I and IV only I II and III only ,Closure Property,22 Which of the following statements is FALSE The intersection of a context free language with a regular language is context free The intersection of two regular languages is regular The intersection of two context free languages is context free The intersection of a context free language and the complement of a regular language is context free The intersection of a regular language and the complement of a regular language is regular ,Closure Property,22 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is an example of a spooled device The terminal used to input data for a program being executed The secondary memory device in a virtual memory system A line printer used to print the output of a number of jobs None of the above ,Computer Peripherals,23 The following two functions P1 and P2 that share a variable B with an initial value of 2 execute concurrently P1 C B 1 B 2 C P2 D 2 B B D 1 The number of distinct values that B can possibly take after the execution is______________________ ,Concurrency,24 Consider the following functions f and g f x x 50 y y 50 g a a x a a y Suppose we start with initial values of 100 for x 200 for y and 0 for a and then execute f and g in parallel u2014that is at each step we either execute one statement from f or one statement from g Which of the following is not a possible final value of a 300 250 350 200 ,Concurrency,24 Consider the following database schedule with two transactions T_ 1 and T_ 2 S r_ 2 left X right r_ 1 left X right r_ 2 left Y right w_ 1 left X right r_ 1 left Y right w_ 2 left X right a_ 1 a_ 2 Where r_ i Z denotes a read operation by transaction T_ i on a variable Z w_ i Z denotes a write operation by T_ i on a variable Z and a_ i denotes an abort by transaction T_ i Which one of the following statements about the above schedule is TRUE S is non recoverable S is recoverable but has a cascading abort S does not have a cascading abort S is strict ,Concurrency,24 Consider the concurrent program x 1 cobegin x x x 1 x x 2 coend Reading and writing of a variable is atomic but evaluation of an expression is not atomic The set of possible values of variable x at the end of execution of the program is left 3 right left 7 right left 3 5 7 right left 3 7 right left 3 5 right ,Concurrency,24 Suppose that a shop has an equal number of LED bulbs of two different types The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0 7 and given that it is of Type 2 is 0 4 The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________ ,Conditional Probability,25 Let A and B be any two arbitrary events then which one of the following is true P A cap B P A P B P A cup B P A P B P A mid B P A cap B P B P A cup B leq P A P B ,Conditional Probability,25 Karan tells truth with probability dfrac 1 3 and lies with probability dfrac 2 3 Independently Arjun tells truth with probability dfrac 3 4 and lies with probability dfrac 1 4 Both watch a cricket match Arjun tells you that India won Karan tells you that India lost What probability will you assign to India s win left dfrac 1 2 right left dfrac 2 3 right left dfrac 3 4 right left dfrac 5 6 right left dfrac 6 7 right ,Conditional Probability,25 Amar and Akbar both tell the truth with probability dfrac 3 4 and lie with probability dfrac 1 4 Amar watches a test match and talks to Akbar about the outcome Akbar in turn tells Anthony Amar told me that India won What probability should Anthony assign to India s win left dfrac 9 16 right left dfrac 6 16 right left dfrac 7 16 right left dfrac 10 16 right None of the above ,Conditional Probability,25 P and Q are considering to apply for a job The probability that P applies for the job is dfrac 1 4 the probability that P applies for the job given that Q applies for the job is dfrac 1 2 and the probability that Q applies for the job given that P applies for the job is dfrac 1 3 Then the probability that P does not apply for the job given that Q does not apply for this job is left dfrac 4 5 right left dfrac 5 6 right left dfrac 7 8 right left dfrac 11 12 right ,Conditional Probability,25 Two transactions T_1 and T_2 are given as T_1 r_1 X w_1 X r_1 Y w_1 Y T_2 r_2 Y w_2 Y r_2 Z w_2 Z where r_i V denotes a extit read operation by transaction T_i on a variable V and w_i V denotes a extit write operation by transaction T_i on a variable V The total number of conflict serializable schedules that can be formed by T_1 and T_2 is ______,Conflict Serializable,26 State whether the following statements are TRUE or FALSE The intersection of two CFL s is also a CFL ,Context Free Language,27 Show that the language L left xcx mid x in left 0 1 right ext and c ext is a terminal symbol right is not context free c is not 0 or 1 ,Context Free Language,27 Let L_1 0 n m 1 n0 m mid n m geq 0 L_2 0 n m 1 n m 0 m mid n m geq 0 and L_3 0 n m 1 n m 0 n m mid n m geq 0 Which of these languages are NOT context free L_1 only L_3 only L_1 and L_2 L_2 and L_3 ,Context Free Language,27 Let G left left S right left a b right R S right be a context free grammar where the rule set R is S o a S b mid S S mid epsilon Which of the following statements is true G is not ambiguous There exist x y in L G such that xy otin L G There is a deterministic pushdown automaton that accepts L G We can find a deterministic finite state automaton that accepts L G ,Context Free Language,27 In the context free grammar below S is the start symbol a and b are terminals and epsilon denotes the empty string S o aSAb mid epsilon A o bA mid epsilon The grammar generates the language a b b a mb n mid m leq n a mb n mid m n a b ,Context Free Language,27 If L_1 and L_2 are context free languages and R a regular set one of the languages below is not necessarily a context free language Which one L_1 L_2 L_1 cap L_2 L_1 cap R L_1 cup L_2 ,Context Free Language,27 Define a context free languages L in 0 1 ext init L u mid uv in L for some v in 0 1 in other words ext init L is the set of prefixes of L Let L w mid w ext is nonempty and has an equal number of 0 u2019s and 1 u2019s Then ext init L is the set of all binary strings with unequal number of 0 u2019s and 1 u2019s the set of all binary strings including null string the set of all binary strings with exactly one more 0 than the number of 1 u2019s or one more 1 than the number of 0 u2019s None of the above ,Context Free Language,27 Context free languages are closed under Union intersection Union Kleene closure Intersection complement Complement Kleene closure ,Context Free Language,27 Consider the languages L_1 left ww R mid w in 0 1 right L_2 left w ext w R mid w in 0 1 right where ext is a special symbol L_3 left ww mid w in 0 1 right Which one of the following is TRUE L_1 is a deterministic CFL L_2 is a deterministic CFL L_3 is a CFL but not a deterministic CFL L_3 is a deterministic CFL ,Context Free Language,27 Choose the correct alternatives more than one may be correct and write the corresponding letters only If G is a context free grammar and w is a string of length l in L G how long is a derivation of w in G if G is in Chomsky normal form 2l 2l 1 2l 1 l ,Context Free Language,27 A context free grammar is ambiguous if The grammar contains useless non terminals It produces more than one parse tree for some sentence Some production has two non terminals side by side on the right hand side None of the above ,Context Free Language,27 02 Choose the correct alternatives more than one may be correct and write the corresponding letters only xix Context free languages are closed under union closed under complementation closed under intersection closed under Kleene closure ,Context Free Language,27 Construct as minimal finite state machine that accepts the language over 0 1 of all strings that contain neither the sub string 00 nor the sub string 11 Consider the grammar S u2192 aSAb S u2192 u220a A u2192 bA A u2192 u220a where S A are non terminal symbols with S being the start symbol a b are terminal symbols and epsilon is the empty string This grammar generates strings of the form a ib i for some i j geq 0 where i and j satisfy some condition What is the condition on the values of i and j ,Context Free Language,27 Which of the following actions is are typically not performed by the operating system when switching context from process A to process B Saving current register values and restoring saved register values for process B Changing address translation tables Swapping out the memory image of process A to the disk Invalidating the translation look aside buffer ,Context Switch,28 Let the time taken to switch from user mode to kernel mode of execution be T1 while time taken to switch between two user processes be T2 Which of the following is correct T1 gt T2 T1 T2 T1 lt T2 Nothing can be said about the relation between T1 and T2 ,Context Switch,28 The function y 2 3x u200b a is continuous u2200 x u2208 R and differentiable u2200 x u2208 R b is continuous u2200 x u2208 R and differentiable u2200 x u2208 R except at x frac 3 2 c is continuous u2200 x u2208 R and differentiable u2200 x u2208 R except at x frac 2 3 d is continuous u2200 x u2208 R except x 3 and differentiable u2200 x u2208 R,Continuity,29 Let f x x left frac 1 3 right and A denote the area of region bounded by f x and the X axis when x varies from 1 to 1 Which of the following statements is are TRUE f is continuous in 1 1 f is not bounded in 1 1 A is nonzero and finite II only III only II and III only I II and III ,Continuity,29 A function f x is continuous in the interval 0 2 It is known that f 0 f 2 1 and f 1 1 Which one of the following statements must be true There exists a y in the interval 0 1 such that f y f y 1 For every y in the interval 0 1 f y f 2 y The maximum value of the function in the interval 0 2 is 1 There exists a y in the interval 0 1 such that f y f 2 y ,Continuity,29 The cost function for a product in a firm is given by 5q 2 where q is the amount of production The firm can sell the product at a market price of u20b9 50 per unit The number of units to be produced by the firm such that the profit is maximized is A 5 B 10 C 15 D 25,Cost Market Price,30 Given Sigma a b which one of the following sets is not countable a Set of all strings over Sigma b Set of all languages over Sigma c Set of all regular languages over Sigma d Set of all languages over Sigma accepted by Turing machines,Countable Set,31 What is the minimum number of ordered pairs of non negative numbers that should be chosen to ensure that there are two pairs a b and c d in the chosen set such that a equiv c mod 3 and b equiv d mod 5 4 6 16 24 ,Counting,32 The number of distinct simple graphs with up to three nodes is 15 10 7 9 ,Counting,32 Let G be a complete undirected graph on 6 vertices If vertices of G are labeled then the number of distinct cycles of length 4 in G is equal to 15 30 90 360 ,Counting,32 How many undirected graphs not necessarily connected can be constructed out of a given set V v_1 v_2 dots v_n of n vertices frac n n 1 2 2 n n 2 frac n n 1 2 ,Counting,32 How many graphs on n labeled vertices exist which have at least frac n 2 3n 2 edges left frac n 2 n 2 right C_ left frac n 2 3n 2 right large sum limits_ k 0 left frac n 2 3n 2 right left n 2 n right C_k left frac n 2 n 2 right C_n large sum limits_ k 0 n left frac n 2 n 2 right C_k ,Counting,32 How many distinct binary search trees can be created out of 4 distinct keys 5 14 24 42 ,Counting,32 An undirected graph is complete if there is an edge between every pair of vertices Given a complete undirected graph on n vertices in how many ways can you choose a direction for the edges so that there are no directed cycles n frac n n 1 2 n 2 n 2 m ext where m frac n n 1 2 ,Counting,32 A critical region is One which is enclosed by a pair of P and V operations on semaphores A program segment that has not been proved bug free A program segment that often causes unexpected system crashes A program segment where shared resources are accessed ,Critical Section,33 State True or False with reason Logical data independence is easier to achieve than physical data independence,Data Independence,34 The table below has question wise data on the performance of students in an examination The marks for each question are also listed There is no negative or partial marking in the examination Q No Marks Answered Correctly Answered Wrongly Not Attempted 1 2 21 17 6 2 3 15 27 2 3 2 23 18 3 What is the average of the marks obtained by the class in the examination 1 34 1 74 3 02 3 91 ,Data Interpretation,35 The ratio of male to female students in a college for five years is plotted in the following line graph If the number of female students doubled in 2009 by what percent did the number of male students increase in 2009 ,Data Interpretation,35 The pie chart below has the breakup of the number of students from different departments in an engineering college for the year 2012 The proportion of male to female students in each department is 5 4 There are 40 males in Electrical Engineering What is the difference between the numbers of female students in the civil department and the female students in the Mechanical department ,Data Interpretation,35 In a survey 300 respondents were asked whether they own a vehicle or not If yes they were further asked to mention whether they own a car or scooter or both Their responses are tabulated below What percent of respondents do not own a scooter Men Women Own vehicle Car 40 34 Scooter 30 20 Both 60 46 Do not own vehicle 20 50 ,Data Interpretation,35 An air pressure contour line joins locations in a region having the same atmospheric pressure The following is an air pressure contour plot of a geographical religion Contour lines are shown at 0 05 bar intervals in this plot If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region which of the following regions is most likely to have a thunderstorm P Q R S ,Data Interpretation,35 A contour line joins locations having the same height above the mean sea level The following is a contour plot of a geographical region Contour lines are shown at 25 m intervals in this plot If in a flood the water level rises to 525 m which of the villages P Q R S T get submerged P Q P Q T R S T Q R S ,Data Interpretation,35 The exports and imports in crores of Rs of a country from the year 2000 to 2007 are given in the following bar chart In which year is the combined percentage increase in imports and exports the highest ,Data Interpretation,35 P Q R and S are four types of dangerous microbes recently found in a human habitat The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within 24 hours of entering the body The danger to human beings varies proportionately with the toxicity potency and growth attributed to a microbe shown in the figure below A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe Which microbe should the company target in its first attempt P Q R S ,Data Interpretation,35 f x 1 x 1 f x 1 x 1 f x 2 x 1 f x 2 x 1 ,Data Interpretation,35 An ER model of a database consists of entity types A and B These are connected by a relationship R which does not have its own attribute Under which one of the following conditions can the relational table for R be merged with that of A Relationship R is one to many and the participation of A in R is total Relationship R is one to many and the participation of A in R is partial Relationship R is many to one and the participation of A in R is total Relationship R is many to one and the participation of A in R is partial ,Database,36 Which normal form is considered adequate for normal relational database design 2NF 5NF 4NF 3NF ,Database Normalization,37 The relation scheme ext Student Performance name courseNo rollNo grade has the following functional dependencies name courseNo rightarrow grade rollNo courseNo rightarrow grade name rightarrow rollNo rollNo rightarrow name The highest normal form of this relation scheme is 2NF 3NF ext BCNF 4NF ,Database Normalization,37 State True or False with reason There is always a decomposition into Boyce Codd normal form BCNF that is lossless and dependency preserving ,Database Normalization,37 Relation R is decomposed using a set of functional dependencies F and relation S is decomposed using another set of functional dependencies G One decomposition is definitely ext BCNF the other is definitely 3NF but it is not known which is which To make a guaranteed identification which one of the following tests should be used on the decompositions Assume that the closures of F and G are available Dependency preservation Lossless join ext BCNF definition 3NF definition ,Database Normalization,37 R A B C D is a relation Which of the following does not have a lossless join dependency preserving BCNF decomposition A rightarrow B B rightarrow CD A rightarrow B B rightarrow C C rightarrow D AB rightarrow C C rightarrow AD A rightarrow BCD ,Database Normalization,37 For relation R L M N O P the following dependencies hold M rightarrow O NO rightarrow P P rightarrow L and L rightarrow MN R is decomposed into R1 L M N P and R2 M O Is the above decomposition a lossless join decomposition Explain Is the above decomposition dependency preserving If not list all the dependencies that are not preserved What is the highest normal form satisfied by the above decomposition ,Database Normalization,37 Consider the schema R S T U V and the dependencies S rightarrow T T rightarrow U U rightarrow V and V rightarrow S Let R R1 ext and R2 be a decomposition such that R1 cap R2 eq phi The decomposition is not in 2NF in 2NF but not 3NF in 3NF but not in 2NF in both 2NF and 3NF ,Database Normalization,37 Consider the relation scheme R A B C with the following functional dependencies A B u2192 C C u2192 A Show that the scheme R is in 3NF but not in ext BCNF Determine the minimal keys of relation R ,Database Normalization,37 Consider the following functional dependencies in a database Date_of_Birth gt Age Age gt Eligibility Name gt Roll_number Roll_number gt Name Course_number gt Course_name Course_number gt Instructor Roll_number Course_number gt Grade The relation Roll_number Name Date_of_birth Age is in second normal form but not in third normal form in third normal form but not in BCNF in BCNF in none of the above ,Database Normalization,37 A database of research articles in a journal uses the following schema ext VOLUME NUMBER STARTPAGE ENDPAGE TITLE YEAR PRICE The primary key is ext VOLUME NUMBER STARTPAGE ENDPAGE and the following functional dependencies exist in the schema begin align amp ext VOLUME NUMBER STARTPAGE ENDPAGE amp rightarrow ext TITLE amp ext VOLUME NUMBER amp rightarrow ext YEAR amp ext VOLUME NUMBER STARTPAGE ENDPAGE amp rightarrow ext PRICE end align The database is redesigned to use the following schemas ext VOLUME NUMBER STARTPAGE ENDPAGE TITLE PRICE ext VOLUME NUMBER YEAR Which is the weakest normal form that the new database satisfies but the old one does not 1NF 2NF 3NF ext BCNF ,Database Normalization,37 Which of the following is NOT a superkey in a relational schema with attributes V W X Y Z and primary key V Y VXYZ VWXZ VWXY VWXYZ ,Database Normalization,37 Let R A B C D E F be a relation scheme with the following dependencies C rightarrow F E rightarrow A EC rightarrow D A rightarrow B Which one of the following is a key for R CD EC AE AC ,Database Normalization,37 For a database relation R a b c d where the domains a b c d include only atomic values only the following functional dependencies and those that can be inferred from them hold a rightarrow c b rightarrow d This relation is in first normal form but not in second normal form in second normal form but not in first normal form in third normal form none of the above ,Database Normalization,37 Consider the following database relations containing the attributes Book_id Subject_Category_of_book Name_of_Author Nationality_of_Author With Book_id as the primary key What is the highest normal form satisfied by this relation Suppose the attributes Book_title and Author_address are added to the relation and the primary key is changed to Name_of_Author Book_title what will be the highest normal form satisfied by the relation ,Database Normalization,37 Consider a schema R A B C D and functional dependencies A rightarrow B and C rightarrow D Then the decomposition of R into R_1 A B and R_2 C D is dependency preserving and lossless join lossless join but not dependency preserving dependency preserving but not lossless join not dependency preserving and not lossless join ,Database Normalization,37 Let L be a language over Sigma i e L subseteq Sigma Suppose L satisfies the two conditions given below L is in NP and For every n there is exactly one string of length n that belongs to L Let L c be the complement of L over Sigma Show that L c is also in NP ,Decidability,38 Consider two languages L_1 and L_2 each on the alphabet Sigma Let f Sigma o Sigma be a polynomial time computable bijection such that forall x x in L_1 iff f x in L_2 Further let f 1 be also polynomial time computable Which of the following CANNOT be true L_1 in P and L_2 is finite L_1 in NP and L_2 in P L_1 is undecidable and L_2 is decidable L_1 is recursively enumerable and L_2 is recursive ,Decidability,38 Consider the following problem X Given a Turing machine M over the input alphabet Sigma any state q of M and a word w in Sigma does the computation of M on w visit the state of q Which of the following statements about X is correct X is decidable X is undecidable but partially decidable X is undecidable and not even partially decidable X is not a decision problem ,Decidability,38 Consider the following decision problems P1 Does a given finite state machine accept a given string P2 Does a given context free grammar generate an infinite number of strings Which of the following statements is true Both P1 and P2 are decidable Neither P1 nor P2 is decidable Only P1 is decidable Only P2 is decidable ,Decidability,38 Choose the correct alternatives More than one may be correct It is undecidable whether An arbitrary Turing machine halts after 100 steps A Turing machine prints a specific letter A Turing machine computes the products of two numbers None of the above ,Decidability,38 Answer the following questions Which of the following problems are undecidable Membership problem in context free languages Whether a given context free language is regular Whether a finite state automation halts on all inputs Membership problem for type 0 languages ,Decidability,38 Which one of the following is not decidable Given a Turing machine M a string s and an integer k M accepts s within k steps Equivalence of two given Turing machines Language accepted by a given finite state machine is not empty Language generated by a context free grammar is non empty ,Decidability,38 Consider three decision problems P_1 P_2 and P_3 It is known that P_1 is decidable and P_2 is undecidable Which one of the following is TRUE P_3 is decidable if P_1 is reducible to P_3 P_3 is undecidable if P_3 is reducible to P_2 P_3 is undecidable if P_2 is reducible to P_3 P_3 is decidable if P_3 is reducible to P_2 s complement ,Decidability,38 How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 ,Decoder,39 The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order Which of the following sequences can not be the degree sequence of any graph 7 6 5 4 4 3 2 1 6 6 6 6 3 3 2 2 7 6 6 4 4 3 2 2 8 7 7 6 4 2 1 1 I and II III and IV IV only II and IV ,Degree Of Graph,40 The 2 n vertices of a graph G corresponds to all subsets of a set of size n for n geq 6 Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements The number of vertices of degree zero in G is 1 n n 1 2 n ,Degree Of Graph,40 The 2 n vertices of a graph G corresponds to all subsets of a set of size n for n geq 6 Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements The maximum degree of a vertex in G is binom frac n 2 2 2 frac n 2 2 n 2 2 n 3 imes 3 2 n 1 ,Degree Of Graph,40 Show that all vertices in an undirected finite graph cannot have distinct degrees if the graph has at least two vertices ,Degree Of Graph,40 Prove that in finite graph the number of vertices of odd degree is always even ,Degree Of Graph,40 In a graph the degree of a vertex is the number of edges incident connected on it Which of the following is true for every graph G There are even number of vertices of even degree There are odd number of vertices of even degree There are even number of vertices of odd degree There are odd number of vertices of odd degree All the vertices are of even degree ,Degree Of Graph,40 In a directed graph every vertex has exactly seven edges coming in What can one always say about the number of edges going out of its vertices Exactly seven edges leave every vertex Exactly seven edges leave some vertex Some vertex has at least seven edges leaving it The number of edges coming out of vertex is odd None of the above ,Degree Of Graph,40 An undirected graph has 10 vertices labelled 1 2 dots 10 and 37 edges Vertices 1 3 5 7 9 have degree 8 and vertices 2 4 6 8 have degree 7 What is the degree of vertex 10 5 6 7 8 ,Degree Of Graph,40 An ordered n tuple d_1 d_2 d_n with d_1 geq d_2 geq geq d_n is called graphic if there exists a simple undirected graph with n vertices having degrees d_1 d_2 d_n respectively Which one of the following 6 tuples is NOT graphic 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 1 0 0 3 2 1 1 1 0 ,Degree Of Graph,40 A graph G V E satisfies E leq 3 V 6 The min degree of G is defined as min_ v in V left degree v right Therefore min degree of G cannot be 3 4 5 6 ,Degree Of Graph,40 G is an undirected graph with n vertices and 25 edges such that each vertex of G has degree at least 3 Then the maximum possible value of n is _________ ,Degree Of Graph,40 The determinant of the matrix given below is begin bmatrix 0 amp 1 amp 0 amp 2 1 amp 1 amp 1 amp 3 0 amp 0 amp 0 amp 1 1 amp 2 amp 0 amp 1 end bmatrix 1 0 1 2 ,Determinant,41 The determinant of the matrix begin bmatrix 6 amp 8 amp 1 amp 1 0 amp 2 amp 4 amp 6 0 amp 0 amp 4 amp 8 0 amp 0 amp 0 amp 1 end bmatrix 11 48 0 24 ,Determinant,41 The determinant of the matrix begin bmatrix 2 amp 0 amp 0 amp 0 8 amp 1 amp 7 amp 2 2 amp 0 amp 2 amp 0 9 amp 0 amp 6 amp 1 end bmatrix 4 0 15 20 ,Determinant,41 If the matrix A is such that A begin bmatrix 2 u22124 7 end bmatrix begin bmatrix 1 amp 9 amp 5 end bmatrix then the determinant of A is equal to ______ ,Determinant,41 Let the function f heta begin vmatrix sin heta amp cos heta amp an heta sin frac pi 6 amp cos frac pi 6 amp an frac pi 6 amp sin frac pi 3 amp cos frac pi 3 amp an frac pi 3 end vmatrix where heta in left frac pi 6 frac pi 3 right and f heta denote the derivative of f with respect to heta Which of the following statements is are TRUE There exists heta in frac pi 6 frac pi 3 such that f heta 0 There exists heta in frac pi 6 frac pi 3 such that f heta eq 0 I only II only Both I and II Neither I Nor II ,Differentiability,42 Let f x be a polynomial and g x f x be its derivative If the degree of f x f x is 10 then the degree of g x g x is __________ ,Differentiability,42 Let f be a function defined by f x begin cases x 2 amp ext for x leq 1 ax 2 bx c amp ext for 1 lt x leq 2 x d amp ext for x gt 2 end cases Find the values for the constants a b c and d so that f is continuous and differentiable everywhere on the real line ,Differentiability,42 If f x R sin frac pi x 2 S f u2019 frac 1 2 sqrt 2 and int_0 1 f x dx frac 2R pi then the constants R and S are frac 2 pi and frac 16 pi frac 2 pi and 0 frac 4 pi and 0 frac 4 pi and frac 16 pi ,Differentiability,42 In the following truth table V 1 if and only if the input is valid Inputs Outputs D_0 D_1 D_2 D_3 X_0 X_1 V 0 0 0 0 x x 0 1 0 0 0 0 0 1 x 1 0 0 0 1 1 x x 1 0 1 0 1 x x x 1 1 1 1 What function does the truth table represent Priority encoder Decoder Multiplexer Demultiplexer ,Digital Circuits,43 Consider the following combinational function block involving four Boolean variables x y a b where x a b are inputs and y is the output f x a b y if x is 1 y a else y b Which one of the following digital logic blocks is the most suitable for implementing this function Full adder Priority encoder Multiplexor Flip flop ,Digital Circuits,43 A logic network has two data inputs A and B and two control inputs C_0 and C_1 It implements the function F according to the following table C_1 C_2 F 0 0 overline A B 0 1 A B 1 0 A oplus B Implement the circuit using one 4 to 1 Multiplexer one 2 input Exclusive OR gate one 2 input AND gate one 2 input OR gate and one Inverter ,Digital Circuits,43 The number of flip flops required to construct a binary modulo N counter is __________,Digital Counter,44 The next state table of a 2 bit saturating up counter is given below begin array cc cc Q_1 amp Q_0 amp Q_1 amp Q_0 hline 0 amp 0 amp 0 amp 1 0 amp 1 amp 1 amp 0 1 amp 0 amp 1 amp 1 1 amp 1 amp 1 amp 1 end array The counter is built as a synchronous sequential circuit using T flip flops The expressions for T_1 and T_0 are T_1 Q_1Q_0 quad T_0 bar Q_1 bar Q_0 T_1 bar Q_1 Q_0 quad T_0 bar Q_1 bar Q_0 T_1 Q_1 Q_0 quad T_0 bar Q_1 bar Q_0 T_1 bar Q_1 Q_0 quad T_0 Q_1 Q_0 ,Digital Counter,44 The minimum number of JK flip flops required to construct a synchronous counter with the count sequence 0 0 1 1 2 2 3 3 0 0 is _______ ,Digital Counter,44 The minimum number of ext D flip flops needed to design a mod 258 counter is 9 8 512 258 ,Digital Counter,44 Let k 2 n A circuit is built by giving the output of an n bit binary counter as input to an n ext to 2 n bit decoder This circuit is equivalent to a k bit binary up counter k bit binary down counter k bit ring counter k bit Johnson counter ,Digital Counter,44 How many pulses are needed to change the contents of a 8 bit up counter from 10101100 to 00100111 rightmost bit is the LSB 134 133 124 123 ,Digital Counter,44 Consider a 4 bit Johnson counter with an initial value of 0000 The counting sequence of this counter is 0 1 3 7 15 14 12 8 0 0 1 3 5 7 9 11 13 15 0 0 2 4 6 8 10 12 14 0 0 8 12 14 15 7 3 1 0 ,Digital Counter,44 We want to design a synchronous counter that counts the sequence 0 1 0 2 0 3 and then repeats The minimum number of ext J K flip flops required to implement this counter is _____________ ,Digital Counter,44 Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii ,Dining Philosopher,45 There are five buildings called V W X Y and Z in a row not necessarily in that order V is to the West of W Z is to the East of X and the West of V W is to the West of Y Which is the building in the middle V W X Y ,Direction Sense,46 Four branches of a company are located at M N O and P M is north of N at a distance of 4 km P is south of O at a distance of 2 km N is southeast of O by 1 km What is the distance between M and P in km 5 34 6 74 28 5 45 49 ,Direction Sense,46 The head of a moving head disk with 100 tracks numbered 0 to 99 is currently serving a request at track 55 If the queue of requests kept in FIFO order is 10 70 75 23 65 which of the two disk scheduling algorithms FCFS First Come First Served and SSTF Shortest Seek Time First will require less head movement Find the head movement for each of the algorithms ,Disk Scheduling,47 The head of a hard disk serves requests following the shortest seek time first SSTF policy The head is initially positioned at track number 180 Which of the request sets will cause the head to change its direction after servicing every request assuming that the head does not change direction if there is a tie in SSTF and all the requests arrive before the servicing starts 11 139 170 178 181 184 201 265 10 138 170 178 181 185 201 265 10 139 169 178 181 184 201 265 10 138 170 178 181 185 200 265 ,Disk Scheduling,47 The head of a hard disk serves requests following the shortest seek time first SSTF policy The head is initially positioned at track number 180 What is the maximum cardinality of the request set so that the head changes its direction after servicing every request if the total number of tracks are 2048 and the head can start from any track 9 10 11 12 ,Disk Scheduling,47 The correct matching for the following pairs is A Disk Scheduling 1 Round robin B Batch Processing 2 SCAN C Time sharing 3 LIFO D Interrupt processing 4 FIFO A 3 B 4 C 2 D 1 A 4 B 3 C 2 D 1 A 2 B 4 C 1 D 3 A 3 B 4 C 3 D 2 ,Disk Scheduling,47 Suppose the following disk request sequence track numbers for a disk with 100 tracks is given 45 20 90 10 50 60 80 25 70 Assume that the initial position of the R W head is on track 50 The additional distance that will be traversed by the R W head when the Shortest Seek Time First SSTF algorithm is used compared to the SCAN Elevator algorithm assuming that SCAN algorithm moves towards 100 when it starts execution is________________tracks ,Disk Scheduling,47 Suppose a disk has 201 cylinders numbered from 0 to 200 At some time the disk arm is at cylinder 100 and there is a queue of disk access requests for cylinders 30 85 90 100 105 110 135 and 145 If Shortest Seek Time First SSTF is being used for scheduling the disk access the request for cylinder 90 is serviced after servicing ____________ number of requests ,Disk Scheduling,47 Provide short answers to the following questions Disk requests come to disk driver for cylinders 10 22 20 2 40 6 and 38 in that order at a time when the disk drive is reading from cylinder 20 The seek time is 6 msec per cylinder Compute the total seek time if the disk arm scheduling algorithm is First come first served Closest cylinder next ,Disk Scheduling,47 Cylinder a disk queue with requests for I O to blocks on cylinders 47 38 121 191 87 11 92 10 The C LOOK scheduling algorithm is used The head is initially at cylinder number 63 moving towards larger cylinder numbers on its servicing pass The cylinders are numbered from 0 to 199 The total head movement in number of cylinders incurred while servicing these requests is__________ ,Disk Scheduling,47 Consider an operating system capable of loading and executing a single sequential user process at a time The disk head scheduling algorithm used is First Come First Served FCFS If FCFS is replaced by Shortest Seek Time First SSTF claimed by the vendor to give 50 better benchmark results what is the expected improvement in the I O performance of user programs 50 40 25 0 ,Disk Scheduling,47 Consider a disk system with 100 cylinders The requests to access the cylinders occur in following sequence 4 34 10 7 19 73 2 15 6 20 Assuming that the head is currently at cylinder 50 what is the time taken to satisfy all requests if it takes 1ms to move from one cylinder to adjacent one and shortest seek time first policy is used 95 ms 119 ms 233 ms 276 ms ,Disk Scheduling,47 A disk has 200 tracks numbered 0 through 199 At a given time it was servicing the request of reading data from track 120 and at the previous request service was for track 90 The pending requests in order of their arrival are for track numbers 30 70 115 130 110 80 20 25 How many times will the head change its direction for the disk scheduling policies SSTF Shortest Seek Time First and FCFS First Come Fist Serve 2 and 3 3 and 3 3 and 4 4 and 4 ,Disk Scheduling,47 The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 ,Dual Function,48 Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds ,Effective Memory Access,49 What are the eigenvalues of the matrix P given below P begin pmatrix a amp 1 amp 0 1 amp a amp 1 0 amp 1 amp a end pmatrix a a u221a2 a u221a2 a a a 0 a 2a a 2a 2a ,Eigen Value,50 Two eigenvalues of a 3 imes 3 real matrix P are 2 sqrt 1 and 3 The determinant of P is _______,Eigen Value,50 The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a 4 by 4 symmetric positive definite matrix is ___________,Eigen Value,50 The product of the non zero eigenvalues of the matrix is ____ begin pmatrix 1 amp 0 amp 0 amp 0 amp 1 0 amp 1 amp 1 amp 1 amp 0 0 amp 1 amp 1 amp 1 amp 0 0 amp 1 amp 1 amp 1 amp 0 1 amp 0 amp 0 amp 0 amp 1 end pmatrix ,Eigen Value,50 The larger of the two eigenvalues of the matrix begin bmatrix 4 amp 5 2 amp 1 end bmatrix is _______ ,Eigen Value,50 Let A be the matrix begin bmatrix 3 amp 1 1 amp 2 end bmatrix What is the maximum value of xT Ax where the maximum is taken over all x that are the unit eigenvectors of A 3 frac 5 u221a5 2 3 frac 5 u221a5 2 ,Eigen Value,50 Let A be the 2 u00d7 2 matrix with elements a_ 11 a_ 12 a_ 21 1 and a_ 22 u22121 Then the eigenvalues of the matrix A 19 are A 1024 and u22121024 B 1024 sqrt 2 and u22121024 sqrt 2 C 4 sqrt 2 and u22124 sqrt 2 D 512 sqrt 2 and u2212512 sqrt 2 ,Eigen Value,50 Let A be a 4 imes 4 matrix with eigen values 5 2 1 4 Which of the following is an eigen value of the matrix begin bmatrix A amp I I amp A end bmatrix where I is the 4 imes 4 identity matrix 5 7 2 1 ,Eigen Value,50 In questions 1 1 to 1 7 below one or more of the alternatives are correct Write the code letter s a b c d corresponding to the correct alternative s in the answer book Marks will be given only if all the correct alternatives have been selected and no incorrect alternative is picked up 1 1 The eigen vector s of the matrix begin bmatrix 0 amp 0 amp alpha 0 amp 0 amp 0 0 amp 0 amp 0 end bmatrix alpha eq 0 is are a 0 0 alpha b alpha 0 0 c 0 0 1 d 0 alpha 0 ,Eigen Value,50 How many of the following matrices have an eigenvalue 1 left begin array cc 1 amp 0 0 amp 0 end array right left begin array cc 0 amp 1 0 amp 0 end array right left begin array cc 1 amp 1 1 amp 1 end array right and left begin array cc 1 amp 0 1 amp 1 end array right one two three four ,Eigen Value,50 Consider the matrix as given below begin bmatrix 1 amp 2 amp 3 0 amp 4 amp 7 0 amp 0 amp 3 end bmatrix Which one of the following options provides the CORRECT values of the eigenvalues of the matrix A 1 4 3 B 3 7 3 C 7 3 2 D 1 2 3,Eigen Value,50 Consider the following matrix A left begin array cc 2 amp 3 x amp y end array right If the eigenvalues of A are 4 and 8 then x 4 y 10 x 5 y 8 x 3 y 9 x 4 y 10 ,Eigen Value,50 Consider the following 2 imes 2 matrix A where two elements are unknown and are marked by a and b The eigenvalues of this matrix are 1 and 7 What are the values of a and b qquad A bigl begin smallmatrix 1 amp 4 b amp a end smallmatrix bigr a 6 b 4 a 4 b 6 a 3 b 5 a 5 b 3 ,Eigen Value,50 Obtain the eigen values of the matrix A begin bmatrix 1 amp 2 amp 34 amp 49 0 amp 2 amp 43 amp 94 0 amp 0 amp 2 amp 104 0 amp 0 amp 0 amp 1 end bmatrix ,Eigen Value,50 The Tamil version of __________ John Abraham starrer Madras Cafe __________ cleared by the Censor Board with no cuts last week but the film s distributor _______ no takers among the exhibitors for a release in Tamilnadu _______ this Friday Mr was found on a was found at the was found on a being find at ,English Grammar,51 The man who is now Municipal Commissioner worked as ________________ the security guard at a university a security guard at the university a security guard at university the security guard at the university ,English Grammar,51 Saturn is ___________ to be seen on a clear night with the naked eye enough bright bright enough as enough bright bright as enough ,English Grammar,51 Out of the following 4 sentences select the most suitable sentence with respect to grammar and usage Since the report lacked needed information it was of no use to them The report was useless to them because there were no needed information in it Since the report did not contain the needed information it was not real useful to them Since the report lacked needed information it would not had been useful to them ,English Grammar,51 Didn t you buy ____ when you went shopping any paper much paper no paper a few paper ,English Grammar,51 Archimedes said Give me a lever long enough and a fulcrum on which to place it and I will move the world The sentence above is an example of a ____________ statement figurative collateral literal figurine ,English Grammar,51 Which one of the parts A B C D in the sentence contains an ERROR No sooner had the doctor seen the results of the blood test than he suggested the patient to see the specialist A no sooner had B results of the blood test C suggested the patient D see the specialist ,English Grammar,51 Out of the following four sentences select the most suitable sentence with respect to grammar and usage I will not leave the place until the minister does not meet me I will not leave the place until the minister doesn t meet me I will not leave the place until the minister meet me I will not leave the place until the minister meets me ,English Grammar,51 Choose the grammatically CORRECT sentence He laid in bed till 8 o u2019clock in the morning He layed in bed till 8 o u2019clock in the morning He lain in bed till 8 o u2019clock in the morning He lay in bed till 8 o u2019clock in the morning ,English Grammar,51 Let E_1 and E_2 be two entities in an E R diagram with simple valued attributes R_1 and R_2 are two relationships between E_1 and E_2 where R_1 is one to many and R_2 is many to many R_1 and R_2 do not have any attributes of their own What is the minimum number of tables required to represent this situation in the relational model 2 3 4 5 ,Er Diagram,52 Given the basic ER and relational models which of the following is INCORRECT An attribute of an entity can have more than one value An attribute of an entity can be composite In a row of a relational table an attribute can have more than one value In a row of a relational table an attribute can have exactly one value or a NULL value ,Er Diagram,52 Consider the following ER diagram The minimum number of tables needed to represent M N P R1 R2 is 2 3 4 5 ,Er Diagram,52 Consider the following ER diagram The minimum number of tables needed to represent M N P R1 R2 is Which of the following is a correct attribute set for one of the tables for the minimum number of tables needed to represent M N P R1 R2 M1 M2 M3 P1 M1 P1 N1 N2 M1 P1 N1 M1 P1 ,Er Diagram,52 Consider the following entity relationship diagram ERD where two entities E1 and E2 have a relation R of cardinality 1 m The attributes of E1 are A11 A12 and A13 where A11 is the key attribute The attributes of E2 are A21 A22 and A23 where A21 is the key attribute and A23 is a multi valued attribute Relation R does not have any attribute A relational database containing minimum number of tables with each table satisfying the requirements of the third normal form 3NF is designed from the above ERD The number of tables in the database is 2 3 5 4 ,Er Diagram,52 Consider the entities hotel room and person with a many to many relationship lodging as shown below If we wish to store information about the rent payment to be made by person s occupying different hotel rooms then this information should appear as an attribute of Person Hotel Room Lodging None of these ,Er Diagram,52 Consider an Entity Relationship ER model in which entity sets E _ 1 and E _ 2 are connected by an m n relationship R _ 12 E _ 1 and E _ 3 are connected by a 1 n 1 on the side of E _ 1 and n on the side of E _ 3 relationship R _ 13 E _ 1 has two singled attributes a _ 11 and a _ 12 of which a _ 11 is the key attribute E _ 2 has two singled valued attributes a _ 21 and a _ 22 of which a _ 21 is the key attribute E _ 3 has two single valued attributes a _ 31 and a _ 32 of which a _ 31 is the key attribute The relationships do not have any attributes If a relational model is derived from the above ER model then the minimum number of relations that would be generated if all relation are in 3NF is________________ ,Er Diagram,52 We are given a set X X_1 X_n where X_i 2 i A sample S subseteq X is drawn by selecting each X_i independently with probability P_i frac 1 2 The expected value of the smallest number in sample S is left frac 1 n right 2 sqrt n n ,Expectation,53 Suppose that the expectation of a random variable X is 5 Which of the following statements is true There is a sample point at which X has the value 5 There is a sample point at which X has value greater than 5 There is a sample point at which X has a value greater than equal to 5 None of the above ,Expectation,53 Consider an undirected random graph of eight vertices The probability that there is an edge between a pair of vertices is dfrac 1 2 What is the expected number of unordered cycles of length three dfrac 1 8 1 7 8 ,Expectation,53 Assume that you are flipping a fair coin i e probability of heads or tails is equal Then the expected number of coin flips required to obtain two consecutive heads for the first time is 4 3 6 10 5 ,Expectation,53 An examination paper has 150 multiple choice questions of one mark each with each question having four choices Each incorrect answer fetches 0 25 marks Suppose 1000 students choose all their answers randomly with uniform probability The sum total of the expected marks obtained by all these students is 0 2550 7525 9375 ,Expectation,53 Ram has a fair coin i e a toss of the coin results in either head or tail and each event happens with probability exactly half 1 2 He repeatedly tosses the coin until he gets heads in two consecutive tosses The expected number of coin tosses that Ram does is 2 4 6 8 None of the above ,Expectation,53 Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta ,Exponential Distribution,54 What is the average of all multiples of 10 from 2 to 198 90 100 110 120 ,Factors,55 Out of all the 2 digit integers between 1 and 100 a 2 digit number has to be selected at random What is the probability that the selected number is not divisible by 7 left dfrac 13 90 right left dfrac 12 90 right left dfrac 78 90 right left dfrac 77 90 right ,Factors,55 Consider the field C of complex numbers with addition and multiplication Which of the following form s a subfield of C with addition and multiplication S1 the set of real numbers S2 a ib a and b are rational numbers S3 a ib a2 b2 u2264 1 S4 ia a is real only S1 S1 and S3 S2 and S3 S1 and S2 ,Fields,56 A FAT file allocation table based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size Given a 100 imes 10 6 bytes disk on which the file system is stored and data block size is 10 3 bytes the maximum size of a file that can be stored on this disk in units of 10 6 bytes is _________ ,File,57 The data blocks of a very large file in the Unix file system are allocated using continuous allocation linked allocation indexed allocation an extension of indexed allocation ,File System,58 In the index allocation scheme of blocks to a file the maximum possible size of the file depends on the size of the blocks and the size of the address of the blocks the number of blocks used for the index and the size of the blocks the size of the blocks the number of blocks used for the index and the size of the address of the blocks None of the above ,File System,58 In a particular Unix OS each data block is of size 1024 bytes each node has 10 direct data block addresses and three additional addresses one for single indirect block one for double indirect block and one for triple indirect block Also each block can contain addresses for 128 blocks Which one of the following is approximately the maximum size of a file in the file system 512 MB 2 GB 8 GB 16 GB ,File System,58 In a file allocation system which of the following allocation scheme s can be used if no external fragmentation is allowed Contiguous Linked Indexed 1 and 3 only 2 only 3 only 2 and 3 only ,File System,58 A file system with a one level directory structure is implemented on a disk with disk block size of 4K bytes The disk is used as follows Disk block 0 File Allocation Table consisting of one 8 bit entry per data block representing the data block address of the next data block in the file Disk block 1 Directory with one 32 bit entry per file Disk block 2 Data block 1 Disk block 3 Data block 2 etc What is the maximum possible number of files What is the maximum possible file size in blocks ,File System,58 State whether the following statements are TRUE or FALSE A minimal DFA that is equiavlent to an NDFA with n nodes has always 2 n states ,Finite Automata,59 State True or False with one line explanation A FSM Finite State Machine can be designed to add two integers of any arbitrary length arbitrary number of digits ,Finite Automata,59 Let L be the set of all binary strings whose last two symbols are the same The number of states in the minimal state deterministic finite state automaton accepting L is 2 5 8 3 ,Finite Automata,59 Let L be the language of all binary strings in which the third symbol from the right is a 1 Give a non deterministic finite automaton that recognizes L How many states does the minimized equivalent deterministic finite automaton have Justify your answer briefly ,Finite Automata,59 Indicate whether the following statement is true or false providing a short explanation to substantiate your answers If a language L is accepted by an NFA with n states then there is a DFA with no more than 2 n states accepting L ,Finite Automata,59 Indicate whether the following statement is true or false providing a short explanation to substantiate your answers A DFA that has n states and accepts an infinite language must accept at least one string x such that 2n lt x lt 3n where x denotes the length of x ,Finite Automata,59 Given that L is a language accepted by a finite state machine show that L P and L R are also accepted by some finite state machines where L P left s mid ss in L ext some string s right L R left s mid s ext obtained by reversing some string in L right ,Finite Automata,59 Given below are the transition diagrams for two finite state machines M_1 and M_2 recognizing languages L_1 and L_2 respectively Display the transition diagram for a machine that recognizes L_1 L_2 obtained from transition diagrams for M_1 and M_2 by adding only varepsilon transitions and no new states Modify the transition diagram obtained in part a obtain a transition diagram for a machine that recognizes L_1 L_2 by adding only varepsilon transitions and no new states Final states are enclosed in double circles ,Finite Automata,59 Draw the state transition of a deterministic finite state automaton which accepts all strings from the alphabet a b such that no string has 3 consecutive occurrences of the letter b ,Finite Automata,59 Design a deterministic finite state automaton using minimum number of states that recognizes the following language L w in 0 1 mid w interpreted as binary number ignoring the leading zeros is divisible by five ,Finite Automata,59 Construct a finite state machine with minimum number of states accepting all strings over a b such that the number of a s is divisible by two and the number of b s is divisible by three ,Finite Automata,59 Consider the regular expression 0 1 0 1 dots N times The minimum state finite automaton that recognizes the language represented by this regular expression contains n states n 1 states n 2 states None of the above ,Finite Automata,59 Consider the following state table for a sequential machine The number of states in the minimized machine will be Input 0 1 Present State A D 0 B 1 B A 0 C 1 C A 0 B 1 D A 1 C 1 Next state Output 4 3 2 1 ,Finite Automata,59 A finite state machine with the following state table has a single input x and a single out z present state next state z x 1 x 0 A D 0 B 0 B B 1 C 1 C B 0 D 1 D B 1 C 0 If the initial state is unknown then the shortest input sequence to reach the final state C is 01 10 101 110 ,Finite Automata,59 What is the first order predicate calculus statement equivalent to the following Every teacher is liked by some student u2200 x left ext teacher left x right u2192 u2203 y left ext student left y right u2192 ext likes left y x right right right u2200 x left ext teacher left x right u2192 u2203 y left ext student left y right u2227 ext likes left y x right right right u2203 y u2200 x left ext teacher left x right u2192 left ext student left y right u2227 ext likes left y x right right right u2200 x left ext teacher left x right u2227 u2203 y left ext student left y right u2192 ext likes left y x right right right ,First Order Logic,60 Let P x and Q x be arbitrary predicates Which of the following statements is always TRUE left left forall x left P left x right vee Q left x right right right right implies left left forall x P left x right right vee left forall xQ left x right right right left forall x left P left x right implies Q left x right right right implies left left forall x P left x right right implies left forall xQ left x right right right left forall x left P left x right right implies forall x left Q left x right right right implies left forall x left P left x right implies Q left x right right right left forall x left P left x right right Leftrightarrow left forall x left Q left x right right right right implies left forall x left P left x right Leftrightarrow Q left x right right right ,First Order Logic,60 Let ext fsa and ext pda be two predicates such that ext fsa x means x is a finite state automaton and ext pda y means that y is a pushdown automaton Let ext equivalent be another predicate such that ext equivalent a b means a and b are equivalent Which of the following first order logic statements represent the following Each finite state automaton has an equivalent pushdown automaton left forall x ext fsa left x right right implies left exists y ext pda left y right wedge ext equivalent left x y right right eg forall y left exists x ext fsa left x right implies ext pda left y right wedge ext equivalent left x y right right forall x exists y left ext fsa left x right wedge ext pda left y right wedge ext equivalent left x y right right forall x exists y left ext fsa left y right wedge ext pda left x right wedge ext equivalent left x y right right ,First Order Logic,60 Let a x y b x y and c x y be three statements with variables x and y chosen from some universe Consider the following statement qquad exists x forall y a x y wedge b x y wedge eg c x y Which one of the following is its equivalent forall x exists y a x y vee b x y o c x y exists x forall y a x y vee b x y wedge eg c x y eg forall x exists y a x y wedge b x y o c x y eg forall x exists y a x y vee b x y o c x y ,First Order Logic,60 Identify the correct translation into logical notation of the following assertion Some boys in the class are taller than all the girls Note ext taller x y is true if x is taller than y exists x ext boy x rightarrow forall y ext girl y land ext taller x y exists x ext boy x land forall y ext girl y land ext taller x y exists x ext boy x rightarrow forall y ext girl y rightarrow ext taller x y exists x ext boy x land forall y ext girl y rightarrow ext taller x y ,First Order Logic,60 Consider the following formula and its two interpretations I_1 and I_2 alpha forall x left P_x Leftrightarrow forall y left Q_ xy Leftrightarrow eg Q_ yy right right Rightarrow forall x left eg P_x right I_1 Domain the set of natural numbers P_x x is a prime number Q_ xy y divides x I_2 same as I_1 except that P_x x is a composite number Which of the following statements is true I_1 satisfies alpha I_2 does not I_2 satisfies alpha I_1 does not Neither I_1 nor I_2 satisfies alpha Both I_1 and I_2 satisfies alpha ,First Order Logic,60 Consider the following first order logic formula in which R is a binary relation symbol u2200x u2200y R x y implies R y x The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable ,First Order Logic,60 def graph ext Graph def connected ext Connected Let graph x be a predicate which denotes that x is a graph Let connected x be a predicate which denotes that x is connected Which of the following first order logic sentences DOES NOT represent the statement qquad ext Not every graph is connected lnot forall x Bigl graph x implies connected x Bigr exists x Bigl graph x land lnot connected x Bigr lnot forall x Bigl lnot graph x lor connected x Bigr forall x Bigl graph x implies lnot connected x Bigr ,First Order Logic,60 b Consider the following first order formula left matrix forall x exists y R x y 1em Large land 1em forall x forall y Bigl R x y implies lnot R y x Bigr 1em Large land 1em forall x forall y forall z Bigl R x y land R y z implies R x z Bigr 1em Large land 1em forall x lnot R x x right Does it have finite models Is it satisfiable If so give a countable model for it ,First Order Logic,60 The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right ,Fixed Point Representation,61 In an SR latch made by cross coupling two NAND gates if both S and R inputs are set to 0 then it will result in Q 0 Q 1 Q 1 Q 0 Q 1 Q 1 Indeterminate states ,Flip Flop,62 Find the maximum clock frequency at which the counter in the figure below can be operated Assume that the propagation delay through each flip flop and each AND gate is 10 ext ns Also assume that the setup time for the JK inputs of the flip flops is negligible ,Flip Flop,62 Design a 3 bit counter using D flip flops such that not more than one flip flop changes state between any two consecutive states ,Flip Flop,62 Consider a combination of T and D flip flops connected as shown below The output of the D flip flop is connected to the input of the T flip flop and the output of the T flip flop is connected to the input of the D flip flop Initially both Q_ 0 and Q_ 1 are set to 1 before the 1st clock cycle The outputs Q_ 1 Q_ 0 after the 3rd cycle are 11 and after the 4th cycle are 00 respectively Q_ 1 Q_ 0 after the 3rd cycle are 11 and after the 4th cycle are 01 respectively Q_ 1 Q_ 0 after the 3rd cycle are 00 and after the 4th cycle are 11 respectively Q_ 1 Q_ 0 after the 3rd cycle are 01 and after the 4th cycle are 01 respectively ,Flip Flop,62 A sequential circuit takes an input stream of 0 s and 1 s and produces an output stream of 0 s and 1 s Initially it replicates the input on its output until two consecutive 0 s are encountered on the input From then onward it produces an output stream which is the bit wise complement of input stream until it encounters two consecutive 1 s whereupon the process repeats An example input and output stream is shown below The input stream 101100 01001011 0 11 The desired output 101100 10110100 0 11 J K master slave flip flops are to be used to design the circuit Give the state transition diagram,Flip Flop,62 A positive edge triggered D flip flop is connected to a positive edge triggered JK flip flop as follows The Q output of the D flip flop is connected to both the J and K inputs of the JK flip flop while the Q output of the JK flip flop is connected to the input of the D flip flop Initially the output of the D flip flop is set to logic one and the output of the JK flip flop is cleared Which one of the following is the bit sequence including the initial state generated at the Q output of the JK flip flop when the flip flops are connected to a free running common clock Assume that J K 1 is the toggle mode and J K 0 is the state holding mode of the JK flip flops Both the flip flops have non zero propagation delays 0110110 0100100 011101110 011001100 ,Flip Flop,62 The following is a scheme for floating point number representation using 16 bits Bit Position 15 14 9 8 0 s e m Sign Exponent Mantissa Let s e and m be the numbers represented in binary in the sign exponent and mantissa fields respectively Then the floating point number represented is begin cases 1 s left 1 m imes 2 9 right 2 e 31 amp ext if the exponent eq 111111 0 amp ext otherwise end cases What is the maximum difference between two successive real numbers representable in this system 2 40 2 9 2 22 2 31 ,Floating Point Representation,63 The exponent of a floating point number is represented in excess N code so that The dynamic range is large The precision is high The smallest number is represented by all zeros Overflow is avoided ,Floating Point Representation,63 Given the following binary number in 32 bit single precision IEEE 754 format large 00111110011011010000000000000000 The decimal value closest to this floating point number is 1 45 10 1 1 45 10 1 2 27 10 1 2 27 10 1 ,Floating Point Representation,63 Consider the following floating point format Mantissa is a pure fraction in sign magnitude form The normalized representation for the above format is specified as follows The mantissa has an implicit 1 preceding the binary radix point Assume that only 0 u2019s are padded in while shifting a field The normalized representation of the above number 0 239 imes 2 13 is 0A 20 11 34 49 D0 4A E8 ,Floating Point Representation,63 Consider the following floating point format Mantissa is a pure fraction in sign magnitude form The decimal number 0 239 imes 2 13 has the following hexadecimal representation without normalization and rounding off 0D 24 0D 4D 4D 0D 4D 3D ,Floating Point Representation,63 A 32 bit floating point number is represented by a 7 bit signed exponent and a 24 bit fractional mantissa The base of the scale factor is 16 The range of the exponent is ___________,Floating Point Representation,63 A process executes the following segment of code for i 1 i lt n i fork The number of new processes created is n n n 1 2 2 n 1 3 n 1 ,Fork,64 A process executes the following code for i 0 i lt n i fork The total number of child processes created is n 2n 1 2n 2n 1 1 ,Fork,64 A process executes the code fork fork fork The total number of child processes created is 3 4 7 8 ,Fork,64 Consider the following code fragment if fork 0 a a 5 printf d p n a amp a else a a 5 printf d p n a amp a Let u v be the values printed by the parent process and x y be the values printed by the child process Which one of the following is TRUE u x 10 and v y u x 10 and v y u 10 x and v y u 10 x and v y ,Fork,64 A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND ,Functional Completeness,65 The implication gate shown below has two inputs x ext and y the output is 1 except when x 1 ext and y 0 ext realize f bar x y x bar y using only four implication gates Show that the implication gate is functionally complete ,Functional Completeness,65 The following functional dependencies hold true for the relational schema R left V W X Y Z right V rightarrow W VW rightarrow X Y rightarrow VX Y rightarrow Z Which of the following is irreducible equivalent for this set of functional dependencies V rightarrow W V rightarrow X Y rightarrow V Y rightarrow Z V rightarrow W W rightarrow X Y rightarrow V Y rightarrow Z V rightarrow W V rightarrow X Y rightarrow V Y rightarrow X Y rightarrow Z V rightarrow W W rightarrow X Y rightarrow V Y rightarrow X Y rightarrow Z ,Functional Dependencies,66 The following functional dependencies are given AB rightarrow CD AF rightarrow D DE rightarrow F C rightarrow G F rightarrow E G rightarrow A Which one of the following options is false left CF right left ACDEFG right left BG right left ABCDG right left AF right left ACDEFG right left AB right left ABCDG right ,Functional Dependencies,66 Suppose we have a relation R A B C D E with the functional dependencies A rightarrow D B rightarrow C D rightarrow E CE rightarrow B If we project R and therefore its functional dependencies onto the schema ABC what will the key s for ABC be ,Functional Dependencies,66 State whether the following statements are TRUE or FALSE A relation r with schema X Y satisfies the function dependency X rightarrow Y The tuples langle 1 2 rangle and langle 2 2 rangle can both be in r simultaneously ,Functional Dependencies,66 Relation R with an associated set of functional dependencies F is decomposed into ext BCNF The redundancy arising out of functional dependencies in the resulting set of relations is Zero More than zero but less than that of an equivalent 3NF decomposition Proportional to the size of F Indeterminate ,Functional Dependencies,66 Relation R has eight attributes ext ABCDEFGH Fields of R contain only atomic values F ext CH u2192G A u2192BC B u2192CFH E u2192A F u2192EG is a set of functional dependencies FDs so that F is exactly the set of FDs that hold for R How many candidate keys does the relation R have 3 4 5 6 ,Functional Dependencies,66 Relation R has eight attributes ext ABCDEFGH Fields of R contain only atomic values F ext CH rightarrow G A rightarrow BC B rightarrow CFH E rightarrow A F rightarrow EG is a set of functional dependencies FDs so that F is exactly the set of FDs that hold for R The relation R is in 1NF but not in 2NF in 2NF but not in 3NF in 3NF but not in ext BCNF in ext BCNF ,Functional Dependencies,66 In a schema with attributes A B C D and E following set of functional dependencies are given A u2192 B A u2192 C CD u2192 E B u2192 D E u2192 A Which of the following functional dependencies is NOT implied by the above set CD u2192 AC BD u2192 CD BC u2192 CD AC u2192 BC ,Functional Dependencies,66 Given the following relation instance X Y Z 1 4 2 1 5 3 1 6 3 3 2 2 Which of the following functional dependencies are satisfied by the instance XY u2192 Z and Z u2192 Y YZ u2192 X and Y u2192 Z YZ u2192 X and X u2192 Z XZ u2192 Y and Y u2192 X ,Functional Dependencies,66 Form the following instance of a relation schema R A B C we can conclude that A B C 1 1 1 1 1 0 2 3 2 2 3 2 A functionally determines B and B functionally determines C A functionally determines B and B does not functionally determine C B does not functionally determine C A does not functionally determine B and B does not functionally determine C ,Functional Dependencies,66 Consider the relation X P Q R S T U with the following set of functional dependencies F P R rightarrow S T P S U rightarrow Q R Which of the following is the trivial functional dependency in F where F is closure to F P R rightarrow S T P R rightarrow R T P S rightarrow S P S U rightarrow Q ,Functional Dependencies,66 Consider the relation scheme R E F G H I J K L M N and the set of functional dependencies left E F o G F o I J E H o K L K o M L o N right on R What is the key for R E F E F H E F H K L E ,Functional Dependencies,66 Consider a relation R with five attributes V W X Y and Z The following functional dependencies hold VY u2192 W WX u2192 Z and ZY u2192 V Which of the following is a candidate key for R VXZ VXY VWXY VWXYZ ,Functional Dependencies,66 What is the maximum number of different Boolean functions involving n Boolean variables n 2 2 n 2 2 n 2 n 2 ,Functions,67 The number of functions from an m element set to an n element set is m n m n n m m n ,Functions,67 Let X Y Z be sets of sizes x y and z respectively Let W X imes Y and E be the set of all subsets of W The number of functions from Z to E is z 2 xy z imes 2 xy z 2 x y 2 xyz ,Functions,67 Let Sigma left a b c d e right be an alphabet We define an encoding scheme as follows g a 3 g b 5 g c 7 g d 9 g e 11 Let p_i denote the i th prime number left p_1 2 right For a non empty string s a_1 dots a_n where each a_i in Sigma define f s Pi n_ i 1 P_i g a_i For a non empty sequence left langle s_j dots s_n right rangle of stings from Sigma define h left left langle s_i dots s_n right rangle right Pi n_ i 1 P_i f left s_i right Which of the following numbers is the encoding h of a non empty sequence of strings 2 73 75 7 2 83 85 8 2 93 95 9 2 10 3 10 5 10 ,Functions,67 Let S 1 2 3 m m gt 3 Let X1 Xn be subsets of S each of size 3 Define a function f from S to the set of natural numbers as f i is the number of sets Xj that contain the element i That is f i left left j mid i in X_j right right then sum_ i 1 m f i is 3m 3n 2m 1 2n 1 ,Functions,67 Let R denote the set of real numbers Let f R imes R rightarrow R imes R be a bijective function defined by f x y x y x y The inverse function of f is given by a f 1 x y left frac 1 x y frac 1 x y right b f 1 x y x y x y c f 1 x y left frac x y 2 frac x y 2 right d f 1 x y left 2 left x y right 2 left x y right right ,Functions,67 Let F be the set of one to one functions from the set 1 2 dots n to the set 1 2 dots m where m geq n geq1 How many functions are members of F How many functions f in F satisfy the property f i 1 for some i 1 leq i leq n How many functions f in F satisfy the property f i lt f j for all 1 leq i leq j leq n ,Functions,67 Let f be a function from a set A to a set B g a function from B to C and h a function from A to C such that h a g f a for all a u2208 A Which of the following statements is always true for all such functions f and g g is onto gt h is onto h is onto gt f is onto h is onto gt g is onto h is onto gt f and g are onto ,Functions,67 Let f B o C and g A o B be two functions and let h f o g Given that h is an onto function which one of the following is TRUE f and g should both be onto functions f should be onto but g need not to be onto g should be onto but f need not be onto both f and g need not be onto ,Functions,67 Let f A rightarrow B a function and let E and F be subsets of A Consider the following statements about images S1 f E cup F f E cup f F S2 f E cap F f E cap f F Which of the following is true about S1 and S2 Only S1 is correct Only S2 is correct Both S1 and S2 are correct None of S1 and S2 is correct ,Functions,67 Let f A o B be an injective one to one function Define g 2 A o 2 B as g C left f x mid x in C right for all subsets C of A Define h 2 B o 2 A as h D x mid x in A f x in D for all subsets D of B Which of the following statements is always true g h D subseteq D g h D supseteq D g h D cap D phi g h D cap B D e phi ,Functions,67 Let A and B be sets with cardinalities m and n respectively The number of one one mappings from A to B when m lt n is m n nP_m mC_n nC_m mP_n ,Functions,67 Given a boolean function f x1 x2 xn which of the following equations is NOT true f x1 x2 xn x1 f x1 x2 xn x1f x1 x2 xn f x1 x2 xn x2f x1 x2 u2026 xn x2 f x1 x2 u2026 xn f x1 x2 xn xn f x1 x2 u2026 0 xnf x1 x2 u2026 1 f x1 x2 xn f 0 x2 u2026 xn f 1 x2 xn ,Functions,67 A function f Bbb N rightarrow Bbb N defined on the set of positive integers Bbb N satisfies the following properties f n f n 2 if n is even f n f n 5 if n is odd Let R i mid exists j f j i be the set of distinct values that f takes The maximum possible size of R is ___________ ,Functions,67 Suppose X and Y are sets and X ext and Y are their respective cardinalities It is given that there are exactly 97 functions from X to Y From this one can conclude that X 1 Y 97 X 97 Y 1 X 97 Y 97 None of the above ,Functions,67 What is the generating function G z for the sequence of Fibonacci numbers ,Generating Functions,68 The coefficient of x 3 in the expansion of 1 x 3 2 x 2 10 is 2 14 31 left frac 3 3 right left frac 10 1 right left frac 3 3 right 2 left frac 10 1 right left frac 3 3 right left frac 10 1 right 2 9 ,Generating Functions,68 The coefficient of x 12 in left x 3 x 4 x 5 x 6 dots right 3 is ___________ ,Generating Functions,68 If the ordinary generating function of a sequence big a_n big _ n 0 infty is large frac 1 z 1 z 3 then a_3 a_0 is equal to ___________ ,Generating Functions,68 When a point inside of a tetrahedron a solid with four triangular surfaces is connected by straight lines to its corners how many new internal planes are created with these lines ,Geometry,69 In a triangle PQR PS is the angle bisector of angle QPR ext and angle QPS 60 circ What is the length of PS left dfrac q r qr right left dfrac qr q r right large sqrt q 2 r 2 left dfrac q r 2 qr right ,Geometry,69 A cube is built using 64 cubic blocks of side one unit After it is built one cubic block is removed from every corner of the cube The resulting surface area of the body in square units after the removal is ________ 56 64 72 96 ,Geometry,69 An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code ,Goto,70 What is the chromatic number of the following graph 2 3 4 5 ,Graph Coloring,71 What is the chromatic number of an n vertex simple connected graph which does not contain any odd length cycle Assume n gt 2 2 3 n 1 n ,Graph Coloring,71 The minimum number of colours that is sufficient to vertex colour any planar graph is ________ ,Graph Coloring,71 The minimum number of colours required to colour the vertices of a cycle with n nodes in such a way that no two adjacent nodes have the same colour is 2 3 4 n 2 left lfloor frac n 2 right rfloor 2 ,Graph Coloring,71 The minimum number of colours required to colour the following graph such that no two adjacent vertices are assigned the same color is 2 3 4 5 ,Graph Coloring,71 Let G V E be a simple undirected graph on n vertices A colouring of G is an assignment of colours to each vertex such that endpoints of every edge are given different colours Let chi G denote the chromatic number of G i e the minimum numbers of colours needed for a valid colouring of G A set B subseteq V is an independent set if no pair of vertices in B is connected by an edge Let a G be the number of vertices in a largest possible independent set in G In the absence of any further information about G we can conclude chi left G right geq a left G right chi left G right leq a left G right a left G right geq frac n chi left G right a left G right leq frac n chi left G right None of the above ,Graph Coloring,71 How many ways are there to assign colours from range left 1 2 r right to vertices of the following graph so that adjacent vertices receive distinct colours r 4 r 4 4r 3 r 4 5r 3 8r 2 4r r 4 4r 3 9r 2 3r r 4 5r 3 10r 2 15r ,Graph Coloring,71 Consider the undirected graph G defined as follows The vertices of G are bit strings of length n We have an edge between vertex u and vertex v if and only if u and v differ in exactly one bit position in other words v can be obtained from u by flipping a single bit The ratio of the chromatic number of G to the diameter of G is frac 1 left 2 n 1 right left frac 1 n right left frac 2 n right left frac 3 n right ,Graph Coloring,71 A vertex colouring with three colours of a graph G V E is a mapping c V rightarrow R G B so that adjacent vertices receive distinct colours Consider the following undirected graph How many vertex colouring with three colours does this graph have 3 9 6 3 3 imes 2 8 27 24 ,Graph Coloring,71 A vertex colouring of a graph G V E with k coulours is a mapping c V rightarrow 1 dots k such that c u eq c v for every u v in E Consider the following statements If every vertex in G has degree at most d then G admits a vertex coulouring using d 1 colours Every cycle admits a vertex colouring using 2 colours Every tree admits a vertex colouring using 2 colours Which of the above statements is are TRUE Choose from the following options only i only i and ii only i and iii only ii and iii i ii and iii ,Graph Coloring,71 What is the number of vertices in an undirected connected graph with 27 edges 6 vertices of degree 2 3 vertices of degree 4 and remaining of degree 3 10 11 18 19 ,Graph Connectivity,72 What is the maximum number of edges in an acyclic undirected graph with n vertices n 1 n n 1 2n 1 ,Graph Connectivity,72 The minimum number of edges in a connected cyclic graph on n vertices is a n 1 b n c n 1 d None of the above,Graph Connectivity,72 The maximum number of possible edges in an undirected graph with n vertices and k components is ______ ,Graph Connectivity,72 The maximum number of edges in a n node undirected graph without self loops is n 2 frac n n 1 2 n 1 frac n 1 n 2 ,Graph Connectivity,72 The 2 n vertices of a graph G corresponds to all subsets of a set of size n for n geq 6 Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements The number of connected components in G is n n 2 2 frac n 2 frac 2 n n ,Graph Connectivity,72 Let G be an arbitrary graph with n nodes and k components If a vertex is removed from G the number of components in the resultant graph must necessarily lie down between k and n k 1 and k 1 k 1 and n 1 k 1 and n k ,Graph Connectivity,72 Let G be a directed graph whose vertex set is the set of numbers from 1 to 100 There is an edge from a vertex i to a vertex j iff either j i 1 or j 3i The minimum number of edges in a path in G from vertex 1 to vertex 100 is 4 7 23 99 ,Graph Connectivity,72 Let G be a connected undirected graph A cut in G is a set of edges whose removal results in G being broken into two or more components which are not connected with each other The size of a cut is called its cardinality A min cut of G is a cut in G of minimum cardinality Consider the following graph Which of the following sets of edges is a cut left A B E F B D A E A D right left B D C F A B right What is cardinality of min cut in this graph Prove that if a connected undirected graph G with n vertices has a min cut of cardinality k then G has at least left frac n imes k 2 right edges ,Graph Connectivity,72 If all the edge weights of an undirected graph are positive then any subset of edges that connects all the vertices and has minimum total weight is a Hamiltonian cycle grid hypercube tree ,Graph Connectivity,72 G is a simple undirected graph Some vertices of G are of odd degree Add a node v to G and make it adjacent to each odd degree vertex of G The resultant graph is sure to be regular complete Hamiltonian Euler ,Graph Connectivity,72 Consider an undirected graph G where self loops are not allowed The vertex set of G is i j mid1 leq i leq 12 1 leq j leq 12 There is an edge between a b and c d if a c leq 1 and b d leq 1 The number of edges in this graph is______ ,Graph Connectivity,72 The number of articulation points of the following graph is 0 1 2 3 ,Graph Connectivity,72 Let G V E be a graph Define bar G to be V bar E where for all u v in V u v in bar E if and only if u v otin E Then which of the following is true bar G is always connected bar G is connected if G is not connected At least one of G and bar G connected G is not connected or bar G is not connected ,Graph Connectivity,72 Consider a simple connected graph G with n vertices and n edges n gt 2 Then which of the following statements are true G has no cycles The graph obtained by removing any edge from G is not connected G has at least one cycle The graph obtained by removing any two edges from G is not connected None of the above ,Graph Connectivity,72 A cycle on n vertices is isomorphic to its complement The value of n is _____ ,Graph Isomorphism,73 Which of the following graphs is isomorphic to ,Graph Isomorphism,73 How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 ,Graph Matching,74 Choose the correct alternatives More than one may be correct A graph is planar if and only if It does not contain subgraphs homeomorphic to k_ 5 and k_ 3 3 It does not contain subgraphs isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph homeomorphic to k_ 5 or k_ 3 3 ,Graph Planarity,75 Answer the following Which of the following graphs is are planner see Fig 2 ,Graph Planarity,75 What is the size of the smallest MIS Maximal Independent Set of a chain of nine nodes 5 4 3 2 ,Graphs,76 Let G V E be a directed graph where V is the set of vertices and E the set of edges Then which one of the following graphs has the same strongly connected components as G G_1 V E_1 where E_1 left u v mid u v otin E right G_2 V E_2 where E_2 left u v mid v u in E right G_3 V E_3 where E_3 u v mid there is a path of length leq2 from u to v in E G_4 V_4 E where V_4 is the set of vertices in G which are not isolated ,Graphs,76 Let G be the graph with 100 vertices numbered 1 to 100 Two vertices i and j are adjacent if vert i j vert 8 or vert i j vert 12 The number of connected components in G is 8 4 12 25 ,Graphs,76 How many edges can there be in a forest with p components having n vertices in all ,Graphs,76 Consider the weighted undirected graph with 4 vertices where the weight of edge i j is given by the entry W_ ij in the matrix W W begin bmatrix 0 amp 2 amp 8 amp 5 2 amp 0 amp 5 amp 8 8 amp 5 amp 0 amp x 5 amp 8 amp x amp 0 end bmatrix The largest possible integer value of x for which at least one shortest path between some pair of vertices will contain the edge with weight x is ___________,Graphs,76 G is a graph on n vertices and 2n 2 edges The edges of G can be partitioned into two edge disjoint spanning trees Which of the following is NOT true for G For every subset of k vertices the induced subgraph has at most 2k 2 edges The minimum cut in G has at least 2 edges There are at least 2 edge disjoint paths between every pair of vertices There are at least 2 vertex disjoint paths between every pair of vertices ,Graphs,76 Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 ,Gray Code,77 The set 1 2 4 7 8 11 13 14 is a group under multiplication modulo 15 the inverses of 4 and 7 are respectively a 3 and 13 b 2 and 11 c 4 and 13 d 8 and 14,Groups,78 The following is the incomplete operation table of a 4 element group e a b c e e a b c a a b c e b c The last row of the table is c a e b c b a e c b e a c e a b ,Groups,78 Let S 0 1 2 3 4 5 6 7 and u2297 denote multiplication modulo 8 that is x u2297 y xy mod 8 Prove that 0 1 u2297 is not a group Write 3 distinct groups G u2297 where G u2282 S and G has 2 elements ,Groups,78 Let left Z right be an algebraic structure where Z is the set of integers and the operation is defined by n m max n m Which of the following statements is true for u00a0 left Z right left Z right is a monoid left Z right is an Abelian group left Z right is a group None of the above ,Groups,78 Let left p q right be a semigroup where p p q Show that p q q p and q q q ,Groups,78 If G is a group of even order then show that there exists an element a u2260e e the identity in G such that a 2 e ,Groups,78 Consider the set Sigma of all strings over the alphabet Sigma 0 1 Sigma with the concatenation operator for strings does not form a group forms a non commutative group does not have a right identity element forms a group if the empty string is removed from Sigma ,Groups,78 Consider the set H of all 3 3 matrices of the type left begin array ccc a amp f amp e 0 amp b amp d 0 amp 0 amp c end array right where a b c d e and f are real numbers and abc u2260 0 under the matrix multiplication operation the set H is a group a monoid but not a group a semi group but not a monoid neither a group nor a semi group ,Groups,78 Which of the following statements is false The set of rational numbers is an abelian group under addition The set of integers in an abelian group under addition The set of rational numbers form an abelian group under multiplication The set of real numbers excluding zero is an abelian group under multiplication ,Groups,78 Some group G o is known to be abelian Then which one of the following is true for G g g 1 ext for every g in G g g 2 ext for every g in G goh 2 g 2oh 2 ext for every g h in G G is of finite order ,Groups,78 Let G_1 and G_2 be subgroups of a group G Show that G_1 cap G_2 is also a subgroup of G Is G_1 cup G_2 always a subgroup of G ,Groups,78 Let A be the set of all non singular matrices over real number and let be the matrix multiplication operation Then A is closed under but langle A rangle is not a semigroup langle A rangle is a semigroup but not a monoid langle A rangle is a monoid but not a group langle A rangle is a a group but not an abelian group ,Groups,78 Let A be a semigroup Furthermore for every a and b in A if a eq b then a b eq b a Show that for every a in A a a a Show that for every a b in A a b a a Show that for every a b c in A a b c a c ,Groups,78 Consider the set of integers 1 2 3 4 6 8 12 24 together with the two binary operations LCM lowest common multiple and GCD greatest common divisor Which of the following algebraic structures does this represent group ring field lattice ,Groups,78 A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ ,Half Adder,79 The keys 12 18 13 2 3 23 5 and 15 are inserted into an initially empty hash table of length 10 using open addressing with hash function h k k mod 10 and linear probing What is the resultant hash table A B C D 0 1 2 2 3 23 4 5 15 6 7 8 18 9 0 1 2 12 3 13 4 5 5 6 7 8 18 9 0 1 2 12 3 13 4 2 5 3 6 23 7 5 8 18 9 15 0 1 2 2 12 3 13 3 23 4 5 5 15 6 7 8 18 9 ,Hashing,80 Insert the characters of the string K R P C S N Y T J M into a hash table of size 10 Use the hash function h x ord x u2013 ord a 1 mod 10 and linear probing to resolve collisions Which insertions cause collisions Display the final hash table ,Hashing,80 Given the following input 4322 1334 1471 9679 1989 6171 6173 4199 and the hash function x mod 10 which of the following statements are true 9679 1989 4199 hash to the same value 1471 6171 hash to the same value All elements hash to the same value Each element hashes to a different value I only II only I and II only III or IV ,Hashing,80 Consider a hash table with n buckets where external overflow chaining is used to resolve collisions The hash function is such that the probability that a key value is hashed to a particular bucket is frac 1 n The hash table is initially empty and K distinct values are inserted in the table What is the probability that bucket number 1 is empty after the K th insertion What is the probability that no collision has occurred in any of the K insertions What is the probability that the first collision occurs at the K th insertion ,Hashing,80 Consider a hash table with 9 slots The hash function is h k k mod 9 The collisions are resolved by chaining The following 9 keys are inserted in the order 5 28 19 15 20 33 12 17 10 The maximum minimum and average chain lengths in the hash table respectively are 3 0 and 1 3 3 and 3 4 0 and 1 3 0 and 2 ,Hashing,80 Consider a hash table with 100 slots Collisions are resolved using chaining Assuming simple uniform hashing what is the probability that the first 3 slots are unfilled after the first 3 insertions 97 imes 97 imes 97 100 3 99 imes 98 imes 97 100 3 97 imes 96 imes 95 100 3 97 imes 96 imes 95 3 imes 100 3 ,Hashing,80 Consider a hash table of size seven with starting index zero and a hash function 3x 4 mod 7 Assuming the hash table is initially empty which of the following is the contents of the table when the sequence 1 3 8 10 is inserted into the table using closed hashing Note that u2212 denotes an empty location in the table 8 u2212 u2212 u2212 u2212 u2212 10 1 8 10 u2212 u2212 u2212 3 1 u2212 u2212 u2212 u2212 u2212 3 1 10 8 u2212 u2212 u2212 3 ,Hashing,80 Consider a hash table of size 11 that uses open addressing with linear probing Let h k k mod 11 be the hash function used A sequence of records with keys 43 36 92 87 11 4 71 13 14 is inserted into an initially empty hash table the bins of which are indexed from zero to ten What is the index of the bin into which the last record is inserted 3 4 6 7 ,Hashing,80 Consider a hash function that distributes keys uniformly The hash table size is 20 After hashing of how many keys will the probability that any new key hashed collides with an existing one exceed 0 5 5 6 7 10 ,Hashing,80 A hash table with ten buckets with one slot per bucket is shown in the following figure The symbols S1 to S7 initially entered using a hashing function with linear probing The maximum number of comparisons needed in searching an item that is not present is 4 5 6 3 ,Hashing,80 A hash table of length 10 uses open addressing with hash function h k k mod 10 and linear probing After inserting 6 values into an empty hash table the table is shown as below 0 1 2 42 3 23 4 34 5 52 6 46 7 33 8 9 Which one of the following choices gives a possible order in which the key values could have been inserted in the table 46 42 34 52 23 33 34 42 23 52 33 46 46 34 42 23 52 33 42 46 33 23 34 52 ,Hashing,80 A hash table of length 10 uses open addressing with hash function h k k mod 10 and linear probing After inserting 6 values into an empty hash table the table is shown as below 0 1 2 42 3 23 4 34 5 52 6 46 7 33 8 9 How many different insertion sequences of the key values using the same hash function and linear probing will result in the hash table shown above 10 20 30 40 ,Hashing,80 A hash table contains 10 buckets and uses linear probing to resolve collisions The key values are integers and the hash function used is key 10 If the values 43 165 62 123 142 are inserted in the table in what location would the key value 142 be inserted 2 3 4 6 ,Hashing,80 An advantage of chained hash table external hashing over the open addressing scheme is Worst case complexity of search operations is less Space used is less Deletion is easier None of the above ,Hashing,80 The minimum number of interchanges needed to convert the array into a max heap is 89 19 40 17 12 10 2 5 7 11 6 9 70 0 1 2 3 ,Heap,81 The elements 32 15 20 30 12 25 16 are inserted one by one in the given order into a maxHeap The resultant maxHeap is ,Heap,81 Statement for Linked Answer Questions 76 amp 77 A 3 ary max heap is like a binary max heap but instead of 2 children nodes have 3 children A 3 ary heap can be represented by an array as follows The root is stored in the first location a 0 nodes in the next level from left to right is stored from a 1 to a 3 The nodes from the second level of the tree from left to right are stored from a 4 location onward An item x can be inserted into a 3 ary heap containing n items by placing x in the location a n and pushing it up the tree to satisfy the heap property 77 Suppose the elements 7 2 10 and 4 are inserted in that order into the valid 3 ary max heap found in the previous question Q 76 Which one of the following is the sequence of items in the array representing the resultant heap 10 7 9 8 3 1 5 2 6 4 10 9 8 7 6 5 4 3 2 1 10 9 4 5 7 6 8 2 1 3 10 8 6 9 7 2 3 4 1 5 ,Heap,81 Statement for Linked Answer Questions 76 amp 77 A 3 ary max heap is like a binary max heap but instead of 2 children nodes have 3 children A 3 ary heap can be represented by an array as follows The root is stored in the first location a 0 nodes in the next level from left to right is stored from a 1 to a 3 The nodes from the second level of the tree from left to right are stored from a 4 location onward An item x can be inserted into a 3 ary heap containing n items by placing x in the location a n and pushing it up the tree to satisfy the heap property 76 Which one of the following is a valid sequence of elements in an array representing 3 ary max heap 1 3 5 6 8 9 9 6 3 1 8 5 9 3 6 8 5 1 9 5 6 8 3 1 ,Heap,81 In a min heap with n elements with the smallest element at the root the 7 th smallest element can be found in time Theta n log n Theta n Theta log n Theta 1 ,Heap,81 In a binary max heap containing n numbers the smallest element can be found in time O n O log n O log log n O 1 ,Heap,81 Consider the process of inserting an element into a Max Heap where the Max Heap is represented by an array Suppose we perform a binary search on the path from the new leaf to the root to find the position for the newly inserted element the number of comparisons performed is Theta log_2n Theta log_2 log_2n Theta n Theta n log_2n ,Heap,81 Consider any array representation of an n element binary heap where the elements are stored from index 1 to index n of the array For the element stored at index i of the array i leq n the index of the parent is i 1 lfloor frac i 2 rfloor lceil frac i 2 rceil frac i 1 2 ,Heap,81 Consider a binary max heap implemented using an array Which one of the following array represents a binary max heap left 25 12 16 13 10 8 14 right left 25 14 13 16 10 8 12 right left 25 14 16 13 10 8 12 right left 25 14 12 13 10 8 16 right ,Heap,81 An operator delete i for a binary heap data structure is to be designed to delete the item in the i th node Assume that the heap is implemented in an array and i refers to the i th index of the array If the heap tree has depth d number of edges on the path from the root to the farthest leaf then what is the time complexity to re fix the heap efficiently after the removal of the element O 1 O d but not O 1 O 2 d but not O d O d 2 d but not O 2 d ,Heap,81 An array X of n distinct integers is interpreted as a complete binary tree The index of the first element of the array is 0 If only the root node does not satisfy the heap property the algorithm to convert the complete binary tree into a heap has the best asymptotic time complexity of O n O log n O n log n O n log log n ,Heap,81 An array of integers of size n can be converted into a heap by adjusting the heaps rooted at each internal node of the complete binary tree starting at the node left lfloor n 1 2 right rfloor and doing this adjustment up to the root node root node is at index 0 in the order left lfloor n 1 2 right rfloor left lfloor n 3 2 right rfloor 0 The time required to construct a heap in this manner is O log n O n O n log log n O n log n ,Heap,81 A priority queue is implemented as a Max Heap Initially it has 5 elements The level order traversal of the heap is 10 8 5 3 2 Two new elements 1 and 7 are inserted into the heap in that order The level order traversal of the heap after the insertion of the elements is 10 8 7 5 3 2 1 10 8 7 2 3 1 5 10 8 7 1 2 3 5 10 8 7 3 2 1 5 ,Heap,81 In binary tree a full node is defined to be a node with 2 children Use induction on the height of the binary tree to prove that the number of full nodes plus one is equal to the number of leaves Draw the min heap that results from insertion of the following elements in order into an initially empty min heap 7 6 5 4 3 2 1 Show the result after the deletion of the root of this heap ,Heap,81 The language left a mb nc m n mid m n geq1 right is regular context free but not regular context sensitive but not context free type 0 but not context sensitive ,Identify Class Language,82 The language L left 0 i21 i mid i geq 0 right over the alphabet left 0 1 2 right is not recursive is recursive and is a deterministic CFL is a regular language is not a deterministic CFL but a CFL ,Identify Class Language,82 The language accepted by a Pushdown Automaton in which the stack is limited to 10 items is best described as Context free Regular Deterministic Context free Recursive ,Identify Class Language,82 The language 0 n 1 n 2 n mid 1 leq n leq 10 6 is regular context free but not regular context free but its complement is not context free not context free ,Identify Class Language,82 Show that the Turing machines which have a read only input tape and constant size work tape recognize precisely the class of regular languages ,Identify Class Language,82 Multiple choices may be correct If L1 is context free language and L2 is a regular language which of the following is are false L1 L2 is not context free L1 cap L2 is context free sim L1 is context free sim L2 is regular ,Identify Class Language,82 Let L_1 be a regular language L_2 be a deterministic context free language and L_3 a recursively enumerable but not recursive language Which one of the following statements is false L_1 cap L_2 is a deterministic CFL L_3 cap L_1 is recursive L_1 cup L_2 is context free L_1 cap L_2 cap L_3 is recursively enumerable ,Identify Class Language,82 Let L denote the languages generated by the grammar S o 0S0 mid 00 Which of the following is TRUE L 0 L is regular but not 0 L is context free but not regular L is not context free ,Identify Class Language,82 Let L be a regular language and M be a context free language both over the alphabet u03a3 Let L c and M c denote the complements of L and M respectively Which of the following statements about the language L c cup M c is TRUE It is necessarily regular but not necessarily context free It is necessarily context free It is necessarily non regular None of the above ,Identify Class Language,82 Let L L_1 cap L_2 where L_1 and L_2 are languages as defined below L_1 left a m b mca nb n mid m n geq 0 right L_2 left a i b j c k mid i j k geq 0 right Then L is Not recursive Regular Context free but not regular Recursively enumerable but not context free ,Identify Class Language,82 For s in 0 1 let d s denote the decimal value of s e g d 101 5 Let L left s in 0 1 mid d s ext mod 5 2 ext and d s ext mod 7 eq 4 right Which one of the following statements is true L is recursively enumerable but not recursive L is recursive but not context free L is context free but not regular L is regular ,Identify Class Language,82 Consider the languages L_1 left a nb nc m mid n m gt 0 right and L_2 left a nb mc m mid n m gt 0 right Which one of the following statements is FALSE L_1 cap L_2 is a context free language L_1 cup L_2 is a context free language L_1 ext and L_2 are context free languages L_1 cap L_2 is a context sensitive language ,Identify Class Language,82 Consider the following languages L_1 a i b j c k mid i j k geq 1 L_2 a i b j mid j 2i i geq 0 Which of the following is true L_1 is not a CFL but L_2 is L_1 cap L_2 varnothing and L_1 is non regular L_1 cup L_2 is not a CFL but L_2 is There is a 4 state PDA that accepts L_1 but there is no DPDA that accepts L_2 ,Identify Class Language,82 a Given a set S left x mid ext there is an x block of 5 s in the decimal expansion of pi right Note x block is a maximal block of x successive 5 s Which of the following statements is true with respect to S No reason to be given for the answer S is regular S is recursively enumerable S is not recursively enumerable S is recursive b Given that a language L_1 is regular and and that the language L_1 cup L_2 is regular is the language L_2 always regular Prove your answer ,Identify Class Language,82 The following bit pattern represents a floating point number in IEEE 754 single precision format 1 10000011 101000000000000000000000 The value of the number in decimal form is 10 13 26 None of the above ,Ieee Representation,83 The decimal value 0 5 in IEEE single precision floating point representation has fraction bits of 000 dots 000 and exponent value of 0 fraction bits of 000 dots 000 and exponent value of u22121 fraction bits of 100 dots 000 and exponent value of 0 no exact representation ,Ieee Representation,83 In the IEEE floating point representation the hexadecimal value 0 ext x 00000000 corresponds to The normalized value 2 127 The normalized value 2 126 The normalized value 0 The special value 0 ,Ieee Representation,83 There are five records in a database Name Age Occupation Category Rama 27 CON A Abdul 22 ENG A Jennifer 28 DOC B Maya 32 SER D Dev 24 MUS C There is an index file associated with this and it contains the values 1 3 2 5 and 4 Which one of the fields is the index built from Age Name Occupation Category ,Indexing,84 In a B Tree if the search key value is 8 bytes long the block size is 512 bytes and the pointer size is 2 B then the maximum order of the B Tree is ____ ,Indexing,84 Consider a relational table r with sufficient number of records having attributes A_1 A_2 dots A_n and let 1 leq p leq n Two queries Q1 and Q2 are given below Q1 pi_ A_1 dots A_p left sigma_ A_p c left r right right where c is a constant Q2 pi_ A_1 dots A_p left sigma_ c_1 leq A_p leq c_2 left r right right where c_1 and c_2 are constants The database can be configured to do ordered indexing on A_p or hashing on A_p Which of the following statements is TRUE Ordered indexing will always outperform hashing for both queries Hashing will always outperform ordered indexing for both queries Hashing will outperform ordered indexing on Q1 but not on Q2 Hashing will outperform ordered indexing on Q2 but not on Q1 ,Indexing,84 Consider a file of 16384 records Each record is 32 bytes long and its key field is of size 6 bytes The file is ordered on a non key field and the file organization is unspanned The file is stored in a file system with block size 1024 bytes and the size of a block pointer is 10 bytes If the secondary index is built on the key field of the file and a multi level index scheme is used to store the secondary index the number of first level and second level blocks in the multi level index are respectively 8 and 0 128 and 6 256 and 4 512 and 5 ,Indexing,84 An index is clustered if it is on a set of fields that form a candidate key it is on a set of fields that include the primary key the data records of the file are organized in the same order as the data entries of the index the data records of the file are organized not in the same order as the data entries of the index ,Indexing,84 An ext ISAM indexed sequential file consists of records of size 64 bytes each including key field of size 14 bytes An address of a disk block takes 2 bytes If the disk block size is 512 bytes and there are 16 K records compute the size of the data and index areas in terms of number blocks How many levels of ext tree do you have for the index ,Indexing,84 A file is organized so that the ordering of the data records is the same as or close to the ordering of data entries in some index Than that index is called Dense Sparse Clustered Unclustered ,Indexing,84 A clustering index is defined on the fields which are of type non key and ordering non key and non ordering key and ordering key and non ordering ,Indexing,84 Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG ,Inference,85 The value of the integral given below is int limits_0 pi x 2 cos x dx 2 pi pi pi 2 pi ,Integration,86 Let S sum_ i 3 100 i log_ 2 i and T int_ 2 100 x log_ 2 x dx Which of the following statements is true S gt T S T S lt T and 2S gt T 2S u2264 T ,Integration,86 If int limits_0 2 pi x sin x dx k pi then the value of k is equal to ______ ,Integration,86 Given i sqrt 1 what will be the evaluation of the definite integral int limits_0 pi 2 dfrac cos x i sin x cos x i sin x dx A 0 B 2 C i D i ,Integration,86 Compute the value of large int_ frac 1 pi frac 2 pi frac cos 1 x x 2 dx ,Integration,86 int pi 4 _0 1 an x 1 an x dx 0 1 ln 2 1 2 ln 2 ,Integration,86 If for non zero x af x bf frac 1 x frac 1 x 25 where a a eq b ext then int_1 2 f x dx is frac 1 a 2 b 2 begin bmatrix a ln 2 25 frac 47b 2 end bmatrix frac 1 a 2 b 2 begin bmatrix a 2 ln 2 25 frac 47b 2 end bmatrix frac 1 a 2 b 2 begin bmatrix a 2 ln 2 25 frac 47b 2 end bmatrix frac 1 a 2 b 2 begin bmatrix a ln 2 25 frac 47b 2 end bmatrix ,Integration,86 I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above ,Inter Process Communication,87 Consider the relations r1 P Q R and r2 R S T with primary keys P and R respectively The relation r1 contains 2000 tuples and r2 contains 2500 tuples The maximum size of the join r1 u22c8 r2 is 2000 2500 4500 5000 ,Joins,88 Consider the following relation schemas b Schema b name b city assets a Schema a num b name bal d Schema c name a number Let branch account and depositor be respectively instances of the above schemas Assume that account and depositor relations are much bigger than the branch relation Consider the following query u041fc name u03c3b city Agra u22c0 bal lt 0 branch u22c8 account u22c8 depositor Which one of the following queries is the most efficient version of the above query u041fc name u03c3bal lt 0 u03c3b city Agra branch u22c8 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3bal lt 0 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3b city Agra u22c0 bal lt 0 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3b city Agra u22c0 bal lt 0 account u22c8 depositor ,Joins,88 Consider the following relation schema pertaining to a students database Students rollno name address Enroll rollno courseno coursename where the primary keys are shown underlined The number of tuples in the student and Enroll tables are 120 and 8 respectively What are the maximum and minimum number of tuples that can be present in Student Enroll where u2018 u2019 denotes natural join 8 8 120 8 960 8 960 120 ,Joins,88 Consider a join relation algebra between relations r R and s S using the nested loop method There are 3 buffers each of size equal to disk block size out of which one buffer is reserved for intermediate results Assuming size r R lt size s S the join will have fewer number of disk block accesses if relation r R is in the outer loop relation s S is in the outer loop join selection factor between r R and s S is more than 0 5 join selection factor between r R and s S is less than 0 5 ,Joins,88 A database table T_1 has 2000 records and occupies 80 disk blocks Another table T_2 has 400 records and occupies 20 disk blocks These two tables have to be joined as per a specified join condition that needs to be evaluated for every pair of records from these two tables The memory buffer space available can hold exactly one block of records for T_1 and one block of records for T_2 simultaneously at any point in time No index is available on either table If Nested loop join algorithm is employed to perform the join with the most appropriate choice of table to be used in outer loop the number of block accesses required for reading the data are 800000 40080 32020 100 ,Joins,88 A database table T_1 has 2000 records and occupies 80 disk blocks Another table T_2 has 400 records and occupies 20 disk blocks These two tables have to be joined as per a specified join condition that needs to be evaluated for every pair of records from these two tables The memory buffer space available can hold exactly one block of records for T_1 and one block of records for T_2 simultaneously at any point in time No index is available on either table If instead of Nested loop join Block nested loop join is used again with the most appropriate choice of table in the outer loop the reduction in number of block accesses required for reading the data will be 0 30400 38400 798400 ,Joins,88 Consider the following relations A B and C A Id Name Age 12 Arun 60 15 Shreya 24 99 Rohit 11 B Id Name Age 15 Shreya 24 25 Hari 40 98 Rohit 20 99 Rohit 11 C Id Phone Area 10 2200 02 99 2100 01 How many tuples does the result of the following relational algebra expression contain Assume that the schema of A cup B is the same as that of A A cup B bowtie _ A Id gt 40 vee C Id lt 15 C 7 4 5 9 ,Joins,88 Which functions does NOT implement the Karnaugh map given below w x y xy yw w x bar w y bar x y None of the above ,K Map,89 What is the minimal form of the Karnaugh map shown below Assume that X denotes a don u2019t care term A bar b bar d B bar b bar d bar b bar c C bar b bar d a bar b bar c d D bar b bar d bar b bar c bar c bar d ,K Map,89 What is the equivalent Boolean expression in product of sums form for the Karnaugh map given in Fig B overline D overline B D B overline C D overline B C overline D B D overline B overline D B overline D overline B D ,K Map,89 The literal count of a Boolean expression is the sum of the number of times each literal appears in the expression For example the literal count of left xy xz right is 4 What are the minimum possible literal counts of the product of sum and sum of product representations respectively of the function given by the following Karnaugh map Here X denotes don t care 11 9 9 13 9 10 11 11 ,K Map,89 The function represented by the Karnaugh map is given below is A B AB BC CA overline B oplus C A BC ,K Map,89 The Boolean function in sum of products form where K map is given below figure is _______ ,K Map,89 The boolean function for a combinational circuit with four inputs is represented by the following Karnaugh map Which of the product terms given below is an essential prime implicant of the function QRS PQS PQ S Q S ,K Map,89 Minimum sum of product expression for f w x y z shown in Karnaugh map below xz y z xz zx x y zx None of the above ,K Map,89 In the Karnaugh map shown below X denotes a don u2019t care term What is the minimal form of the function represented by the Karnaugh map bar b bar d bar a bar d bar a bar b bar b bar d bar a b bar d bar b bar d bar a b bar d bar a bar b bar b bar d bar a bar d ,K Map,89 Given the following karnaugh map which one of the following represents the minimal Sum Of Products of the map XY Y Z WX Y XY XZ W X Y Z XY XZ Y ,K Map,89 Consider the Karnaugh map given below where X represents don t care and blank represents 0 Assume for all inputs left a b c d right the respective complements left bar a bar b bar c bar d right are also available The above logic is implemented using 2 input NOR gates only The minimum number of gates required is ____________ ,K Map,89 Consider the following expression a bar d bar a bar c b bar cd Which of the following Karnaugh Maps correctly represents the expression c d c d cd cd a b X X a b X X ab X X X ab X X c d c d cd cd a b X X a b X ab X X X ab X X X c d c d cd cd a b X X a b X X X ab X X X ab X X c d c d cd cd a b X X a b X X X ab X X X ab X X X ,K Map,89 Consider the following expression a bar d bar a bar c b bar cd Which of the following expressions does not correspond to the Karnaugh Map obtained for the given expression bar c bar d a bar d ab bar c bar a bar cd bar a bar c bar c bar d a bar d ab bar cd bar a bar c a bar d ab bar c bar cd bar b bar c bar d ac bar d bar a bar c ab bar c ,K Map,89 A Boolean function f is to be realized only by NOR gates Its K map is given below The realization is ,K Map,89 The following is the Hasse diagram of the poset a b c d e u227a The poset is not a lattice a lattice but not a distributive lattice a distributive lattice but not a Boolean algebra a Boolean algebra ,Lattice,90 In the lattice defined by the Hasse diagram given in following figure how many complements does the element u2018e u2019 have 2 3 0 1 ,Lattice,90 Consider the set X a b c d e under partial ordering R a a a b a c a d a e b b b c b e c c c e d d d e e e The Hasse diagram of the partial order X R is shown below The minimum number of ordered pairs that need to be added to R to make X R a lattice is ______,Lattice,90 Consider the following Hasse diagrams Which all of the above represent a lattice i and iv only ii and iii only iii only i ii and iv only ,Lattice,90 Suppose L left p q r s t right is a lattice represented by the following Hasse diagram For any x y isin L not necessarily distinct x or y and x and y are join and meet of x y respectively Let L 3 left left x y z right x y z isin L right be the set of all ordered triplets of the elements of L Let p_ r be the probability that an element left x y z right isin L 3 chosen equiprobably satisfies x or y and z x or y and x or z Then p_r 0 p_r 1 0 lt p_r le frac 1 5 frac 1 5 lt p_r lt 1 ,Lattice,90 S 1 2 2 1 is binary relation on set A 1 2 3 Is it irreflexive Add the minimum number of ordered pairs to S to make it an equivalence relation Give the modified S Let S a b and let square S be the powerset of S Consider the binary relation subseteq set inclusion on square S Draw the Hasse diagram corresponding to the lattice square S subseteq ,Lattice,90 Let wedge vee denote the meet and join operations of lattice A lattice is called distributive if for all x y z x wedge left y vee z right left x wedge y right vee left x wedge z right It is called complete if meet and join exist for every subset It is called modular if for all x y z z leq x Rightarrow x wedge left y vee z right left x wedge y right vee z The positive integers under divisibility ordering i e p leq q if p divides q forms a Complete lattice Modular but not distributive lattice Distributive lattice Lattice but not a complete lattice Under the give ordering positive integers do not form a lattice ,Lattice,90 What is the value of lim_ n o infty left 1 frac 1 n right 2n 0 e 2 e 1 2 1 ,Limits,91 The value of lim_ x rightarrow infty 1 x 2 e x is u00a0 0 frac 1 2 1 infty ,Limits,91 The value of lim_ x rightarrow 1 frac x 7 2x 5 1 x 3 3x 2 2 is 0 is 1 is 1 does not exist ,Limits,91 lim_ x rightarrow infty x frac 1 x is infty 0 1 Not defined ,Limits,91 lim_ x o infty frac x sin x x cos x equals 1 1 infty infty ,Limits,91 lim _ x rightarrow 4 frac sin x 4 x 4 ____ ,Limits,91 The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only,Line Graph,92 The following C function takes a singly linked list of integers as a parameter and rearranges the elements of the list The list is represented as pointer to a structure The function is called with the list containing the integers 1 2 3 4 5 6 7 in the given order What will be the contents of the list after the function completes execution struct node int value struct node next void rearrange struct node list struct node p q int temp if list list gt next return p list q list gt next while q temp p gt value p gt value q gt value q gt value temp p q gt next q p p gt next 0 1 2 3 4 5 6 7 2 1 4 3 6 5 7 1 3 2 5 4 7 6 2 3 4 5 6 7 1 ,Linked Lists,93 The following C function takes a singly linked list as input argument It modifies the list by moving the last element to the front of the list and returns the modified list Some part of the code is left blank ypedef struct node int value struct node next node Node move_to front Node head Node p q if head NULL head gt next NULL return head q NULL p head while p gt next NULL q p p p gt next _______________ return head Choose the correct alternative to replace the blank line q NULL p rightarrow next head head p q rightarrow next NULL head p p rightarrow next head head p p rightarrow next q q rightarrow next NULL q rightarrow next NULL p rightarrow next head head p ,Linked Lists,93 The following C function takes a single linked list of integers as a parameter and rearranges the elements of the list The function is called with the list containing the integers 1 2 3 4 5 6 7 in the given order What will be the contents of the list after function completes execution struct node int value struct node next void rearrange struct node list struct node p q int temp if list list gt next return p list q list gt next while q temp p gt value p gt value q gt value q gt value temp p q gt next q p p gt next 0 1 2 3 4 5 6 7 2 1 4 3 6 5 7 1 3 2 5 4 7 6 2 3 4 5 6 7 1 ,Linked Lists,93 The concatenation of two lists is to be performed on O 1 time Which of the following implementations of a list should be used Singly linked list Doubly linked list Circular doubly linked list Array implementation of list ,Linked Lists,93 Suppose each set is represented as a linked list with elements in arbitrary order Which of the operations among ext union intersection membership cardinality will be the slowest ext union only ext intersection membership ext membership cardinality ext union intersection ,Linked Lists,93 Linked lists are not suitable data structures for which one of the following problems Insertion sort Binary search Radix sort Polynomial manipulation ,Linked Lists,93 Let P be a singly linked list Let Q be the pointer to an intermediate node x in the list What is the worst case time complexity of the best known algorithm to delete the node x from the list O n O log 2 n O log n O 1 ,Linked Lists,93 In the worst case the number of comparisons needed to search a single linked list of length n for a given element is log n frac n 2 log_2 n 1 n ,Linked Lists,93 In a circular linked list oraganisation insertion of a record involves modification of One pointer Two pointers Multiple pointers No pointer ,Linked Lists,93 Consider the function f defined below struct item int data struct item next int f struct item p return p NULL p gt next NULL p gt data lt p gt next gt data amp amp f p gt next For a given linked list p the function f returns 1 if and only if the list is empty or has exactly one element the elements in the list are sorted in non decreasing order of data value the elements in the list are sorted in non increasing order of data value not all elements in the list have the same data value ,Linked Lists,93 Consider the following piece of C code fragment that removes duplicates from an ordered list of integers Node remove duplicates Node head int j Node t1 t2 j 0 t1 head if t1 NULL t2 t1 gt next else return head j 1 if t2 NULL return head while t2 NULL if t1 val t2 val gt S1 j t1 gt next t2 t1 t2 gt S2 t2 t2 gt next t1 gt next NULL return head Assume the list contains n elements n geq 2 in the following questions How many times is the comparison in statement S1 made What is the minimum and the maximum number of times statements marked S2 get executed What is the significance of the value in the integer pointed to by j when the function completes ,Linked Lists,93 A circularly linked list is used to represent a Queue A single variable p is used to access the Queue To which node should p point such that both the operations ext enQueue and ext deQueue can be performed in constant time rear node front node not possible with a single pointer node next to front ,Linked Lists,93 Let p be a pointer as shown in the figure in a single linked list What do the following assignment statements achieve q p gt next p gt next q gt next q gt next q gt next gt next p gt next gt next q ,Linked Lists,93 The Boolean function obtained by adding an inverter to each and every input of an AND gate is OR XOR NAND NOR None of the above ,Logic Gates,94 Consider the following circuit composed of XOR gates and non inverting buffers The non inverting buffers have delays delta_1 2 ns and delta_2 4 ns as shown in the figure Both XOR gates and all wires have zero delay Assume that all gate inputs outputs and wires are stable at logic level 0 at time 0 If the following waveform is applied at input A how many transition s change of logic levels occur s at B during the interval from 0 to 10 ns 1 2 3 4 ,Logic Gates,94 Choose the correct alternatives more than one may be correct and write the corresponding letters only All digital circuits can be realized using only Ex OR gates Multiplexers Half adders OR gates ,Logic Gates,94 Express the function f x y z xy yz with only one complement operation and one or more AND OR operations Draw the logic circuit implementing the expression obtained using a single NOT gate and one or more AND OR gates Transform the following logic circuit without expressing its switching function into an equivalent logic circuit that employs only 6 NAND gates each with 2 inputs ,Logic Gates,94 Three candidates Amar Birendra and Chanchal stand for the local election Opinion polls are conducted and show that fraction a of the voters prefer Amar to Birendra fraction b prefer Birendra to Chanchal and fraction c prefer Chanchal to Amar Which of the following is impossible a b c 0 51 0 51 0 51 a b c 0 61 0 71 0 67 a b c 0 68 0 68 0 68 a b c 0 49 0 49 0 49 None of the above ,Logical Reasoning,95 There are three boxes One contains apples another contains oranges and the last one contains both apples and oranges All three are known to be incorrectly labeled If you are permitted to open just one box and then pull out and inspect only one fruit which box would you open to determine the contents of all three boxes The box labeled u2018Apples u2019 The box labeled u2018Apples and Oranges u2019 The box labeled u2018Oranges u2019 Cannot be determined ,Logical Reasoning,95 There are eight bags of rice looking alike seven of which have equal weight and one is slightly heavier The weighing balance is of unlimited capacity Using this balance the minimum number of weighings required to identify the heavier bag is A 2 B 3 C 4 D 8,Logical Reasoning,95 The action for this problem takes place in an island of Knights and Knaves where Knights always make true statements and Knaves always make false statements and everybody is either a Knight or a Knave Two friends A and B lives in a house The census taker an outsider knocks on the door and it is opened by A The census taker says I need information about you and your friend Which if either is a Knight and which if either is a Knave We are both Knaves says A angrily and slams the door What if any thing can the census taker conclude A is a Knight and B is a Knave A is a Knave and B is a Knight Both are Knaves Both are Knights No conclusion can be drawn ,Logical Reasoning,95 Six people are seated around a circular table There are at least two men and two women There are at least three right handed persons Every woman has a left handed person to her immediate right None of the women are right handed The number of women at the table is 2 3 4 Cannot be determined ,Logical Reasoning,95 Rahul Murali Srinivas and Arul are seated around a square table Rahul is sitting to the left of Murali Srinivas is sitting to the right of Arul Which of the following pairs are seated opposite each other Rahul and Murali Srinivas and Arul u200b u200b u200b u200b u200b u200b u200bSrinvas and Murali u200b u200b u200b u200b u200b u200b u200bSrinivas and Rahul ,Logical Reasoning,95 Long ago in a planet far far away there lived three races of intelligent inhabitants the blues who always tell the truth the whites who always lie and the pinks who when asked a series of questions start with a lie and then tell the truth and lie alternately To three creatures chosen from the planet and seated facing each other at A B and C see figure the following three questions are put i What race is your left hand neighbour ii What race is your right hand neighbour iii What race are you Here are their answers A i White ii Pink iii Blue B i Pink ii Pink iii Blue C i White ii Blue iii Blue What is the actual race of each of the three creatures A is Pink B is White C is Blue A is Blue B is Pink C is White A is Pink B is Blue C is Pink A is White B is Pink C is Blue Cannot be determined from the above data ,Logical Reasoning,95 In a room there are only two types of people namely Type 1 and Type 2 Type 1 people always tell the truth and Type 2 people always lie You give a fair coin to a person in that room without knowing which type he is from and tell him to toss it and hide the result from you till you ask for it Upon asking the person replies the following The result of the toss is head if and only if I am telling the truth Which of the following options is correct The result is head The result is tail If the person is of Type 2 then the result is tail If the person is of Type 1 then the result is tail ,Logical Reasoning,95 If either wages or prices are raised there will be inflation If there is inflation then either the government must regulate it or the people will suffer If the people suffer the government will be unpopular Government will not be unpopular Which of the following can be validly concluded from the above statements People will not suffer If the inflation is not regulated then wages are not raised Prices are not raised If the inflation is not regulated then the prices are not raised Wages are not raised ,Logical Reasoning,95 Consider the following two statements S1 If a candidate is known to be corrupt then he will not be elected S2 If a candidate is kind he will be elected Which one of the following statements follows from S1 and S2 as per sound inference rules of logic If a person is known to be corrupt he is kind If a person is not known to be corrupt he is not kind If a person is kind he is not known to be corrupt If a person is not kind he is not known to be corrupt ,Logical Reasoning,95 Consider the following logical inferences I_ 1 If it rains then the cricket match will not be played The cricket match was played Inference There was no rain I_ 2 If it rains then the cricket match will not be played It did not rain Inference The cricket match was played Which of the following is TRUE A Both I_ 1 and I_ 2 are correct inferences B I_ 1 is correct but I_ 2 is not a correct inference C I_ 1 is not correct but I_ 2 is a correct inference D Both I_ 1 and I_ 2 are not correct inferences,Logical Reasoning,95 All that glitters is gold No gold is silver Claims 1 No silver glitters 2 Some gold glitters Then which of the following is TRUE Only claim 1 follows Only claim 2 follows Either claim 1 or claim 2 follows but not both Neither claim 1 nor claim 2 follows Both claim 1 and claim 2 follow ,Logical Reasoning,95 If relftaga means carefree otaga means careful and fertaga means careless which of the following could mean aftercare zentaga tagafer tagazen relffer ,Logical Reasoning,95 Consider the following two statements There are infinitely many interesting whole numbers There are finitely many uninteresting whole numbers Which of the following is true Statements 1 and 2 are equivalent Statement 1 implies statement 2 Statement 2 implies statement 1 None of the above ,Logical Reasoning,95 Consider the following statements relating to the level of poker play of four players P Q R and S P always beats Q R always beats S S loses to P only sometimes R always loses to Q Which of the following can be logically inferred from the above statements P is likely to beat all the three other players S is the absolute worst player in the set i only ii only i and ii only neither i nor ii ,Logical Reasoning,95 The following function computes X Y for positive integers X and Y int exp int X int Y int res 1 a X b Y while b 0 if b 2 0 a a a b b 2 else res res a b b 1 return res Which one of the following conditions is TRUE before every iteration of the loop X Y a b res a Y res X b X Y res a b X Y res a b ,Loop Invariants,96 Consider the program where a b are integers with b gt 0 x a y b z 0 while y gt 0 do if odd x then z z x y y 1 else y y 2 x 2 x fi Invariant of the loop is a condition which is true before and after every iteration of the loop In the above program the loop invariant is given by 0 leq y and z x y a b Which of the following is true of the program The program will not terminate for some values of a b The program will terminate with z 2 b The program will terminate with z a b The program will not terminate for some values of a b but when it does terminate the condition z a b will hold The program will terminate with z a b ,Loop Invariants,96 Consider the following pseudo code where x and y are positive integers begin q 0 r x while r u2265 y do begin r r y q q 1 end end The post condition that needs to be satisfied after the program terminates is r qx y wedge r lt y x qy r wedge r lt y y qx r wedge 0 lt r lt y q 1 lt r y wedge y gt 0 ,Loop Invariants,96 Consider the following program fragment for reversing the digits in a given integer to obtain a new integer Let n d_1 d_2 ldots d_m int n rev rev 0 while n gt 0 rev rev 10 n 10 n n 10 The loop invariant condition at the end of the i th iteration is n d_1 d_2 ldots d_ m i qquad mathbf and qquad ext rev d_m d_ m 1 ldots d_ m i 1 n d_ m i 1 ldots d_ m 1 d_m qquad mathbf or qquad ext rev d_ m i ldots d_2 d_1 n eq ext rev n d_1 d_2 ldots d_m qquad mathbf or qquad ext rev d_m ldots d_2 d_1 ,Loop Invariants,96 Consider the following program for summing the entries of the array b array 0 N 1 of integers where N is a positive integer The symbol lt gt denotes not equal to var i s integer Program i 0 s 0 while i lt gt N do s s b i i i 1 od Which of the following gives the invariant that holds at the beginning of each loop that is each time the program arrives at point s sum limits N _ j 0 b j amp 0 leq i leq N s sum limits i 1 _ j 0 b j amp 0 leq i lt N s sum limits i _ j 0 b j amp 0 lt i leq N s sum limits N _ j 1 b j amp 0 leq i lt N s sum limits i 1 _ j 0 b j amp 0 leq i leq N ,Loop Invariants,96 Consider the C program fragment below which is meant to divide x by y using repeated subtractions The variables x y q and r are all unsigned int while r gt y r r y q q 1 Which of the following conditions on the variables x y q and r before the execution of the fragment will ensure that the loop terminated in a state satisfying the condition x y q r q r amp amp r 0 x gt 0 amp amp r x amp amp y gt 0 q 0 amp amp r x amp amp y gt 0 q 0 amp amp y gt 0 ,Loop Invariants,96 Consider the following PASCAL program segment if i mod 2 0 then while i gt 0 do begin i i div 2 if i mod 2 lt gt 0 then i i 1 else i i ndash 2 end An appropriate loop invariant for the while loop is ________ ,Loop Invariants,96 The number of different n imes n symmetric matrices with each element being either 0 or 1 is Note ext power left 2 X right is same as 2 X ext power left 2 n right ext power left 2 n 2 right ext power left 2 frac left n 2 n right 2 right ext power left 2 frac left n 2 n right 2 right ,Matrices,97 The matrices begin bmatrix cos heta amp amp sin heta sin heta amp amp cos heta end bmatrix and begin bmatrix a amp amp 0 0 amp amp b end bmatrix commute under multiplication if a b ext or heta n pi n an integer always never if a cos heta b sin heta ,Matrices,97 Let A be an n u00d7 n matrix of the following form What is the value of the determinant of A left frac 5 sqrt3 2 right n 1 left frac 5 sqrt3 7 2 sqrt 3 right left frac 5 sqrt3 2 right n 1 left frac 5 sqrt3 7 2 sqrt 3 right left frac 7 sqrt5 2 right n 1 left frac 7 sqrt5 3 2 sqrt 5 right left frac 7 sqrt5 2 right n 1 left frac 7 sqrt5 3 2 sqrt 5 right left frac 3 sqrt7 2 right n 1 left frac 3 sqrt7 5 2 sqrt 7 right left frac 3 sqrt7 2 right n 1 left frac 3 sqrt7 5 2 sqrt 7 right left frac 3 sqrt5 2 right n 1 left frac 3 sqrt5 7 2 sqrt 5 right left frac 3 sqrt5 2 right n 1 left frac 3 sqrt5 7 2 sqrt 5 right ,Matrices,97 Let A B C D be n imes n matrices each with non zero determinant If ABCD I then B 1 is D 1 C 1 A 1 CDA ADC Does not necessarily exist ,Matrices,97 Let A and B be real symmetric matrices of size n imes n Then which one of the following is true AA I A A 1 AB BA AB BA ,Matrices,97 Let a a_ ij be an n rowed square matrix and I_ 12 be the matrix obtained by interchanging the first and second rows of the n rowed Identify matrix Then AI_ 12 is such that its first row is the same as its second row row is the same as the second row of A column is the same as the second column of A row is all zero ,Matrices,97 In an M imes N matrix all non zero entries are covered in a rows and b columns Then the maximum number of non zero entries such that no two are on the same row or column is leq a b leq max a b leq min M a N b leq min a b ,Matrices,97 If A begin pmatrix 1 amp 0 amp 0 amp 1 0 amp 1 amp 0 amp 1 0 amp 0 amp i amp i 0 amp 0 amp 0 amp i end pmatrix the matrix A 4 calculated by the use of Cayley Hamilton theorem or otherwise is ____,Matrices,97 Find the inverse of the matrix begin bmatrix 1 amp 0 amp 1 1 amp 1 amp 1 0 amp 1 amp 0 end bmatrix ,Matrices,97 Consider the following statements S1 The sum of two singular n imes n matrices may be non singular S2 The sum of two n imes n non singular matrices may be singular Which one of the following statements is correct S1 and S2 both are true S1 is true S2 is false S1 is false S2 is true S1 and S2 both are false ,Matrices,97 A square matrix is singular whenever The rows are linearly independent The columns are linearly independent The row are linearly dependent None of the above ,Matrices,97 The rank of the matrix given below is begin bmatrix 1 amp 4 amp 8 amp 7 0 amp 0 amp 3 amp 0 4 amp 2 amp 3 amp 1 3 amp 12 amp 24 amp 2 end bmatrix 3 1 2 4 ,Matrices,97 The rank of the following n 1 imes n 1 matrix where a is a real number is begin bmatrix 1 amp a amp a 2 amp dots amp a n 1 amp a amp a 2 amp dots amp a n vdots amp vdots amp vdots amp amp vdots vdots amp vdots amp vdots amp amp vdots 1 amp a amp a 2 amp dots amp a n end bmatrix 1 2 n Depends on the value of a ,Matrices,97 The rank of matrix begin bmatrix 0 amp 0 amp 3 9 amp 3 amp 5 3 amp 1 amp 1 end bmatrix is 0 1 2 3 ,Matrices,97 Consider the following determinant Delta begin vmatrix 1 amp a amp bc 1 amp b amp ca 1 amp C amp ab end vmatrix Which of the following is a factor of Delta a b a b a b c abc ,Matrices,97 The number of roots of e x 0 5x 2 2 0 in the range 5 5 is 0 1 2 3 ,Maxima Minima,98 Find the minimum value of 3 4x 2x 2 Determine the number of positive integers amp le 720 which are not divisible by any of 2 3 or 5 ,Maxima Minima,98 Consider the function f x sin x in the interval x left frac pi 4 frac 7 pi 4 right The number and location s of the local minima of this function are A One at dfrac pi 2 B One at dfrac 3 pi 2 C Two at dfrac pi 2 and dfrac 3 pi 2 D Two at dfrac pi 4 and dfrac 3 pi 2 ,Maxima Minima,98 A point on a curve is said to be an extremum if it is a local minimum or a local maximum The number of distinct extrema for the curve 3x 4 16x 3 24x 2 37 is 0 1 2 3 ,Maxima Minima,98 Solve min x 2 y 2 subject to x y geq 10 2x 3y geq 20 x geq 4 y geq 4 32 50 52 100 None of the above ,Maxima Minima,98 Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB ,Memory Allocation,99 Let the page reference and the working set window be c c d b c e c e a d and 4 respectively The initial working set at time t 0 contains the pages a d e where a was referenced at time t 0 d was referenced at time t 1 and e was referenced at time t 2 Determine the total number of page faults and the average number of page frames used by computing the working set at each reference ,Memory Management,100 Let a memory have four free blocks of sizes 4k 8k 20k 2k These blocks are allocated following the best fit strategy The allocation requests are stored in a queue as shown below Request No J1 J2 J3 J4 J5 J6 J7 J8 Request Sizes 2k 14k 3k 6k 6k 10k 7k 20k Usage Time 4 10 2 8 4 1 8 6 The time at which the request for J7 will be completed will be 16 19 20 37 ,Memory Management,100 For each of the four processes P1 P2 P3 and P4 The total size in kilobytes KB and the number of segments are given below Process Total size in KB Number of segments P1 195 4 P2 254 5 P3 45 3 P4 364 8 The page size is 1 KB The size of an entry in the page table is 4 bytes The size of an entry in the segment table is 8 bytes The maximum size of a segment is 256 KB The paging method for memory management uses two level paging and its storage overhead is P The storage overhead for the segmentation method is S The storage overhead for the segmentation and paging method is T What is the relation among the overheads for the different methods of memory management in the concurrent execution of the above four processes P lt S lt T S lt P lt T S lt T lt P T lt S lt P ,Memory Management,100 Consider a main memory system that consists of 8 memory modules attached to the system bus which is one word wide When a write request is made the bus is occupied for 100 nanoseconds ns by the data address and control signals During the same 100 ns and for 500 ns thereafter the addressed memory module executes one cycle accepting and storing the data The internal operation of different memory modules may overlap in time but only one request can be on the bus at any time The maximum number of stores of one word each that can be initiated in 1 millisecond is ________,Memory Management,100 A computer installation has 1000k of main memory The jobs arrive and finish in the following sequences Job 1 requiring 200k arrives Job 2 requiring 350k arrives Job 3 requiring 300k arrives Job 1 finishes Job 4 requiring 120k arrives Job 5 requiring 150k arrives Job 6 requiring 80k arrives Draw the memory allocation table using Best Fit and First Fit algorithms Which algorithm performs better for this sequence ,Memory Management,100 A 1000 Kbyte memory is managed using variable partitions but no compaction It currently has two partitions of sizes 200 Kbytes and 260 Kbytes respectively The smallest allocation request in Kbytes that could be denied is for 151 181 231 541 ,Memory Management,100 What is the minimum number of NAND gates required to implement a 2 input EXCLUSIVE OR function without using any other logic gate 2 4 5 6 ,Min No Gates,101 What is the minimum number of gates required to implement the Boolean function AB C if we have to use only 2 input NOR gates 2 3 4 5 ,Min No Gates,101 Design a logic circuit to convert a single digit BCD number to the number modulo six as follows Do not detect illegal input Write the truth table for all bits Label the input bits I1 I2 with I1 as the least significant bit Label the output bits R1 R2 with R1 as the least significant bit Use 1 to signify truth Draw one circuit for each output bit using altogether two two input AND gates one two input OR gate and two NOT gates ,Min No Gates,101 A circuit outputs a digit in the form of 4 bits 0 is represented by 0000 1 by 0001 u2026 9 by 1001 A combinational circuit is to be designed which takes these 4 bits as input and outputs 1 if the digit geq 5 and 0 otherwise If only AND OR and NOT gates may be used what is the minimum number of gates required 2 3 4 5 ,Min No Gates,101 Given f w x y z Sigma_m 0 1 2 3 7 8 10 Sigma_d 5 6 11 15 where d represents the don t care condition in Karnaugh maps Which of the following is a minimum product of sums POS form of f w x y z f bar w bar z bar x z f bar w z x z f w z bar x z f w bar z bar x z ,Min Product Of Sums,102 Three switching functions f_1 f_2 and f_3 are expressed below as sum of minterms f_1 w x y z sum 0 1 2 3 5 12 f_2 w x y z sum 0 1 2 10 13 14 15 f_3 w x y z sum 2 4 5 8 Express the function f realised by the circuit shown in the below figure as the sum of minterms in decimal notation ,Min Sum Of Products Form,103 The switching expression corresponding to f A B C D Sigma 1 4 5 9 11 12 is BC u2019D u2019 A u2019C u2019D AB u2019D ABC u2019 ACD B u2019C u2019D ACD u2019 A u2019BC u2019 AC u2019D u2019 A u2019BD ACD u2019 BCD u2019 ,Min Sum Of Products Form,103 The simplified SOP Sum of Product from the Boolean expression P bar Q bar R P bar Q R P Q bar R is bar P Q bar R P bar Q bar R bar P Q R P Q R ,Min Sum Of Products Form,103 Let f bar w y bar x y w bar x z bar w z bar x z Express f as the minimal sum of products Write only the answer If the output line is stuck at 0 for how many input combinations will the value of f be correct ,Min Sum Of Products Form,103 Find the minimum sum of products form of the logic function f A B C D Sigma m 0 2 8 10 15 Sigma d 3 11 12 14 where m and d represent minterm and don t care term respectively ,Min Sum Of Products Form,103 Consider the following minterm expression for F F P Q R S sum 0 2 5 7 8 10 13 15 The minterms 2 7 8 and 13 are do not care terms The minimal sum of products form for F is Q bar S bar QS bar Q bar S QS bar Q bar R bar S bar QR bar S Q bar R S QRS bar P bar Q bar S bar P QS PQS P bar Q bar S ,Min Sum Of Products Form,103 Consider the following Boolean function of four variables f w x y z Sigma 1 3 4 6 9 11 12 14 The function is independent of one variables independent of two variables independent of three variables dependent on all variables ,Min Sum Of Products Form,103 Consider the following Boolean function of four variables f A B C D u03a3 2 3 6 7 8 9 10 11 12 13 The function is independent of one variable independent of two variables independent of three variable dependent on all the variables ,Min Sum Of Products Form,103 Consider the following Boolean expression for F F P Q R S PQ bar P QR bar P Q bar R S The minimal sum of products form of F is PQ QR QS P Q R S bar P bar Q bar R bar S bar P R bar R bar P S P ,Min Sum Of Products Form,103 Consider the 4 to 1 multiplexer with two select lines S_1 and S_0 given below The minimal sum of products form of the Boolean expression for the output F of the multiplexer is bar P Q Q bar R P bar Q R bar P Q bar P Q bar R PQ bar R P bar Q R bar P QR bar P Q bar R Q bar R P bar Q R PQ bar R ,Min Sum Of Products Form,103 Is the 3 variable function f Sigma 0 1 2 4 its self dual Justify your answer Give a minimal product of sum form of the b output of the following excess 3 to BCD converter ,Min Sum Of Products Form,103 Following is a state table for time finite state machine Present State Next State Output Input 0 Input 1 A B C D E F G H B 1 F 1 D 0 C 0 D 1 C 1 C 1 C 0 H 1 D 1 E 1 F 1 C 1 C 1 D 1 A 1 Find the equivalence partition on the states of the machine Give the state table for the minimal machine Use appropriate names for the equivalent states For example if states X and Y are equivalent then use XY as the name for the equivalent state in the minimal machine ,Minimal State Automata,104 A 1 input 2 output synchronous sequential circuit behaves as follows Let z_k n_k denote the number of 0 u2019s and 1 u2019s respectively in initial k bits of the input z_k n_k k The circuit outputs 00 until one of the following conditions holds z_k n_k 2 In this case the output at the k th and all subsequent clock ticks is 10 n_k z_k 2 In this case the output at the k th and all subsequent clock ticks is 01 What is the minimum number of states required in the state transition graph of the above circuit 5 6 7 8 ,Minimal State Automata,104 The value of the expression 13 99 pmod 17 in the range 0 to 16 is ________ ,Modular Arithmetic,105 The following circuit implements a two input AND gate using two 2 1 multiplexers What are the values of X1 X2 X3 X1 b X2 0 X3 a X1 b X2 1 X3 b X1 a X2 b X3 1 X1 a X2 0 X3 b ,Multiplexer,106 The circuit shown below implements a 2 input NOR gate using two 2 4 MUX control signal 1 selects the upper input What are the values of signals x y and z 1 0 B 1 0 A 0 1 B 0 1 A ,Multiplexer,106 Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of n variables What is the minimum size of the multiplexer needed 2 n line to 1 line 2 n 1 line to 1 line 2 n 1 line to 1 line 2 n 2 line to 1 line ,Multiplexer,106 Consider the two cascade 2 to 1 multiplexers as shown in the figure The minimal sum of products form of the output X is overline P overline Q PQR overline P Q QR PQ overline P overline Q R overline Q overline R PQR ,Multiplexer,106 Consider the circuit shown below The output of a 2 1 Mux is given by the function ac bc Which of the following is true f X1 X2 f X1 X2 X1X2 f X1X2 X1 X2 f X1 X2 ,Multiplexer,106 Consider a multiplexer with X and Y as data inputs and Z the as control input Z 0 selects input X and Z 1 selects input Y What are the connections required to realize the 2 variable Boolean function f T R without using any additional hardware R to X 1 to Y T to Z T to X R to Y T to Z T to X R to Y 0 to Z R to X 0 to Y T to Z ,Multiplexer,106 A priority encoder accepts three input signals A B and C and produce a two bit output X1 X0 corresponding to the highest priority active input signal Assume A has the highest priority followed by B and C has the lowest priority If none of the inputs are active the output should be 00 design the priority encoder using 4 1 multiplexers as the main components ,Multiplexer,106 A multiplexer with a 4 bit data select input is a 4 1 multiplexer 2 1 multiplexer 16 1 multiplexer 8 1 multiplexer ,Multiplexer,106 Consider the following implications relating to functional and multivalued dependencies given below which may or may not be correct If A u2192 u2192 B and A u2192 u2192 C then A u2192 BC If A u2192 B and A u2192 C then A u2192 u2192 BC If A u2192 u2192 BC and A u2192 B then A u2192 C If A u2192 BC and A u2192 B then A u2192 u2192 C Exactly how many of the above implications are valid 0 1 2 3 ,Multivalued Dependency 4nf,107 The following functional dependencies hold for relations R A B C and S B D E B o A A o C The relation R contains 200 tuples and the relation S contains 100 tuples What is the maximum number of tuples possible in the natural join R bowtie S 100 200 300 2000 ,Natural Join,108 Let r be a relation instance with schema R A B C D We define r_1 pi_ A B C R and r_2 pi_ A D r Let s r_1 r_2 where denotes natural join Given that the decomposition of r into r_1 and r_2 is lossy which one of the following is TRUE s subset r r cup s r r subset s r s s ,Natural Join,108 Consider two relations R_1 A B with the tuples 1 5 3 7 and R_2 A C 1 7 4 9 Assume that R A B C is the full natural outer join of R_1 and R_2 Consider the following tuples of the form A B C a 1 5 null b 1 null 7 c 3 null 9 d 4 7 null e 1 5 7 f 3 7 null g 4 null 9 Which one of the following statements is correct R contains a b e f g but not c d R contains all a b c d e f g R contains e f g but not a b R contains e but not f g ,Natural Join,108 Consider two hosts X and Y connected by a single direct link of rate 10 6 bits sec The distance between the two hosts is 10 000 km and the propagation speed along the link is 2 imes 10 8 m sec Host X sends a file of 50 000 bytes as one large message to host Y continuously Let the transmission and propagation delays be p milliseconds and q milliseconds respectively Then the value of p and q are p 50 and q 100 p 50 and q 400 p 100 and q 50 p 400 and q 50 ,Network Communication,109 In a data link protocol the frame delimiter flag is given by 0111 Assuming that bit stuffing is employed the transmitter sends the data sequence 01110110 as 01101011 011010110 011101100 0110101100 ,Network Flow,110 A TCP message consisting of 2100 bytes is passed to IP for delivery across two networks The first network can carry a maximum payload of 1200 bytes per frame and the second network can carry a maximum payload of 400 bytes per frame excluding network overhead Assume that IP overhead per packet is 20 bytes What is the total IP overhead in the second network for this transmission 40 bytes 80 bytes 120 bytes 160 bytes ,Network Flow,110 A link of capacity 100 Mbps is carrying traffic from a number of sources Each source generates an on off traffic stream when the source is on the rate of traffic is 10 Mbps and when the source is off the rate of traffic is zero The duty cycle which is the ratio of on time to off time is 1 2 When there is no buffer at the link the minimum number of sources that can be multiplexed on the link so that link capacity is not wasted and no data loss occurs is S1 Assuming that all sources are synchronized and that the link is provided with a large buffer the maximum number of sources that can be multiplexed so that no data loss occurs is S2 The values of S1 and S2 are respectively 10 and 30 12 and 25 5 and 33 15 and 22 ,Network Flow,110 A channel has a bit rate of 4 kbps and one way propagation delay of 20 ms The channel uses stop and wait protocol The transmission time of the acknowledgement frame is negligible To get a channel efficiency of at least 50 the minimum frame size should be 80 bytes 80 bits 160 bytes 160 bits ,Network Flow,110 Choose the best matching between ext Group 1 and ext Group 2 Group 1 Group 2 P Data link layer 1 Ensures reliable transport of data over a physical point to point link Q Network layer 2 Encodes decodes data for physical transmission R Transport layer 3 Allows end to end communication between two processes 4 Routes data from one network node to the next P 1 Q 4 R 3 P 2 Q 4 R 1 P 2 Q 3 R 1 P 1 Q 3 R 2 ,Network Layering,111 Assume that source S and destination D are connected through two intermediate routers labeled R Determine how many times each packet has to visit the network layer and the data link layer during a transmission from S to D A Network layer u2013 4 times and Data link layer u2013 4 times B Network layer u2013 4 times and Data link layer u2013 3 times C Network layer u2013 4 times and Data link layer u2013 6 times D Network layer u2013 2 times and Data link layer u2013 6 times,Network Layering,111 Match the following P SMTP 1 Application layer Q BGP 2 Transport layer R TCP 3 Data link layer S PPP 4 Network layer 5 Physical layer P 2 Q 1 R 3 S 5 P 1 Q 4 R 2 S 3 P 1 Q 4 R 2 S 5 P 2 Q 4 R 1 S 3 ,Network Protocols,112 Consider the following clauses Not inherently suitable for client authentication Not a state sensitive protocol Must be operated with more than one server Suitable for structured message organization May need two ports on the serve side for proper operation The option that has the maximum number of correct matches is IMAP i FTP ii HTTP iii DNS iv POP3 v FTP i POP3 ii SMTP iii HTTP iv IMAP v POP3 i SMTP ii DNS iii IMAP iv HTTP v SMTP i HTTP ii IMAP iii DNS iv FTP v ,Network Protocols,112 Which one of the following protocols is NOT used to resolve one form of address to another one DNS ARP DHCP RARP ,Network Protocols,112 In one of the pairs of protocols given below both the protocols can use multiple TCP connections between the same client and the server Which one is that HTTP FTP HTTP TELNET FTP SMTP HTTP SMTP ,Network Protocols,112 Using public key cryptography X adds a digital signature u03c3 to message M encrypts lt M sigma gt and sends it to Y where it is decrypted Which one of the following sequences of keys is used for the operations Encryption X u2019s private key followed by Y u2019s private key Decryption X u2019s public key followed by Y u2019s public key Encryption X u2019s private key followed by Y u2019s public key Decryption X u2019s public key followed by Y u2019s private key Encryption X u2019s public key followed by Y u2019s private key Decryption Y u2019s public key followed by X u2019s private key Encryption X u2019s private key followed by Y u2019s public key Decryption Y u2019s private key followed by X u2019s public key ,Network Security,113 The total number of keys required for a set of n individuals to be able to communicate with each other using secret key and public key cryptosystems respectively are n n 1 and 2n 2n and dfrac n n 1 2 dfrac n n 1 2 and 2n dfrac n n 1 2 and n ,Network Security,113 Suppose that two parties A and B wish to setup a common secret key D H key between themselves using the Diffie Hellman key exchange technique They agree on 7 as the modulus and 3 as the primitive root Party A chooses 2 and party B chooses 5 as their respective secrets Their D H key is 3 4 5 6 ,Network Security,113 Suppose that everyone in a group on N people wants to communicate secretly withhe ext N 1 others using symmetric Key cryptographic system The communication between any two person should not be decodable by the others in the group The numbers of keys required in the system as a whole to satisfyhe confidentiality requirement is 2N N N 1 dfrac N N 1 2 N 1 2 ,Network Security,113 In the RSA public key cryptosystem the private and public keys are e n and d n respectively where n p imes q and p and q are large primes Besides n is public and p and q are private Let M be an integer such that 0 lt M lt n and phi n p 1 q 1 Now consider the following equations M u2019 M e ext mod n M M u2019 d ext mod n ed equiv 1 ext mod n ed equiv 1 ext mod phi n M u2019 M e ext mod phi n M M u2019 d ext mod phi n Which of the above equations correctly represents RSA cryptosystem I and II I and III II and IV III and IV ,Network Security,113 Consider the following two statements A hash function these are often used for computing digital signatures is an injective function A encryption technique such as DES performs a permutation on the elements of its input alphabet Which one of the following options is valid for the above two statements Both are false Statement i is true and the other is false Statement ii is true and the other is false Both are true ,Network Security,113 Consider malware programs Which of the following is true A worm is a parasite A virus cannot affect a linux operating system A trojan can be in the payload of only a worm A worm and virus are self replicating programs There is no difference between a virus and a worm ,Network Security,113 Consider a parity check code with three data bits and four parity check bits Three of the Code Words are 0101011 1001101 and 1110001 Which of the following are also code words 0010111 0110110 1011010 0111010 I and III I II and III II and IV I II III and IV ,Network Security,113 An IP machine Q has a path to another IP machine H via three IP routers R1 R2 and R3 Q R1 R2 R3 H H acts as an HTTP server and Q connects to H via HTTP and downloads a file Session layer encryption is used with DES as the shared key encryption protocol Consider the following four pieces of information I1 The URL of the file downloaded by Q I2 The TCP port numbers at Q and H I3 The IP addresses of Q and H I4 The link layer addresses of Q and H Which of I1 I2 I3 and I4 can an intruder learn through sniffing at R2 alone Only I1 and I2 Only I1 Only I2 and I3 Only I3 and I4 ,Network Security,113 A sender is employing public key cryptography to send a secret message to a receiver Which one of the following statements is TRUE Sender encrypts using receiver s public key Sender encrypts using his own public key Receiver decrypts using sender s public key Receiver decrypts using his own public key ,Network Security,113 A firewall is to be configured to allow hosts in a private network to freely open TCP connections and send packets on open connections However it will only allow external hosts to send packets on existing open TCP connections or connections that are being opened by internal hosts but not allow them to open TCP connections to hosts in the private network To achieve this the minimum capability of the firewall should be that of A combinational circuit A finite automaton A pushdown automaton with one stack A pushdown automaton with two stacks ,Network Security,113 Consider that B wants to send a message m that is digitally signed to A Let the pair of private and public keys for A and B be denoted by K_ x and K_ x for x A B respectively Let K_ x m represent the operation of encrypting m with a key K_ x and H m represent the message digest Which one of the following indicates the CORRECT way of sending the message m along with the digital signature to A left m K_ B H m right left m K_ B H m right left m K_ A H m right left m K_ A m right ,Network Security,113 Two hosts are connected via a packet switch with 10 7 bits per second links Each link has a propagation delay of 20 microseconds The switch begins forwarding a packet 35 microseconds after it receives the same If 10000 bits of data are to be transmitted between the two hosts using a packet size of 5000 bits the time elapsed between the transmission of the first bit of data and the reception of the last bit of the data in microseconds is ______ ,Network Switching,114 In a packet switching network packets are routed from source to destination along a single path having two intermediate nodes If the message size is 24 bytes and each packet contains a header of 3 bytes then the optimum packet size is 4 6 7 9 ,Network Switching,114 Consider the store and forward packet switched network given below Assume that the bandwidth of each link is 10 6 bytes sec A user on host A sends a file of size 10 3 bytes to host B through routers R1 and R2 in three different ways In the first case a single packet containing the complete file is transmitted from A to B In the second case the file is split into 10 equal parts and these packets are transmitted from A to B In the third case the file is split into 20 equal parts and these packets are sent from A to B Each packet contains 100 bytes of header information along with the user data Consider only transmission time and ignore processing queuing and propagation delays Also assume that there are no errors during transmission Let T1 T2 and T3 be the times taken to transmit the file in the first second and third case respectively Which one of the following is CORRECT T lt T2 lt T3 T1 gt T2 gt T3 T2 T3 T3 lt T1 T1 T3 T3 gt T2 ,Network Switching,114 X is a 30 digit number starting with the digit 4 followed by the digit 7 Then the number X 3 will have 90 digits 91 digits 92 digits 93 digits ,No Of Digits,115 Regarding the power of recognition of languages which of the following statements is false The non deterministic finite state automata are equivalent to deterministic finite state automata Non deterministic Push down automata are equivalent to deterministic Push down automata Non deterministic Turing machines are equivalent to deterministic Push down automata Non deterministic Turing machines are equivalent to deterministic Turing machines Multi tape Turing machines are available are equivalent to Single tape Turing machines ,Non Determinism,116 Let N_f and N_p denote the classes of languages accepted by non deterministic finite automata and non deterministic push down automata respectively Let D_f and D_p denote the classes of languages accepted by deterministic finite automata and deterministic push down automata respectively Which one of the following is TRUE D_f subset N_f ext and D_p subset N_p D_f subset N_f ext and D_p N_p D_f N_f ext and D_p N_p D_f N_f ext and D_p subset N_p ,Non Determinism,116 02 Choose the correct alternatives more than one may be correct and write the corresponding letters only In which of the cases stated below is the following statement true For every non deterministic machine M_ 1 there exists an equivalent deterministic machine M_ 2 recognizing the same language M_ 1 is non deterministic finite automaton M_ 1 is non deterministic PDA M_ 1 is a non deteministic Turing machine For no machines M_ 1 and M_2 the above statement true ,Non Determinism,116 Let X be a random variable following normal distribution with mean 1 and variance 4 Let Y be another normal variable with mean 1 and variance unknown If P X u2264 1 P Y u2265 2 the standard deviation of Y is 3 2 sqrt 2 1 ,Normal Distribution,117 When two 4 bit numbers A a_3a_2a_1a_0 and B b_3b_2b_1b_0 are multiplied the bit c_1 of the product C is given by ________,Number Representation,118 The octal representation of an integer is 342 _8 If this were to be treated as an eight bit integer in an 8085 based computer its decimal equivalent is 226 98 76 30 ,Number Representation,118 The number 43 in 2 s complement representation is 01010101 11010101 00101011 10101011 ,Number Representation,118 The decimal value 0 25 is equivalent to the binary value 0 1 is equivalent to the binary value 0 01 is equivalent to the binary value 0 00111 cannot be represented precisely in binary ,Number Representation,118 The 2 s complement representation of the decimal value 15 is 1111 11111 111111 10001 ,Number Representation,118 The 2 s complement representation of 539 10 in hexadecimal is ABE DBC DE5 9E7 ,Number Representation,118 Suppose the domain set of an attribute consists of signed four digit numbers What is the percentage of reduction in storage space of this attribute if it is stored as an integer rather than in character form 80 20 60 40 ,Number Representation,118 Given sqrt 224 _r 13 _r The value of the radix r is 10 8 5 6 ,Number Representation,118 Convert the following numbers in the given bases into their equivalents in the desired bases 110 101 2 x 10 1118 10 y H ,Number Representation,118 Consider the values of A 2 0 x 10 30 B 2 0 x 10 30 C 1 0 and the sequence X A B Y A C X X C Y Y B executed on a computer where floating point numbers are represented with 32 bits The values for X and Y will be X 1 0 Y 1 0 X 1 0 Y 0 0 X 0 0 Y 1 0 X 0 0 Y 0 0 ,Number Representation,118 Consider the number given by the decimal expression 16 3 9 16 2 7 16 5 3 The number of 1 u2019s in the unsigned binary representation of the number is ______,Number Representation,118 Consider the following floating point number representation 31 24 23 0 Exponent Mantissa The exponent is in 2 u2019s complement representation and mantissa is in the sign magnitude representation The range of the magnitude of the normalized numbers in this representation is 0 to 1 0 5 to 1 2 23 to 0 5 0 5 to left 1 2 23 right ,Number Representation,118 Consider n bit including sign bit 2 s complement representation of integer numbers The range of integer values N that can be represented is _____ leq N leq _____ ,Number Representation,118 The number of 1 s in the binary representation of 3 4096 15 256 5 16 3 are 8 9 10 12 ,Number Representation,118 The value of sqrt 12 sqrt 12 sqrt 12 dots is 3 464 3 932 4 000 4 444 ,Number Series,119 Find the sum of the expression frac 1 sqrt 1 sqrt 2 frac 1 sqrt 2 sqrt 3 frac 1 sqrt 3 sqrt 4 frac 1 sqrt 80 sqrt 81 7 8 9 10 ,Number Series,119 Consider the quadratic equation x 2 13x 36 0 with coefficients in a base b The solutions of this equation in the same base b are x 5 and x 6 Then b _____,Number System,120 The number of divisors of 2100 is ____ ,Number Theory,121 The number of distinct positive integral factors of 2014 is _____________,Number Theory,121 The minimum positive integer p such that 3 p pmod 17 1 is 5 8 12 16 ,Number Theory,121 Show that the product of the least common multiple and the greatest common divisor of two positive integers a and b is a imes b ,Number Theory,121 Let n p2q where p and q are distinct prime numbers How many numbers m satisfy 1 u2264 m u2264 n and gcd m n 1 Note that gcd m n is the greatest common divisor of m and n p q 1 pq p2 1 q 1 p p 1 q 1 ,Number Theory,121 A CPU has two modes privileged and non privileged In order to change the mode from privileged to non privileged a hardware interrupt is needed a software interrupt is needed a privileged instruction which does not generate an interrupt is needed a non privileged instruction which does not generate an interrupt is needed ,Os Protection,122 In the following pairs of OSI protocol layer sub layer and its functionality the INCORRECT pair is Network layer and Routing Data Link Layer and Bit synchronization Transport layer and End to end process communication Medium Access Control sub layer and Channel sharing ,Osi Protocol,123 The overlay tree for a program is as shown below What will be the size of the partition in physical memory required to load and run this program 12 KB 14 KB 10 KB 8 KB ,Overlay,124 Thrashing reduces page I O decreases the degree of multiprogramming implies excessive page I O improve the system performance ,Page Replacement,125 The optimal page replacement algorithm will select the page that Has not been used for the longest time in the past Will not be used for the longest time in the future Has been used least number of times Has been used most number of times ,Page Replacement,125 The minimum number of page frames that must be allocated to a running process in a virtual memory environment is determined by the instruction set architecture page size number of processes in memory physical memory size ,Page Replacement,125 The following page addresses in the given sequence were generated by a program 1 2 3 4 1 3 5 2 1 5 4 3 2 3 This program is run on a demand paged virtual memory system with main memory size equal to 4 pages Indicate the page references for which page faults occur for the following page replacement algorithms LRU FIFO Assume that the main memory is initially empty,Page Replacement,125 The address sequence generated by tracing a particular program executing in a pure demand based paging system with 100 records per page with 1 free main memory frame is recorded as follows What is the number of page faults 0100 0200 0430 0499 0510 0530 0560 0120 0220 0240 0260 0320 0370 13 8 7 10 ,Page Replacement,125 Locality of reference implies that the page reference being made by a process will always be to the page used in the previous page reference is likely to be to one of the pages used in the last few page references will always be to one of the pages existing in memory will always lead to a page fault ,Page Replacement,125 Consider the following heap figure in which blank regions are not in use and hatched region are in use The sequence of requests for blocks of sizes 300 25 125 50 can be satisfied if we use either first fit or best fit policy any one first fit but not best fit policy best fit but not first fit policy None of the above ,Page Replacement,125 Consider a virtual memory system with FIFO page replacement policy For an arbitrary page access pattern increasing the number of page frames in main memory will always decrease the number of page faults always increase the number of page faults sometimes increase the number of page faults never affect the number of page faults ,Page Replacement,125 Consider a computer system with ten physical page frames The system is provided with an access sequence a_ 1 a_ 2 a_ 20 a_ 1 a_ 2 a_ 20 where each a_ i is a distinct virtual page number The difference in the number of page faults between the last in first out page replacement policy and the optimal page replacement policy is_________ ,Page Replacement,125 A virtual memory system uses First In First Out FIFO page replacement policy and allocates a fixed number of frames to a process Consider the following statements P Increasing the number of page frames allocated to a process sometimes increases the page fault rate Q Some programs do not exhibit locality of reference Which one of the following is TRUE Both P and Q are true and Q is the reason for P Both P and Q are true but Q is not the reason for P P is false but Q is true Both P and Q are false ,Page Replacement,125 A memory page containing a heavily used variable that was initialized very early and is in constant use is removed then LRU page replacement algorithm is used FIFO page replacement algorithm is used LFU page replacement algorithm is used None of the above ,Page Replacement,125 Increasing the RAM of a computer typically improves performance because Virtual Memory increases Larger RAMs are faster Fewer page faults occur Fewer segmentation faults occur ,Page Replacement,125 In which one of the following page replacement algorithms it is possible for the page fault rate to increase even when the number of allocated frames increases LRU Least Recently Used OPT Optimal Page Replacement MRU Most Recently Used FIFO First In First Out ,Page Replacement,125 Dirty bit for a page in a page table helps avoid unnecessary writes on a paging device helps maintain LRU information allows only read on a page None of the above ,Page Replacement,125 The inclusion of which of the following sets into S left left 1 2 right left 1 2 3 right left 1 3 5 right left 1 2 4 right left 1 2 3 4 5 right right is necessary and sufficient to make S a complete lattice under the partial order defined by set containment 1 1 2 3 1 1 3 1 1 3 1 2 3 4 1 2 3 5 ,Partial Order,126 Let S leq be a partial order with two minimal elements a and b and a maximum element c Let P S o True False be a predicate defined on S Suppose that P a True P b False and P x implies P y for all x y in S satisfying x leq y where implies stands for logical implication Which of the following statements CANNOT be true P x True for all x in S such that x u2260 b P x False for all x in S such that x u2260 a and x u2260 c P x False for all x in S such that b u2264 x and x u2260 c P x False for all x in S such that a u2264 x and b u2264 x ,Partial Order,126 If the longest chain in a partial order is of length n then the partial order can be written as a _____ of n antichains ,Partial Order,126 Consider the set S a b c d Consider the following 4 partitions u03c0_1 u03c0_2 u03c0_3 u03c0_4 on S u03c0_1 overline abcd u03c0_2 overline ab overline cd quad u03c0_3 overline abc overline d u03c0_4 bar a bar b bar c bar d Let prec be the partial order on the set of partitions S u03c0_1 u03c0_2 u03c0_3 u03c0_4 defined as follows u03c0_i prec u03c0_j if and only if u03c0_i refines u03c0_j The poset diagram for S prec is ,Partial Order,126 A partial order P is defined on the set of natural numbers as follows Here dfrac x y denotes integer division 0 0 in P a b in P if and only if a 10 leq b 10 and frac a 10 frac b 10 in P Consider the following ordered pairs 101 22 22 101 145 265 0 153 Which of these ordered pairs of natural numbers are contained in P i and iii ii and iv i and iv iii and iv ,Partial Order,126 The less than relation lt on reals is a partial ordering since it is asymmetric and reflexive a partial ordering since it is antisymmetric and reflexive not a partial ordering because it is not asymmetric and not reflexive not a partial ordering because it is not antisymmetric and reflexive none of the above ,Partial Order,126 Suppose A a b c d and Pi_1 is the following partition of A Pi_1 left left a b c right left d right right List the ordered pairs of the equivalence relations induced by Pi_1 Draw the graph of the above equivalence relation Let Pi_2 left left a right left b right left C right left d right right Pi_3 left left a b c d right right and Pi_4 left left a b right left c d right right Draw a Poset diagram of the poset left langle left Pi_1 Pi_2 Pi_3 Pi_4 right ext refines right rangle ,Partial Order,126 Let X 2 3 6 12 24 Let leq be the partial order defined by X leq Y if x divides y Number of edges in the Hasse diagram of X leq is 3 4 9 None of the above ,Partial Order,126 A set S together with partial order ll is called a well order if it has no infinite descending chains i e there is no infinite sequence x_1 x_2 ldots of elements from S such that x_ i 1 ll x_i and x_ i 1 eq x_i for all i Consider the set of all words finite sequence of letters a z denoted by W in dictionary order Between aa and az there are only 24 words Between aa and az there are only 2 24 words W is not a partial order W is a partial order but not a well order W is a well order ,Partial Order,126 A partial order le is defined on the set S x a1 a2 an y as x le ai for all i and ai le y for all i where n ge 1 The number of total orders on the set S which contain the partial order le is n n 2 n 1 ,Partial Order,126 The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined ,Passage Reading,127 The Gross Domestic Product GDP in Rupees grew at 7 during 2012 2013 For international comparison the GDP is compared in US Dollars USD after conversion based on the market exchange rate During the period 2012 2013 the exchange rate for the USD increased from Rs 50 USD to Rs 60 USD India s GDP in USD during the period 2012 2013 increased by 5 decreased by 13 decreased by 20 decreased by 11 ,Percentage,128 Round trip tickets to a tourist destination are eligible for a discount of 10 on the total fare In addition groups of 4 or more get a discount of 5 on the total fare If the one way single person fare is Rs 100 a group of 5 tourists purchasing round trip tickets will be charged Rs __________,Percentage,128 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12 ,Permutation Combination,129 We need to choose a team of 11 from a pool of 15 players and also select a captain The number of different ways this can be done is begin pmatrix 15 11 end pmatrix 11 begin pmatrix 15 11 end pmatrix 15 14 13 12 11 10 9 8 7 6 5 15 14 13 12 11 10 9 8 7 6 5 11 ,Permutations And Combinations,130 Two girls have picked 10 roses 15 sunflowers and 15 daffodils What is the number of ways they can divide the flowers among themselves 1638 2100 2640 None of the above ,Permutations And Combinations,130 The number of substrings of all lengths inclusive that can be formed from a character string of length n is n n 2 frac n n 1 2 frac n n 1 2 ,Permutations And Combinations,130 The number of binary strings of n zeros and k ones in which no two ones are adjacent is n 1 C_k nC_k nC_ k 1 None of the above ,Permutations And Combinations,130 Provide short answers to the following questions How many substrings of all lengths inclusive can be formed from a character string of length n Assume all characters to be distinct prove your answer ,Permutations And Combinations,130 Match the pairs in the following questions by writing the corresponding letters only A The number distinct binary trees with n nodes P frac n 2 B The number of binary strings of length of 2n with an equal number of 0 u2019s and 1 u2019s Q binom 3n n C The number of even permutation of n objects R binom 2n n D The number of binary strings of length 6n which are palindromes with 2n 0 u2019s S frac 1 1 n binom 2n n ,Permutations And Combinations,130 Mala has the colouring book in which each English letter is drawn two times She wants to paint each of these 52 prints with one of k colours such that the colour pairs used to colour any two letters are different Both prints of a letter can also be coloured with the same colour What is the minimum value of k that satisfies this requirement 9 8 7 6 ,Permutations And Combinations,130 Let A be a sequence of 8 distinct integers sorted in ascending order How many distinct pairs of sequences B and C are there such that each is sorted in ascending order B has 5 and C has 3 elements and the result of merging B and C gives A 2 30 56 256 ,Permutations And Combinations,130 In how many ways can we distribute 5 distinct balls B1 B2 B5 in 5 distinct cells C1 C2 C5 such that Ball Bi is not in cell Ci u2200i 1 2 5 and each cell contains exactly one ball 44 96 120 3125 ,Permutations And Combinations,130 How many sub strings of different lengths non zero can be found formed from a character string of length n n n 2 2 n frac n n 1 2 ,Permutations And Combinations,130 How many 4 digit even numbers have all 4 digits distinct 2240 2296 2620 4536 ,Permutations And Combinations,130 Find the number of binary strings w of length 2n with an equal number of 1 s and 0 s and the property that every prefix of w has at least as many 0 s as 1 s ,Permutations And Combinations,130 n couples are invited to a party with the condition that every husband should be accompanied by his wife However a wife need not be accompanied by her husband The number of different gatherings possible at the party is 2n mathrm C _n imes 2 n 3 n frac 2n 2 n 2n mathrm C _n ,Permutations And Combinations,130 m identical balls are to be placed in n distinct bags You are given that m geq kn where k is a natural number geq 1 In how many ways can the balls be placed in the bags if each bag must contain at least k balls left begin array c m k n 1 end array right left begin array c m kn n 1 n 1 end array right left begin array c m 1 n k end array right left begin array c m kn n k 2 n k end array right ,Permutations And Combinations,130 In how many ways can a given positive integer n geq 2 be expressed as the sum of 2 positive integers which are not necessarily distinct For example for n 3 the number of ways is 2 i e 1 2 2 1 Give only the answer without any explanation In how many ways can a given positive integer n geq 3 be expressed as the sum of 3 positive integers which are not necessarily distinct For example for n 4 the number of ways is 3 i e 1 2 1 2 1 1 Give only the answer without explanation In how many ways can a given positive integer n geq k be expressed as the sum of k positive integers which are not necessarily distinct Give only the answer without explanation ,Permutations And Combinations,130 The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above ,Pigeonhole Principle,131 Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM and p has a Poisson distribution with mean 3 What is the probability of observing fewer than 3 cars during any given minute in this interval A dfrac 8 2e 3 B dfrac 9 2e 3 C dfrac 17 2e 3 D dfrac 26 2e 3 ,Poisson Distribution,132 In a multi user operating system on an average 20 requests are made to use a particular resource per hour The arrival of requests follows a Poisson distribution The probability that either one three or five requests are made in 45 minutes is given by 6 9 imes 10 6 imes e 20 1 02 imes 10 6 imes e 20 6 9 imes 10 3 imes e 20 1 02 imes 10 3 imes e 20 ,Poisson Distribution,132 If a random variable X has a Poisson distribution with mean 5 then the expectation E X 2 2 equals ___ ,Poisson Distribution,132 If the cube roots of unity are 1 omega and omega 2 then the roots of the following equation are x 1 3 8 0 1 1 2 omega 1 2 omega 2 1 1 2 omega 1 2 omega 2 1 1 2 omega 1 2 omega 2 1 1 2 omega 1 2 omega 2 ,Polynomials,133 A polynomial p x satisfies the following p 1 p 3 p 5 1 p 2 p 4 1 The minimum degree of such a polynomial is 1 2 3 4 ,Polynomials,133 A polynomial p x is such that p 0 5 p 1 4 p 2 9 and p 3 20 The minimum degree it should have is 1 2 3 4 ,Polynomials,133 A non zero polynomial f x of degree 3 has roots at x 1 x 2 and x 3 Which one of the following must be TRUE f 0 f 4 lt 0 f 0 f 4 gt 0 f 0 f 4 gt 0 f 0 f 4 lt 0 ,Polynomials,133 If f x 2x 7 3x 5 which of the following is a factor of f x left x 3 8 right x 1 2x 5 x 1 ,Polynomials,133 A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______,Precedence Graph,134 Which are the essential prime implicants of the following Boolean function f a b c a c ac b c a c and ac a c and b c a c only ac and bc ,Prime Implicants,135 Let f x y z bar x bar y x xz be a switching function Which one of the following is valid bar y x is a prime implicant of f xz is a minterm of f xz is an implicant of f y is a prime implicant of f ,Prime Implicants,135 A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order ,Priority Queue,136 Two n bit binary strings S_1 and S_2 are chosen randomly with uniform probability The probability that the Hamming distance between these strings the number of bit positions where the two strings differ is equal to d is dfrac n C_ d 2 n dfrac n C_ d 2 d dfrac d 2 n dfrac 1 2 d ,Probability,137 Two friends agree to meet at a park with the following conditions Each will reach the park between 4 00 pm and 5 00 pm and will see if the other has already arrived If not they will wait for 10 minutes or the end of the hour whichever is earlier and leave What is the probability that the two will not meet ,Probability,137 Two dice are thrown simultaneously The probability that at least one of them will have 6 facing up is frac 1 36 frac 1 3 frac 25 36 frac 11 36 ,Probability,137 The security system at an IT office is composed of 10 computers of which exactly four are working To check whether the system is functional the officials inspect four of the computers picked at random without replacement The system is deemed functional if at least three of the four computers inspected are working Let the probability that the system is deemed functional be denoted by p Then 100p _____________ ,Probability,137 Seven distinct car accidents occurred in a week What is the probability that they all occurred on the same day dfrac 1 7 7 dfrac 1 7 6 dfrac 1 2 7 dfrac 7 2 7 ,Probability,137 Let P E denote the probability of the event E Given P A 1 P B dfrac 1 2 the values of P A mid B and P B mid A respectively are left dfrac 1 4 right left dfrac 1 2 right left dfrac 1 2 right left dfrac 1 4 right left dfrac 1 2 right 1 1 left dfrac 1 2 right ,Probability,137 E1 and E2 are events in a probability space satisfying the following constraints Pr E1 Pr E2 Pr E1 u222a E2 1 E1 and E2 are independent The value of Pr E1 the probability of the event E1 is 0 dfrac 1 4 dfrac 1 2 1 ,Probability,137 A program consists of two modules executed sequentially Let f_1 t and f_2 t respectively denote the probability density functions of time taken to execute the two modules The probability density function of the overall time taken to execute the program is given by f_1 t f_2 t int_0 t f_1 x f_2 x dx int_0 t f_1 x f_2 t x dx max f_1 t f_2 t ,Probability,137 A probability density function on the interval a 1 is given by 1 x 2 and outside this interval the value of the function is zero The value of a is _________ ,Probability,137 A die is rolled three times The probability that exactly one odd number turns up among the three outcomes is a frac 1 6 b frac 3 8 c frac 1 8 d frac 1 2 ,Probability,137 The probability that top and bottom cards of a randomly shuffled deck are both aces is frac 4 52 imes frac 4 52 frac 4 52 imes frac 3 52 frac 4 52 imes frac 3 51 frac 4 52 imes frac 4 51 ,Probability,137 The probability that it will rain today is 0 5 The probability that it will rain tomorrow is 0 6 The probability that it will rain either today or tomorrow is 0 7 What is the probability that it will rain today and tomorrow 0 3 0 25 0 35 0 4 ,Probability,137 The probability of an event B is P_1 The probability that events A and B occur together is P_2 while the probability that A and bar B occur together is P_3 The probability of the event A in terms of P_1 P_2 and P_3 is _____________ ,Probability,137 Consider the following experiment Step 1 Flip a fair coin twice Step 2 If the outcomes are TAILS HEADS then output Y and stop Step 3 If the outcomes are either HEADS HEADS or HEADS TAILS then output N and stop Step 4 If the outcomes are TAILS TAILS then go to Step 1 The probability that the output of the experiment is Y is up to two decimal places ____________ ,Probability,137 A bag contains 10 white balls and 15 black balls Two balls are drawn in succession The probability that one of them is black and the other is white is frac 2 3 frac 4 5 frac 1 2 frac 1 3 ,Probability,137 Which combination of the following features will suffice to characterize an OS as a multi programmed OS More than one program may be loaded into main memory at the same time for execution If a program waits for certain events such as I O another program is immediately scheduled for execution If the execution of a program terminates another program is immediately scheduled for execution a a and b a and c a b and c ,Process,138 The process state transition diagram of an operating system is as given below Which of the following must be FALSE about the above operating system It is a multiprogrammed operating system It uses preemptive scheduling It uses non preemptive scheduling It is a multi user operating system ,Process,138 The process state transition diagram in the below figure is representative of a batch operating system an operating system with a preemptive scheduler an operating system with a non preemptive scheduler a uni programmed operating system ,Process,138 We wish to schedule three processes P1 P2 and P3 on a uniprocessor system The priorities CPU time requirements and arrival times of the processes are as shown below Process Priority CPU time required Arrival time hh mm ss P1 10 highest 20 sec 00 00 05 P2 9 10 sec 00 00 03 P3 8 lowest 15 sec 00 00 00 We have a choice of preemptive or non preemptive scheduling In preemptive scheduling a late arriving higher priority process can preempt a currently running process with lower priority In non preemptive scheduling a late arriving higher priority process must wait for the currently executing process to complete before it can be scheduled on the processor What are the turnaround times time from arrival till completion of P2 using preemptive and non preemptive scheduling respectively 30 sec 30 sec 30 sec 10 sec 42 sec 42 sec 30 sec 42 sec ,Process Schedule,139 The sequence u2026 u2026 is an optimal non preemptive scheduling sequence for the following jobs which leaves the CPU idle for u2026 u2026 u2026 unit s of time Job Arrival Time Burst Time 1 0 0 9 2 0 6 5 3 1 0 1 3 2 1 1 2 1 3 0 3 2 1 0 1 2 3 5 ,Process Schedule,139 In a computer system where the u2018best fit u2019 algorithm is used for allocating u2018jobs u2019 to u2018memory partitions u2019 the following situation was encountered Partitions size in KB 4K 8K 20K 2K Job sizes in KB 2K 14K 3K 6K 6K 10K 20K 2K Time for execution 4 10 2 1 4 1 8 6 When will the 20K job complete ,Process Schedule,139 Fill in the blanks The highest response ratio next scheduling policy favours ___________ jobs but it also limits the waiting time of _________ jobs ,Process Schedule,139 Consider three processes process id 0 1 2 respectively with compute time bursts 2 4 and 8 time units All processes arrive at time zero Consider the longest remaining time first LRTF scheduling algorithm In LRTF ties are broken by giving priority to the process with the lowest process id The average turn around time is 13 units 14 units 15 units 16 units ,Process Schedule,139 Consider the following set of processes with the arrival times and the CPU burst times gives in milliseconds Process Arrival Time Burst Time P1 P2 P3 P4 0 1 2 4 5 3 3 1 What is the average turnaround time for these processes with the preemptive shortest remaining processing time first SRPT algorithm 5 50 5 75 6 00 6 25 ,Process Schedule,139 Assume that the following jobs are to be executed on a single processor system Job Id CPU Burst Time p 4 q 1 r 8 s 1 t 2 The jobs are assumed to have arrived at time 0 and in the order p q r s t Calculate the departure time completion time for job p if scheduling is round robin with time slice 1 4 10 11 12 None of the above ,Process Schedule,139 A uni processor computer system only has two processes both of which alternate 10 ms CPU bursts with 90 ms I O bursts Both the processes were created at nearly the same time The I O of both processes can proceed in parallel Which of the following scheduling strategies will result in the least CPU utilization over a long period of time for this system First come first served scheduling Shortest remaining time first scheduling Static priority scheduling with different priorities for the two processes Round robin scheduling with a time quantum of 5 ms ,Process Schedule,139 Four jobs to be executed on a single processor system arrive at time 0 in the order A B C D Their burst CPU time requirements are 4 1 8 1 time units respectively The completion time of A under round robin scheduling with time slice of one time unit is 10 4 8 9 ,Process Schedule,139 Four jobs are waiting to be run Their expected run times are 6 3 5 and x In what order should they be run to minimize the average response time Write a concurrent program using ext par begin par end to represent the precedence graph shown below ,Process Schedule,139 Consider three CPU intensive processes which require 10 20 and 30 time units and arrive at times 0 2 and 6 respectively How many context switches are needed if the operating system implements a shortest remaining time first scheduling algorithm Do not count the context switches at time zero and at the end 1 2 3 4 ,Process Schedule,139 Consider n processes sharing the CPU in a round robin fashion Assuming that each process switch takes s seconds what must be the quantum size q such that the overhead resulting from process switching is minimized but at the same time each process is guaranteed to get its turn at the CPU at least every t seconds q leq frac t ns n 1 q geq frac t ns n 1 q leq frac t ns n 1 q geq frac t ns n 1 ,Process Schedule,139 Consider an arbitrary set of CPU bound processes with unequal CPU burst lengths submitted at the same time to a computer system Which one of the following process scheduling algorithms would minimize the average waiting time in the ready queue Shortest remaining time first Round robin with the time quantum less than the shortest CPU burst Uniform random Highest priority first with priority proportional to CPU burst length ,Process Schedule,139 When the result of a computation depends on the speed of the processes involved there is said to be cycle stealing race condition a time lock a deadlock ,Process Synchronization,140 The following solution to the single producer single consumer problem uses semaphores for synchronization define BUFFSIZE 100 buffer buf BUFFSIZE int first last 0 semaphore b_full 0 semaphore b_empty BUFFSIZE void producer while 1 produce an item p1 put the item into buff first first first 1 BUFFSIZE p2 void consumer while 1 c1 take the item from buf last last last 1 BUFFSIZE c2 consume the item Complete the dotted part of the above solution Using another semaphore variable insert one line statement each immediately after p1 immediately before p2 immediately after c1 and immediately before c2 so that the program works correctly for multiple producers and consumers ,Process Synchronization,140 The concurrent programming constructs fork and join are as below fork lt label gt which creates a new process executing from the specified label join lt variable gt which decrements the specified synchronization variable by 1 and terminates the process if the new value is not 0 Show the precedence graph for S1 S2 S3 S4 and S5 of the concurrent program below N 2 M 2 Fork L3 Fork L4 S1 L1 join N S3 L2 join M S5 L3 S2 Goto L1 L4 S4 Goto L2 Next ,Process Synchronization,140 Match the pairs in the following questions a Critical region p Hoare s monitor b Wait Signal q Mutual exclusion c Working Set r Principle of locality d Deadlock s Circular Wait ,Process Synchronization,140 Let m 0 m 4 be mutexes binary semaphores and P 0 P 4 be processes Suppose each process P i executes the following wait m i wait m i 1 mode 4 release m i release m i 1 mod 4 This could cause Thrashing Deadlock Starvation but not deadlock None of the above ,Process Synchronization,140 Each Process P_i i 1 9 is coded as follows repeat P mutex Critical section V mutex forever The code for P_ 10 is identical except it uses V mutex in place of P mutex What is the largest number of processes that can be inside the critical section at any moment 1 2 3 None ,Process Synchronization,140 Draw the process state transition diagram of an OS in which i each process is in one of the five states created ready running blocked i e sleep or wait or terminated and ii only non preemptive scheduling is used by the OS Label the transitions appropriately ,Process Synchronization,140 Consider the following program segment for concurrent processing using semaphore operators P and V for synchronization Draw the precedence graph for the statements S1 to S9 var a b c d e f g h i j k semaphore begin cobegin begin S1 V a V b end begin P a S2 V c V d end begin P c S4 V e end begin P d S5 V f end begin P e P f S7 V k end begin P b S3 V g V h end begin P g S6 V i end begin P h P i S8 V j end begin P j P k S9 end coend end ,Process Synchronization,140 Consider Peterson s algorithm for mutual exclusion between two concurrent processes i and j The program executed by process is shown below repeat flag i true turn j while P do no op Enter critical section perform actions then exit critical section Flag i false Perform other non critical section actions Until false For the program to guarantee mutual exclusion the predicate P in the while loop should be flag j true and turn i flag j true and turn j flag i true and turn j flag i true and turn i ,Process Synchronization,140 A solution to the Dining Philosophers Problem which avoids deadlock is to ensure that all philosophers pick up the left fork before the right fork ensure that all philosophers pick up the right fork before the left fork ensure that one particular philosopher picks up the left fork before the right fork and that all other philosophers pick up the right fork before the left fork None of the above ,Process Synchronization,140 A certain processor provides a test and set instruction that is used as follows TSET register flag This instruction atomically copies flag to register and sets flag to 1 Give pseudo code for implementing the entry and exit code to a critical region using this instruction ,Process Synchronization,140 Draw a precedence graph for the following sequential code The statements are numbered from S_1 to S_6 S_1 read n S_2 i 1 S_3 if i gt n next S_4 a i i 1 S_5 i i 1 S_6 next write a i Can this graph be converted to a concurrent program using parbegin parend construct only ,Process Synchronization,140 a Fill in the boxes below to get a solution for the reader writer problem using a single binary semaphore mutex initialized to 1 and busy waiting Write the box numbers 1 2 and 3 and their contents in your answer book L1 int R 0 W 0 Reader wait mutex if W 0 R R 1 u25ad ______________ 1 else u25ad ______________ 2 goto L1 do the read wait mutex R R 1 signal mutex L2 Writer wait mutex if u25ad _________ 3 signal mutex goto L2 W 1 signal mutex do the write wait mutex W 0 signal mutex b Can the above solution lead to starvation of writers ,Process Synchronization,140 A critical section is a program segment which should run in a certain amount of time which avoids deadlocks where shared resources are accessed which must be enclosed by a pair of semaphore operations P and V ,Process Synchronization,140 Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii ,Programming Constructs,141 The goal of structured programming is to have well indented programs be able to infer the flow of control from the compiled code be able to infer the flow of control from the program text avoid the use of GOTO statements ,Programming Paradigms,142 Choose the best matching between the programming styles in Group 1 and their characteristics in Group 2 Group 1 Group 2 P Functional Q Logic R Object oriented S Imperative 1 Common based procedural 2 Imperative abstract data types 3 Side effect free declarative expression evaluations 4 Declarative clausal representation theorem proving P 2 Q 3 R 4 S 1 P 4 Q 3 R 2 S 1 P 3 Q 4 R 1 S 2 P 3 Q 4 R 2 S 1 ,Programming Paradigms,142 In a process the number of cycles to failure decreases exponentially with an increase in load At a load of 80 units it takes 100 cycles for failure When the load is halved it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02 ,Proportions,143 What is the converse of the following assertion I stay only if you go I stay if you go If I stay then you go If you do not go then I do not stay If I do not stay then you go ,Propositional Logic,144 The proposition p wedge sim p vee q is a tautology logically equivalent to p wedge q logically equivalent to p vee q a contradiction none of the above ,Propositional Logic,144 Obtain the principal canonical conjunctive normal form of the propositional formula p wedge q vee eg q wedge r where wedge is logical and vee is inclusive or and eg is negation ,Propositional Logic,144 Let p q r s represents the following propositions p x in left 8 9 10 11 12 right q x is a composite number r x is a perfect square s x is a prime number The integer x geq2 which satisfies eg left left p Rightarrow q right wedge left eg r vee eg s right right is ____________ ,Propositional Logic,144 Let p and q be propositions Using only the Truth Table decide whether p Longleftrightarrow q does not imply p o lnot q is True or False ,Propositional Logic,144 Let a b c d be propositions Assume that the equivalence a u21d4 b vee eg b and b u21d4c hold Then the truth value of the formula a u2227 b u2192 a u2227 c u2228 d is always True False Same as the truth value of b Same as the truth value of d ,Propositional Logic,144 If the proposition lnot p o v is true then the truth value of the proposition lnot p lor left p o q right where lnot is negation lor is inclusive OR and o is implication is a True b Multiple Values c False d Cannot be determined,Propositional Logic,144 Determine whether each of the following is a tautology a contradiction or neither quot lor quot is disjunction quot land quot is conjunction quot rightarrow quot is implication quot eg quot is negation and quot leftrightarrow quot is biconditional if and only if A leftrightarrow A lor A A lor B rightarrow B A land eg A lor B ,Propositional Logic,144 Consider two well formed formulas in propositional logic F1 P Rightarrow eg P F2 P Rightarrow eg P lor eg P Rightarrow P Which one of the following statements is correct F1 is satisfiable F2 is valid F1 unsatisfiable F2 is satisfiable F1 is unsatisfiable F2 is valid F1 and F2 are both satisfiable ,Propositional Logic,144 Choose the correct alternatives More than one may be correct Indicate which of the following well formed formulae are valid left P Rightarrow Q right wedge left Q Rightarrow R right Rightarrow left P Rightarrow R right left P Rightarrow Q right Rightarrow left eg P Rightarrow eg Q right left P wedge left eg P vee eg Q right right Rightarrow Q left P Rightarrow R right vee left Q Rightarrow R right Rightarrow left left P vee Q right Rightarrow R right ,Propositional Logic,144 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is are a tautology a vee b o b wedge c a wedge b o b vee c a vee b o left b o c right a o b o left b o c right ,Propositional Logic,144 Choose the correct alternatives more than one may be correct and write the corresponding letters only If F_1 F_2 and F_3 are propositional formulae such that F_1 land F_2 rightarrow F_3 and F_1 land F_2 rightarrow sim F_3 are both tautologies then which of the following is true a Both F_1 and F_2 are tautologies b The conjunction F_1 land F_2 is not satisfiable c Neither is tautologous d Neither is satisfiable e None of the above ,Propositional Logic,144 If X then Y unless Z is represented by which of the following formulas in prepositional logic eg is negation land is conjunction and rightarrow is implication X land eg Z rightarrow Y X land Y rightarrow eg Z X rightarrow Y land eg Z X rightarrow Y land eg Z ,Propositional Logic,144 Choose the correct option to fill 1 and 2 so that the program below prints an input string in reverse order Assume that the input string is terminated by a new line character void reverse void int c if 1 reverse 2 main printf Enter text printf reverse printf 1 is getchar u2019 setminus n u2019 2 is getchar c 1 is c getchar u2019 setminus n u2019 2 is getchar c 1 is c u2019 setminus n u2019 2 is putchar c 1 is c getchar u2019 setminus n u2019 2 is putchar c ,Pseudo Code,145 A language L satisfies the Pumping Lemma for regular languages and also the Pumping Lemma for context free languages Which of the following statements about L is TRUE L is necessarily a regular language L is necessarily a context free language but not necessarily a regular language L is necessarily a non regular language None of the above ,Pumping Lemma,146 Let Q left left q_1 q_2 right left a b right left a b bot right delta bot phi right be a pushdown automaton accepting by empty stack for the language which is the set of all nonempty even palindromes over the set left a b right Below is an incomplete specification of the transitions delta Complete the specification The top of the stack is assumed to be at the right end of the string representing stack contents delta q_1 a bot left q_1 bot a right delta q_1 b bot left q_1 bot b right delta q_1 a a left q_1 aa right delta q_1 b a left q_1 ab right delta q_1 a b left q_1 ba right delta q_1 b b left q_1 bb right delta q_1 a a left dots dots right delta q_1 b b left dots dots right delta q_2 a a left q_2 epsilon right delta q_2 b b left q_2 epsilon right delta q_2 epsilon bot left q_2 epsilon right ,Pushdown Automata,147 Let P be a non deterministic push down automaton NPDA with exactly one state q and exactly one symbol Z in its stack alphabet State q is both the starting as well as the accepting state of the PDA The stack is initialized with one Z before the start of the operation of the PDA Let the input alphabet of the PDA be u03a3 Let L P be the language accepted by the PDA by reading a string and reaching its accepting state Let N P be the language accepted by the PDA by reading a string and emptying its stack Which of the following statements is TRUE L P is necessarily u03a3 but N P is not necessarily u03a3 N P is necessarily u03a3 but L P is not necessarily u03a3 Both L P and N P are necessarily u03a3 Neither L P nor N P are necessarily u03a3 ,Pushdown Automata,147 Let M q_0 q_1 0 1 z_0 X delta q_0 z_0 phi be a Pushdown automation where delta is given by delta q_0 1 z_0 q_0 xz_0 delta q_0 epsilon z_0 q_0 epsilon delta q_0 1 X q_0 XX delta q_1 1 X q_1 epsilon delta q_0 0 X q_1 X delta q_0 0 z_0 q_0 z_0 z What is the language accepted by this PDA by empty stack Describe informally the working of the PDA ,Pushdown Automata,147 Let M K u03a3 u0413 u0394 s F be a pushdown automaton where K s f F f Sigma a b u0413 a and u0394 s a epsilon s a s b epsilon s a s a epsilon f epsilon f a a f epsilon f b a f epsilon Which one of the following strings is not a member of L M aaa aabab baaba bab ,Pushdown Automata,147 Let L_1 be the set of all languages accepted by a PDA by final state and L_2 the set of all languages accepted by empty stack Which of the following is true L_1 L_2 L_1 supset L_2 L_1 subset L_2 None ,Pushdown Automata,147 Give a deterministic PDA for the language L a ncb 2n mid n geq 1 over the alphabet Sigma a b c Specify the acceptance state ,Pushdown Automata,147 Consider the transition diagram of a PDA given below with input alphabet Sigma a b and stack alphabet Gamma X Z Z is the initial stack symbol Let L denote the language accepted by the PDA Which one of the following is TRUE L a nb n mid n geq0 and is not accepted by any finite automata L a n mid n geq0 cup a nb n mid n geq 0 and is not accepted by any deterministic PDA L is not accepted by any Turing machine that halts on every input L a n mid n geq0 cup a nb n mid n geq 0 and is deterministic context free ,Pushdown Automata,147 Consider the pushdown automaton PDA below which runs over the input alphabet a b c It has the stack alphabet Z_0 X where Z_0 is the bottom of stack marker The set of states of the PDA is s t u f where s is the start state and f is the final state The PDA accepts by final state The transitions of the PDA given below are depicted in a standard manner For example the transition s b X rightarrow t XZ_0 means that if the PDA is in state s and the symbol on the top of the stack is X then it can read b from the input and move to state t after popping the top of stack and pushing the symbols Z_0 and X in that order on the stack s a Z_0 rightarrow s XXZ_0 s epsilon Z_0 rightarrow f epsilon s a X rightarrow s XXX s b X rightarrow t epsilon t b X rightarrow t epsilon t c X rightarrow u epsilon u c X rightarrow u epsilon u epsilon Z_0 rightarrow f epsilon The language accepted by the PDA is a lb mc n mid l m n a l b m c n mid l m a lb mc n mid 2l m n a lb mc n mid m n ,Pushdown Automata,147 Consider the NPDA left langle Q left q_ 0 q_ 1 q_ 2 right Sigma left 0 1 right Gamma left 0 1 perp right delta q_ 0 perp F left q_ 2 right right rangle where as per usual convention Q is the set of states Sigma is the input alphabet Gamma is the stack alphabet delta is the state transition function q_ 0 is the initial state perp is the initial stack symbol and F is the set of accepting states The state transition is as follows Which one of the following sequences must follow the string 101100 so that the overall string is accepted by the automaton 10110 10010 01010 01001 ,Pushdown Automata,147 A push down automation pda is given in the following extended notation of finite state diagram The nodes denote the states while the edges denote the moves of the pda The edge labels are of the form d s s where d is the input symbol read and s s are the stack contents before and after the move For example the edge labeled 1 s 1 s denotes the move from state q_0 to q_0 in which the input symbol 1 is read and pushed to the stack Introduce two edges with appropriate labels in the above diagram so that the resulting pda accepts the language left x2x R mid x in left 0 1 right x R ext denotes reverse of x right by empty stack Describe a non deterministic pda with three states in the above notation that accept the language left 0 n 1 m mid n leq m leq 2n right by empty stack ,Pushdown Automata,147 The set of values of p for which the roots of the equation 3x 2 2x p p u20131 0 are of opposite sign is A u2013 u221e 0 B 0 1 C 1 u221e D 0 u221e ,Quadratic Equations,148 The roots of ax2 bx c 0 are real and positive a b and c are real Then ax2 b x c 0 has no roots 2 real roots 3 real roots 4 real roots ,Quadratic Equations,148 In a quadratic function the value of the product of the roots alpha beta is 4 Find the value of dfrac alpha n beta n alpha n beta n n 4 4 n 2 2n 1 4 n 1 ,Quadratic Equations,148 What is the minimum number of stacks of size n required to implement a queue of size n One Two Three Four ,Queues,149 Suppose you are given an implementation of a queue of integers The operations that can be performed on the queue are isEmpty Q u2014 returns true if the queue is empty false otherwise delete Q u2014 deletes the element at the front of the queue and returns its value insert Q i u2014 inserts the integer i at the rear of the queue Consider the following function void f queue Q int i if isEmpty Q i delete Q f Q insert Q i What operation is performed by the above function f Leaves the queue Q unchanged Reverses the order of the elements in the queue Q Deletes the element at the front of the queue Q and inserts it at the rear keeping the other elements in the same order Empties the queue Q ,Queues,149 Suppose a circular queue of capacity n u22121 elements is implemented with an array of n elements Assume that the insertion and deletion operations are carried out using REAR and FRONT as array index variables respectively Initially REAR FRONT 0 The conditions to detect queue full and queue empty are full REAR 1 mod n FRONT empty REAR FRONT full REAR 1 mod n FRONT empty FRONT 1 mod n REAR full REAR FRONT empty REAR 1 mod n FRONT full FRONT 1 mod n REAR empty REAR FRONT ,Queues,149 Suggest a data structure for representing a subset S of integers from 1 to n Following operations on the set S are to be performed in constant time independent of cardinality of S i MEMBER X Check whether X is in the set S or not ii FIND ONE S If S is not empty return one element of the set S any arbitrary element will do iii ADD X Add integer X to set S iv DELETE X Delete integer X from S Give pictorial examples of your data structure Give routines for these operations in an English like language You may assume that the data structure has been suitable initialized Clearly state your assumptions regarding initialization ,Queues,149 Let Q denote a queue containing sixteen numbers and S be an empty stack Head Q returns the element at the head of the queue Q without removing it from Q Similarly Top S returns the element at the top of S without removing it from S Consider the algorithm given below while Q is not Empty do if S is Empty OR Top S u2264 Head Q then x Dequeue Q Push S x else x Pop S Enqueue Q x end end The maximum possible number of iterations of the while loop in the algorithm is _______ ,Queues,149 Consider the following statements First in first out types of computations are efficiently supported by STACKS Implementing LISTS on linked lists is more efficient than implementing LISTS on an array for almost all the basic LIST operations Implementing QUEUES on a circular array is more efficient than implementing QUEUES on a linear array with two indices Last in first out type of computations are efficiently supported by QUEUES ii and iii are true i and ii are true iii and iv are true ii and iv are true ,Queues,149 Consider the following operation along with Enqueue and Dequeue operations on queues where k is a global parameter MultiDequeue Q m k while Q is not empty and m gt 0 Dequeue Q m m u2013 1 What is the worst case time complexity of a sequence of n queue operations on an initially empty queue u0398 n u0398 n k u0398 nk u0398 n 2 ,Queues,149 An implementation of a queue Q using two stacks S1 and S2 is given below void insert Q x push S1 x void delete Q if stack empty S2 then if stack empty S1 then print u201cQ is empty u201d return else while stack empty S1 x pop S1 push S2 x x pop S2 let n insert and m leq n delete operations be performed in an arbitrary order on an empty queue Q Let x and y be the number of push and pop operations performed respectively in the process Which one of the following is true for all m and n n m leq x lt 2n and 2m leq y leq n m n m leq x lt 2n and 2m leq y leq 2n 2m leq x lt 2n and 2m leq y leq n m 2m leq x lt 2n and 2m leq y leq 2n ,Queues,149 A queue Q containing n items and an empty stack S are given It is required to transfer all the items from the queue to the stack so that the item at the front of queue is on the TOP of the stack and the order of all other items are preserved Show how this can be done in O n time using only a constant amount of additional storage Note that the only operations which can be performed on the queue and stack are Delete Insert Push and Pop Do not assume any implementation of the queue or stack ,Queues,149 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are performed efficiently Which one of the following statements is CORRECT n refers to the number of items in the queue Both operations can be performed in O 1 time At most one operation can be performed in O 1 time but the worst case time for the operation will be Omega n The worst case time complexity for both operations will be Omega n Worst case time complexity for both operations will be Omega log n ,Queues,149 A circular queue has been implemented using a singly linked list where each node consists of a value and a single pointer pointing to the next node We maintain exactly two external pointers FRONT and REAR pointing to the front node and the rear node of the queue respectively Which of the following statements is are CORRECT for such a circular queue so that insertion and deletion operations can be performed in O 1 time Next pointer of front node points to the rear node Next pointer of rear node points to the front node I only II only Both I and II Neither I nor II ,Queues,149 A main memory unit with a capacity of 4 megabytes is built using 1M imes 1 bit DRAM chips Each DRAM chip has 1K rows of cells with 1K cells in each row The time taken for a single refresh operation is 100 nanoseconds The time required to perform one refresh operation on all the cells in the memory unit is 100 nanoseconds 100 imes 2 10 nanoseconds 100 imes 2 20 nanoseconds 3200 imes 2 20 nanosesonds ,Ram,150 A dynamic RAM has a memory cycle time of 64 nsec It has to be refreshed 100 times per msec and each refresh takes 100 nsec What percentage of the memory cycle time is used for refreshing 10 6 4 1 0 64 ,Ram,150 Suppose X_i for i 1 2 3 are independent and identically distributed random variables whose probability mass functions are Pr X_i 0 Pr X_i 1 frac 1 2 ext for i 1 2 3 Define another random variable Y X_1X_2 oplus X_3 where oplus denotes XOR Then Pr Y 0 mid X_3 0 ______ ,Random Variable,151 Let X be a Gaussian random variable with mean 0 and variance sigma 2 Let Y max left X 0 right where max left a b right is the maximum of a and b The median of Y is ______________ ,Random Variable,151 If the difference between the expectation of the square of a random variable left E left X 2 right right and he square of the expectation of the random variable left E left X right right 2 is denoted by R then A R 0 B R lt 0 C R geq 0 D R gt 0 ,Random Variable,151 For any discrete random variable X with probability mass function P X j p_j p_j geq 0 j in 0 dots N and Sigma_ j 0 N p_j 1 define the polynomial function g_x z Sigma_ j 0 N p_j z j For a certain discrete random variable Y there exists a scalar beta in 0 1 such that g_y z 1 beta beta z N The expectation of Y is N beta 1 beta N beta N 1 beta Not expressible in terms of N and beta alone ,Random Variable,151 Consider a random variable X that takes values 1 and u22121 with probability 0 5 each The values of the cumulative distribution function F x at x u22121 and 1 are A 0 and 0 5 B 0 and 1 C 0 5 and 1 D 0 25 and 0 75,Random Variable,151 Consider a finite sequence of random values X x_1 x_2 dots x_n Let mu_x be the mean and sigma_x be he standard deviation of X Let another finite sequence Y of equal length be derived from this as y_i a x_i b where a and b are positive constants Let mu_y be the mean and sigma_y be the standard deviation of this sequence Which one of the following statements is INCORRECT A Index position of mode of X in X is the same as the index position of mode of Y in Y B Index position of median of X in X is the same as the index position of median of Y in Y C mu_y a mu_x b D sigma_y a sigma_x b ,Random Variable,151 Let f x be the continuous probability density function of a random variable x the probability that a lt x leq b is f b a f b f a int limits_a b f x dx int limits_a b xf x dx ,Random Variable,151 Nobody knows yet if P NP Consider the language L defined as follows L begin cases 0 1 amp ext if P NP phi amp otherwise end cases Which of the following statements is true L is recursive L is recursively enumerable but not recursive L is not recursively enumerable Whether L is recursively enumerable or not will be known after we find out if P NP ,Recursive And Recursively Enumerable Languages,152 Let X be a recursive language and Y be a recursively enumerable but not recursive language Let W and Z be two languages such that overline Y reduces to W and Z reduces to overline X reduction means the standard many one reduction Which one of the following statements is TRUE W can be recursively enumerable and Z is recursive W can be recursive and Z s recursively enumerable W is not recursively enumerable and Z is recursive W is not recursively enumerable and Z is not recursive ,Recursive And Recursively Enumerable Languages,152 Let L1 be a recursive language and let L2 be a recursively enumerable but not a recursive language Which one of the following is TRUE L1 is recursive and L2 is recursively enumerable L1 is recursive and L2 is not recursively enumerable L1 and L2 are recursively enumerable L1 is recursively enumerable and L2 is recursive ,Recursive And Recursively Enumerable Languages,152 Let L_1 be the recursive language Let L_2 and L_3 be languages that are recursively enumerable but not recursive Which of the following statements is not necessarily true L_2 L_1 ext is recursively enumerable L_1 L_3 ext is recursively enumerable L_2 cap L_3 ext is recursively enumerable L_2 cup L_3 ext is recursively enumerable ,Recursive And Recursively Enumerable Languages,152 Let L be a language and bar L be its complement Which one of the following is NOT a viable possibility Neither L nor bar L is recursively enumerable r e One of L and bar L is r e but not recursive the other is not r e Both L and bar L are r e but not recursive Both L and bar L are recursive ,Recursive And Recursively Enumerable Languages,152 Let A leq_m B denotes that language A is mapping reducible also known as many to one reducible to language B Which one of the following is FALSE If A leq_m B and B is recursive then A is recursive If A leq_m B and A is undecidable then B is undecidable If A leq_m B and B is recursively enumerable then A is recursively enumerable If A leq_m B and B is not recursively enumerable then A is not recursively enumerable ,Recursive And Recursively Enumerable Languages,152 If the strings of a language L can be effectively enumerated in lexicographic i e alphabetic order which of the following statements is true L is necessarily finite L is regular but not necessarily finite L is context free but not necessarily regular L is recursive but not necessarily context free ,Recursive And Recursively Enumerable Languages,152 If L and bar L are recursively enumerable then L is regular context free context sensitive recursive ,Recursive And Recursively Enumerable Languages,152 For any two languages L_ 1 and L_ 2 such that L_ 1 is context free and L_ 2 is recursively enumerable but not recursive which of the following is are necessarily true bar L _ 1 Compliment of L_ 1 is recursive bar L _ 2 Compliment of L_ 2 is recursive bar L _ 1 is context free bar L _ 1 u222a L_ 2 is recursively enumerable I only III only III and IV only I and IV only ,Recursive And Recursively Enumerable Languages,152 Choose the correct alternatives More than one may be correct Recursive languages are A proper superset of context free languages Always recognizable by pushdown automata Also called type emptyset languages Recognizable by Turing machines ,Recursive And Recursively Enumerable Languages,152 The following table has two attributes A and C where A is the primary key and C is the foreign key referencing A with on delete cascade A C 2 4 3 4 4 3 5 2 7 2 9 5 6 4 The set of all tuples that must be additionally deleted to preserve referential integrity when the tuple 2 4 is deleted is 3 4 and 6 4 5 2 and 7 2 5 2 7 2 and 9 5 3 4 4 3 and 6 4 ,Referential Integrity,153 Consider the following tables T1 and T2 T1 P Q 2 2 3 8 7 3 5 8 6 9 8 5 9 8 T2 R S 2 2 8 3 3 2 9 7 5 7 7 2 In table T1 P is the primary key and Q is the foreign key referencing R in table T2 with on delete cascade and on update cascade In table T2 R is the primary key and S is the foreign key referencing P in table T1 with on delete set NULL and on update cascade In order to delete record langle 3 8 rangle from the table T1 the number of additional records that need to be deleted from table T1 is _______ ,Referential Integrity,153 Let R a b c and S d e f be two relations in which d is the foreign key of S that refers to the primary key of R Consider the following four operations R and S Insert into R Insert into S Delete from R Delete from S Which of the following can cause violation of the referential integrity constraint above Both I and IV Both II and III All of these None of these ,Referential Integrity,153 The string 1101 does not belong to the set represented by a 110 0 1 b 1 0 1 101 c 10 01 00 11 d 00 11 0 ,Regular Expressions,154 The regular expression 0 10 denotes the same set as 1 0 1 0 0 10 0 1 10 0 1 None of the above ,Regular Expressions,154 Let S and T be languages over Sigma a b represented by the regular expressions a b and a b respectively Which of the following is true S subset T T subset S S T S cap T phi ,Regular Expressions,154 In some programming language an identifier is permitted to be a letter followed by any number of letters or digits If L and D denote the sets of letters and digits respectively which of the following expressions defines an identifier L D L D L L D L L D ,Regular Expressions,154 If the regular set A is represented by A 01 1 and the regular set B is represented by B left left 01 right 1 right which of the following is true a A subset B b B subset A c A and B are incomparable d A B ,Regular Expressions,154 Give a regular expression over the alphabet 0 1 to denote the set of proper non null substrings of the string 0110 ,Regular Expressions,154 Give a regular expression for the set of binary strings where every 0 is immediately followed by exactly k 1 s and preceded by at least k 1 u2019s k is a fixed integer ,Regular Expressions,154 02 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following regular expression identities is are TRUE a r r b r s r s c r s r s d r s r s ,Regular Expressions,154 Which two of the following four regular expressions are equivalent varepsilon is the empty string 00 varepsilon 0 00 0 0 00 i and ii ii and iii i and iii iii and iv ,Regular Expressions,154 Which one of the following regular expressions represents the language the set of all binary strings having two consecutive 0 s and two consecutive 1 s 0 1 0011 0 1 0 1 1100 0 1 0 1 00 0 1 11 11 0 1 00 0 1 0 1 00 0 1 0 1 11 0 1 00 0 1 11 11 0 1 00 ,Regular Expressions,154 The regular expression for the language recognized by the finite state automaton of figure is ______ ,Regular Expressions,154 Choose the correct alternatives more than one may be correct and write the corresponding letters only Let r 1 1 0 s 11 0 ext and t 1 0 be three regular expressions Which one of the following is true L s subseteq L r and L s subseteq L t L r subseteq L s and L s subseteq L t L s subseteq L t and L s subseteq L r L t subseteq L s and L s subseteq L r None of the above ,Regular Expressions,154 Is the language generated by the grammer G regular If so give a regular expression for it else prove otherwise G S rightarrow aB B rightarrow bC C rightarrow xB C rightarrow c ,Regular Grammar,155 Consider the regular grammar below S u2192 bS aA u03f5 A u2192 aS bA The Myhill Nerode equivalence classes for the language generated by the grammar are w u220a a b a w is even and w u220a a b a w is odd w u220a a b a w is even and w u220a a b b w is odd w u220a a b a w b w and w u220a a b a w u2260 b w u03f5 wa w u220a a b and wb w u220a a b ,Regular Grammar,155 Consider the alphabet Sigma 0 1 the null empty string lambda and the set of strings X_0 X_1 ext and X_2 generated by the corresponding non terminals of a regular grammar X_0 X_1 ext and X_2 are related as follows X_0 1 X_1 X_1 0 X_1 1 X_2 X_2 0 X_1 lambda Which one of the following choices precisely represents the strings in X_0 10 0 10 1 10 0 10 1 1 0 10 1 10 0 10 1 110 0 10 1 ,Regular Grammar,155 The number of edges in a regular graph of degree d and n vertices is ____________,Regular Graph,156 What can be said about a regular language L over a whose minimal finite state automaton has two states L must be an n is odd L must be an n is even L must be an n u2265 0 Either L must be an n is odd or L must be an n is even ,Regular Languages,157 Let Sigma left 0 1 right L Sigma and R left 0 n1 n mid n gt 0 right then the languages L cup R and R are respectively A regular regular B not regular regular C regular not regular D not regular not regular,Regular Languages,157 Let L subseteq Sigma where Sigma left a b right Which of the following is true a L left x mid x ext has an equal number of a ext s and b ext s right is regular b L left a nb n mid n geq 1 right is regular c L left x mid x ext has more number of a ext s than b ext s right is regular d L left a mb n mid m geq 1 n geq 1 right is regular,Regular Languages,157 Let L be a regular language Consider the constructions on L below repeat L ww w u220a L prefix L u u2203v uv u220a L suffix L v u2203u uv u220a L half L u u2203v v u and uv u220a L Which of the constructions could lead to a non regular language Both I and IV Only I Only IV Both II and III ,Regular Languages,157 Let L be a regular language Consider the constructions on L below ext repeat L ww mid w in L ext prefix L u mid exists v uv in L ext suffix L v mid exists u uv in L ext half L u mid exists v v u ext and uv in L Which of the constructions could lead to a non regular language Both I and IV Only 1 Only IV Both II and III Which choice of L is best suited to support your answer above a b u03f5 a ab bab ab a nb n mid n geq 0 ,Regular Languages,157 If s is a string over 0 1 then let n0 s denote the number of 0 u2019s in s and n1 s the number of 1 u2019s in s Which one of the following languages is not regular L left s in 0 1 mid n_ 0 s ext is a 3 digit prime right L left s in 0 1 mid ext for every prefix s of s mid n_ 0 s n_ 1 s mid leq 2 right L left s in 0 1 mid n_ 0 s n_ 1 s mid leq 4 right L left s in 0 1 mid n_ 0 s mod 7 n_ 1 s mod 5 0 right ,Regular Languages,157 Consider the following two statements S_1 left 0 2n mid n geq 1 right is a regular language S_2 left 0 m1 n0 m n mid m geq 1 ext and n geq 1 right is a regular language Which of the following statement is correct Only S_1 is correct Only S_2 is correct Both S_1 and S_2 are correct None of S_1 and S_2 is correct ,Regular Languages,157 Consider the following languages L1 left ww mid w in a b right L2 left ww R mid w in a b w R ext is the reverse of w right L3 left 0 2i mid ext i is an integer right L4 left 0 i 2 mid ext i is an integer right Which of the languages are regular Only L1 and L2 Only L2 L3 and L4 Only L3 and L4 Only L3 ,Regular Languages,157 Choose the correct alternatives More than one may be correct Let R_ 1 and R_ 2 be regular sets defined over the alphabet Sigma Then R_ 1 cap R_ 2 is not regular R_ 1 cup R_ 2 is regular Sigma R_ 1 is regular R_ 1 is not regular ,Regular Languages,157 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is the strongest correct statement about a finite language over some finite alphabet Sigma a It could be undecidable b It is Turing machine recognizable c It is a context sensitive language d It is a regular language e None of the above ,Regular Languages,157 Given that A is regular and A cup B is regular does it follow that B is necessarily regular Justify your answer Given two finite automata M1 M2 outline an algorithm to decide if L M1 subset L M2 note strict subset ,Regular Languages,157 Suppose the adjacency relation of vertices in a graph is represented in a table Adj X Y Which of the following queries cannot be expressed by a relational algebra expression of constant length List all vertices adjacent to a given vertex List all vertices which have self loops List all vertices which belong to cycles of less than three vertices List all vertices reachable from a given vertex ,Relational Algebra,158 Let r and s be two relations over the relation schemes R and S respectively and let A be an attribute in R The relational algebra expression sigma_ A a r bowtie s is always equal to sigma_ A a r r sigma_ A a r bowtie s None of the above ,Relational Algebra,158 Information about a collection of students is given by the relation ext studInfo underline ext studId ext name sex The relation ext enroll underline ext studId underline ext courseId gives which student has enrolled for or taken what course s Assume that every course is taken by at least one male and at least one female student What does the following relational algebra expression represent pi _ courceId left left pi_ ext studId left sigma_ sex female left ext studInfo right right imes pi_ courseId left ext enroll right right ext enroll right Courses in which all the female students are enrolled Courses in which a proper subset of female students are enrolled Courses in which only male students are enrolled None of the above ,Relational Algebra,158 Given two union compatible relations R_1 A B and R_2 C D what is the result of the operation R_1 Join_ A C wedge B D R_2 R_1 cup R_2 R_1 imes R_2 R_1 u2013 R_2 R_1 cap R_2 ,Relational Algebra,158 Consider the relation Student name sex marks where the primary key is shown underlined pertaining to students in a class that has at least one boy and one girl What does the following relational algebra expression produce Note rho is the rename operator pi_ name mathcal r _ sex female Student pi_ name Student_ sex female wedge x male wedge marks leq m rho_ n x m Student names of girl students with the highest marks names of girl students with more marks than some boy student names of girl students with marks not less than some boy student names of girl students with more marks than all the boy students ,Relational Algebra,158 Consider the relation scheme AUTHOR ANAME INSTITUTION ACITY AGE PUBLISHER PNAME PCITY BOOK TITLE ANAME PNAME Express the following queries using one or more of SELECT PROJECT JOIN and DIVIDE operations Get the names of all publishers Get values of all attributes of all authors who have published a book for the publisher with PNAME u2019TECHNICAL PUBLISHERS u2019 Get the names of all authors who have published a book for any publisher located in Madras ,Relational Algebra,158 Consider the join of a relation R with a relation S If R has m tuples and S has n tuples then the maximum and minimum sizes of the join respectively are m n and 0 mn and 0 m n and m n mn and m n ,Relational Algebra,158 Consider the following SQL query Select distinct a_1 a_2 u2026 a_n from r_1 r_2 u2026 r_m where P For an arbitrary predicate P this query is equivalent to which of the following relational algebra expressions Pi_ a_1 a_2 u2026 a_n sigma_p left r_1 imes r_2 imes dots imes r_m right Pi_ a_1 a_2 u2026 a_n sigma_p left r_1 bowtie r_2 bowtie dots bowtie r_m right Pi_ a_1 a_2 u2026 a_n sigma_p left r_1 cup r_2 cup dots cup r_m right Pi_ a_1 a_2 u2026 a_n sigma_p left r_1 cap r_2 cap dots cap r_m right ,Relational Algebra,158 Consider the following relational schema COURSES cno cname STUDENTS rollno sname age year REGISTERED FOR cno rollno The underlined attributes indicate the primary keys for the relations The u2018year u2019 attribute for the STUDENTS relation indicates the year in which the student is currently studying First year Second year etc Write a relational algebra query to print the roll number of students who have registered for cno 322 Write a SQL query to print the age and year of the youngest student in each year ,Relational Algebra,158 Consider the following relational database schemes COURSES Cno name PRE REQ Cno pre Cno COMPLETED student_no Cno COURSES gives the number and name of all the available courses PRE REQ gives the information about which courses are pre requisites for a given course COMPLETED indicates what courses have been completed by students Express the following using relational algebra List all the courses for which a student with student_no 2310 has completed all the pre requisites ,Relational Algebra,158 A university placement center maintains a relational database of companies that interview students on campus and make job offers to those successful in the interview The schema of the database is given below COMPANY cname clocation STUDENT scrollno sname sdegree INTERVIEW cname srollno idate OFFER cname srollno osalary The COMPANY relation gives the name and location of the company The STUDENT relation gives the student u2019s roll number name and the degree program for which the student is registered in the university The INTERVIEW relation gives the date on which a student is interviewed by a company The OFFER relation gives the salary offered to a student who is successful in a company u2019s interview The key for each relation is indicated by the underlined attributes Write a relational algebra expressions using only the operator sigma pi cup for the following queries List the rollnumbers and names of students who attended at least one interview but did not receive any job offer List the rollnumbers and names of students who went for interviews and received job offers from every company with which they interviewed Write an SQL query to list for each degree program in which more than five students were offered jobs the name of the degree and the average offered salary of students in this degree program ,Relational Algebra,158 A table student with schema roll name hostel marks and another table hobby with schema roll hobbyname contains records as shown below Table Student Roll Name Hostel Marks 1798 Manoj Rathod 7 95 2154 Soumic Banerjee 5 68 2369 Gumma Reddy 7 86 2581 Pradeep Pendse 6 92 2643 Suhas Kulkarni 5 78 2711 Nitin Kadam 8 72 2872 Kiran Vora 5 92 2926 Manoj Kunkalikar 5 94 2959 Hemant Karkhanis 7 88 3125 Rajesh Doshi 5 82 Table hobby Roll Hobbyname 1798 chess 1798 music 2154 music 2369 swimming 2581 cricket 2643 chess 2643 hockey 2711 volleyball 2872 football 2926 cricket 2959 photography 3125 music 3125 chess The following SQL query is executed on the above tables select hostel from student natural join hobby where marks gt 75 and roll between 2000 and 3000 Relations S and H with the same schema as those of these two tables respectively contain the same information as tuples A new relation S u2019 is obtained by the following relational algebra operation S u2019 u220fhostel u03c3s roll H roll u03c3marks gt 75 and roll gt 2000 and roll lt 3000 S X H The difference between the number of rows output by the SQL statement and the number of tuples in S u2019 is 6 4 2 0 ,Relational Algebra,158 A library relational database system uses the following schema USERS User User Name Home Town BOOKS Book Book Title Author Name ISSUED Book User Date Explain in one English sentence what each of the following relational algebra queries is designed to determine sigma_ ext User 6 left pi_ ext User Book Title left left ext USERS bowtie ext ISSUED right bowtie ext BOOKS right right pi_ ext Author Name left ext BOOKS bowtie sigma_ ext Home Town Delhi left ext USERS bowtie ext ISSUED right right ,Relational Algebra,158 Suppose we have a database consisting of the following three relations FREQUENTS CUSTOMER HOTEL SERVES HOTEL SNACKS LIKES CUSTOMER SNACKS The first indicates the hotels each customer visits the second tells which snacks each hotel serves and last indicates which snacks are liked by each customer Express the following query in relational algebra Print the hotels the serve the snack that customer Rama likes ,Relational Algebra,158 Given the relations employee name salary dept no and department dept no dept name address Which of the following queries cannot be expressed using the basic relational algebra operations left sigma pi imes Join cup cap right Department address of every employee Employees whose name is the same as their department name The sum of all employees salaries All employees of a given department ,Relational Algebra,158 The relational algebra expression equivalent to the following tuple calculus expression left t mid t in r land left t A 10 land t B 20 right right is sigma_ A 10 lor B 20 r sigma_ A 10 r cup sigma_ B 20 r sigma_ A 10 r cap sigma_ B 20 r sigma_ A 10 r sigma_ B 20 r ,Relational Calculus,159 The following relations are used to store data about students courses enrollment of students in courses and teachers of courses Attributes for primary key in each relation are marked by u2018 u2019 Students rollno sname saddr courses cno cname enroll rollno cno grade each tno tname cao cno is course number cname is course name tno is teacher number tname is teacher name sname is student name etc Write a SQL query for retrieving roll number and name of students who got A grade in at least one course taught by teacher names Ramesh for the above relational database ,Relational Calculus,159 Student school id sch roll no sname saddress School school id sch name sch address sch phone Enrolment school id sch roll no erollno examname ExamResult erollno examname marks Consider the following tuple relational calculus query t u2203 E u220a Enrolment t E school id x x u220a Enrolment x school id t u2203 B u220a ExamResult B erollno x erollno B examname x examname B marks gt 35 x x u220a Enrolment x school id t 100 gt 35 If a student needs to score more than 35 marks to pass an exam what does the query return The empty set schools with more than 35 of its students enrolled in some exam or the other schools with a pass percentage above 35 over all exams taken together schools with a pass percentage above 35 over each exam ,Relational Calculus,159 Let R_1 left underline A B C right and R_2 left underline D E right be two relation schema where the primary keys are shown underlined and let C be a foreign key in R_1 referring to R_2 Suppose there is no violation of the above referential integrity constraint in the corresponding relation instances r_1 and r_2 Which of the following relational algebra expressions would necessarily produce an empty relation Pi_D r_2 Pi_C r_1 Pi_C r_1 Pi_D r_2 Pi_D left r_1 bowtie_ C eq D r_2 right Pi_C left r_1 bowtie_ C D r_2 right ,Relational Calculus,159 Let R and S be relational schemes such that R a b c and S c Now consider the following queries on the database pi_ R S r pi_ R S left pi_ R S r imes s pi_ R S S r right left t mid t in pi_ R S r wedge forall u in s left exists v in r left u v S wedge t v left R S right right right right left t mid t in pi_ R S r wedge forall v in r left exists u in s left u v S wedge t v left R S right right right right Select R a R b From R S Where R c S c Which of the above queries are equivalent 1 and 2 1 and 3 2 and 4 3 and 4 ,Relational Calculus,159 Consider the relation employee name sex supervisorName with name as the key supervisorName gives the name of the supervisor of the employee under consideration What does the following Tuple Relational Calculus query produce left e name mid employee e wedge left forall x right left eg employee left x right vee x supervisorName eq e name vee x sex male right right Names of employees with a male supervisor Names of employees with no immediate male subordinates Names of employees with no immediate female subordinates Names of employees with a female supervisor ,Relational Calculus,159 Consider the following relational schema Students rollno integer sname string Courses courseno integer cname string Registration rollno integer courseno integer percent real Which of the following queries are equivalent to this query in English u201cFind the distinct names of all students who score more than 90 in the course numbered 107 u201d SELECT DISTINCT S sname FROM Students as S Registration as R WHERE R rollno S rollno AND R courseno 107 AND R percent gt 90 u220f_ sname u03c3_ courseno 107 u2227 percent gt 90 Registration u22c8 Students left T mid u2203S in Students u2203R in Registration S rollno R rollno u2227 R courseno 107 u2227 R percent gt 90 u2227T sname S sname right left langle S_N rangle mid u2203S_R u2203R_P langle S_R S_N rangle u2208Students u2227 langle S_R 107 R_P rangle u2208Registration u2227 R_P gt 90 right I II III and IV I II and III only I II and IV only II III and IV only ,Relational Calculus,159 The binary relation R 1 1 2 1 2 2 2 3 2 4 3 1 3 2 3 3 3 4 on the set A 1 2 3 4 is reflective symmetric and transitive neither reflective nor irreflexive but transitive irreflexive symmetric and transitive irreflexive and antisymmetric ,Relations,160 Suppose A is a finite set with n elements The number of elements in the largest equivalence relation of A is a n b n 2 c 1 d n 1 ,Relations,160 Let R be a non empty relation on a collection of sets defined by _ A R_ B if and only if A cap B phi Then pick the true statement A is reflexive and transitive R is symmetric and not transitive R is an equivalence relation R is not reflexive and not symmetric ,Relations,160 Let L be a set with a relation R which is transitive anti symmetric and reflexive and for any two elements a b in L let the least upper bound lub a b and the greatest lower bound glb a b exist Which of the following is are true L is a poset L is a Boolean algebra L is a lattice None of the above ,Relations,160 Consider the following relations R1 a b iff a b is even over the set of integers R2 a b iff a b is odd over the set of integers R3 a b iff a b gt 0 over the set of non zero rational numbers R4 a b iff a b leq 2 over the set of natural numbers Which of the following statements is correct R1 and R2 are equivalence relations R3 and R4 are not R1 and R3 are equivalence relations R2 and R4 are not R1 and R4 are equivalence relations R2 and R3 are not R1 R2 R3 and R4 all are equivalence relations ,Relations,160 Amongst the properties left ext reflexivity symmetry anti symmetry transitivity right the relation R x y in N 2 x eq y satisfies _________,Relations,160 A relation R is defined on the set of integers as xRy iff x y is even Which of the following statements is true R is not an equivalence relation R is an equivalence relation having 1 equivalence class R is an equivalence relation having 2 equivalence classes R is an equivalence relation having 3 equivalence classes ,Relations,160 The number of equivalence relations of the set 1 2 3 4 is 15 16 24 4 ,Relations,160 The number of binary relations on a set with n elements is n 2 2 n 2 n 2 None of the above ,Relations,160 Prove by induction that the expression for the number of diagonals in a polygon of n sides is frac n n 3 2 Let R be a binary relation on A a b c d e f g h represented by the following two component digraph Find the smallest integers m and n such that m lt n and R m R n ,Relations,160 Mr X claims the following If a relation R is both symmetric and transitive then R is reflexive For this Mr X offers the following proof ldquo From xRy using symmetry we get yRx Now because R is transitive xRy and yRx together imply xRx Therefore R is reflexive rdquo Give an example of a relation R which is symmetric and transitive but not reflexive ,Relations,160 Let R_1 and R_2 be two equivalence relations on a set Consider the following assertions R_1 cup R_2 is an equivalence relation R_1 cap R_2 is an equivalence relation Which of the following is correct Both assertions are true Assertions i is true but assertions ii is not true Assertions ii is true but assertions i is not true Neither i nor ii is true ,Relations,160 Let R be a symmetric and transitive relation on a set A Then R is reflexive and hence an equivalence relation R is reflexive and hence a partial order R is reflexive and hence not an equivalence relation None of the above ,Relations,160 Let R be a reflexive and transitive relation on a set A Define a new relation E on A as E a b mid a b in R ext and b a in R Prove that E is an equivalence relation on A Define a reason leq on the equivalence classes of E as E_1 leq E_2 if exists a b such that a in E_1 b in E_2 ext and a b in R Prove that leq is a partal order ,Relations,160 Let F be the collection of all functions f 1 2 3 o 1 2 3 If f and g in F define an equivalence relation sim by f sim g if and only if f 3 g 3 Find the number of equivalence classes defined by sim Find the number of elements in each equivalence class ,Relations,160 Two shared resources R1 and R2 are used by processes P1 and P2 Each process has a certain priority for accessing each resource Let Tij denote the priority of Pi for accessing Rj A process Pi can snatch a resource Rh from process Pj if Tik is greater than Tjk Given the following T11 gt T21 T12 gt T22 T11 lt T21 T12 lt T22 Which of the following conditions ensures that P1 and P2 can never deadlock I and IV II and III I and II None of the above ,Resource Allocation,161 Two concurrent processes P1 and P2 want to use resources R1 and R2 in a mutually exclusive manner Initially R1 and R2 are free The programs executed by the two processes are given below Program for P1 Program for P2 S1 While R1 is busy do no op Q1 While R1 is busy do no op S2 Set R1 leftarrow busy Q2 Set R1 leftarrow busy S3 While R2 is busy do no op Q3 While R2 is busy do no op S4 Set R2 leftarrow busy Q4 Set R2 leftarrow busy S5 Use R1 and R2 Q5 Use R1 and R2 S6 Set R1 leftarrow free Q6 Set R2 leftarrow free S7 Set R2 leftarrow free Q7 Set R1 leftarrow free Is mutual exclusion guaranteed for R1 and R2 If not show a possible interleaving of the statements of P1 and P2 such mutual exclusion is violated i e both P1 and P2 use R1 and R2 at the same time Can deadlock occur in the above program If yes show a possible interleaving of the statements of P1 and P2 leading to deadlock Exchange the statements Q1 and Q3 and statements Q2 and Q4 Is mutual exclusion guaranteed now Can deadlock occur ,Resource Allocation,161 Suppose n processes P_1 dots P_n share m identical resource units which can be reserved and released one at a time The maximum resource requirement of process P_i is s_i where s_i gt 0 Which one of the following is a sufficient condition for ensuring that deadlock does not occur forall i s_i lt m forall i s_i lt n Sigma_ i 1 n s_i lt m n Sigma_ i 1 n s_i lt m imes n ,Resource Allocation,161 In a certain operating system deadlock prevention is attemped using the following scheme Each process is assigned a unique timestamp and is restarted with the same timestamp if killed Let Ph be the process holding a resource R Pr be a process requesting for the same resource R and T Ph and T Pr be their timestamps respectively The decision to wait or preempt one of the processes is based on the following algorithm if T Pr lt T Ph then kill Pr else wait Which one of the following is TRUE The scheme is deadlock free but not starvation free The scheme is not deadlock free but starvation free The scheme is neither deadlock free nor starvation free The scheme is both deadlock free and starvation free ,Resource Allocation,161 Consider the resource allocation graph in the figure Find if the system is in a deadlock state Otherwise find a safe sequence ,Resource Allocation,161 Consider the following snapshot of a system running n processes Process i is holding x_i instances of a resource R 1 leq i leq n Currently all instances of R are occupied Further for all i process i has placed a request for an additional y_i instances while holding the x_i instances it already has There are exactly two processes p and q and such that Y_p Y_q 0 Which one of the following can serve as a necessary condition to guarantee that the system is not approaching a deadlock min x_ p x_ q lt max_ k eq p q y_ k x_ p x_ q geq min_ k eq p q y_ k max x_ p x_ q gt 1 min x_ p x_ q gt 1 ,Resource Allocation,161 An operating system handles requests to resources as follows A process which asks for some resources uses them for some time and then exits the system is assigned a unique timestamp are when it starts The timestamps are monotonically increasing with time Let us denote the timestamp of a process P by TS P When a process P requests for a resource the OS does the following If no other process is currently holding the resource the OS awards the resource to P If some process Q with TS Q lt TS P is holding the resource the OS makes P wait for the resources If some process Q with TS Q gt TS P is holding the resource the OS restarts Q and awards the resources to P Restarting means taking back the resources held by a process killing it and starting it again with the same timestamp When a process releases a resource the process with the smallest timestamp if any amongst those waiting for the resource is awarded the resource Can a deadlock over arise If yes show how If not prove it Can a process P ever starve If yes show how If not prove it ,Resource Allocation,161 An operating system contains 3 user processes each requiring 2 units of resource R The minimum number of units of R such that no deadlocks will ever arise is 3 5 4 6 ,Resource Allocation,161 A single processor system has three resource types X Y and Z which are shared by three processes There are 5 units of each resource type Consider the following scenario where the column alloc denotes the number of units of each resource type allocated to each process and the column request denotes the number of units of each resource type requested by a process in order to complete execution Which of these processes will finish LAST alloc request X Y Z X Y Z P0 1 2 1 1 0 3 P1 2 0 1 0 1 2 P2 2 2 1 1 2 0 P0 P1 P2 None of the above since the system is in a deadlock ,Resource Allocation,161 A computer system uses the Banker u2019s Algorithm to deal with deadlocks Its current state is shown in the table below where P0 P1 P2 are processes and R0 R1 R2 are resources types Maximum Need Current Allocation Available R0 R1 R2 R0 R1 R2 R0 R1 R2 P0 4 1 2 P0 1 0 2 2 2 0 P1 1 5 1 P1 0 3 1 P2 1 2 3 P2 1 0 2 Show that the system can be in this state What will the system do on a request by process P0 for one unit of resource type R1 ,Resource Allocation,161 A computer has six tape drives with n processes competing for them Each process may need two drives What is the maximum value of n for the system to be deadlock free 6 5 4 3 ,Resource Allocation,161 02 Choose the correct alternatives more than one may be correct and write the corresponding letters only xi A computer system has 6 tape devices with n processes competing for them Each process may need 3 tape drives The maximum value of n for which the system is guaranteed to be deadlock free is 2 3 4 1 ,Resource Allocation,161 Consider the following proposed solution for the critical section problem There are n processes P_0 P_ n 1 In the code function ext pmax returns an integer not smaller than any of its arguments For all i t i is initialized to zero Code for P_i do c i 1 t i pmax t 0 t n 1 1 c i 0 for every j i in 0 n 1 while c j while t j 0 amp amp t j lt t i Critical Section t i 0 Remainder Section while true Which of the following is TRUE about the above solution At most one process can be in the critical section at any time The bounded wait condition is satisfied The progress condition is satisfied It cannot cause a deadlock ,Resource Allocation,161 Consider a system having m resources of the same type These resources are shared by 3 processes A B and C which have peak demands of 3 4 and 6 respectively For what value of m deadlock will not occur 7 9 10 13 15 ,Resource Allocation,161 What is the minimum size of ROM required to store the complete truth table of an 8 bit imes 8 bit multiplier 32 K imes 16 bits 64 K imes 16 bits 16 K imes 32 bits 64 K x imes 32 bits ,Rom,162 The amount of ROM needed to implement a 4 bit multiplier is 64 bits 128 bits 1 Kbits 2 Kbits ,Rom,162 A ROM is used to store the table for multiplication of two 8 bit unsigned integers The size of ROM required is 256 u2a2f 16 64 K u2a2f 8 4 K u2a2f 16 64 K u2a2f 16 ,Rom,162 Two popular routing algorithms are Distance Vector DV and Link State LS routing Which of the following are true S1 Count to infinity is a problem only with DV and not LS routing S2 In LS the shortest path algorithm is run only at one node S3 In DV the shortest path algorithm is run only at one node S4 DV requires lesser number of network messages than LS S1 S2 and S4 only S1 S3 and S4 only S2 and S3 only S1 and S4 only ,Routing,163 In a network of LANs connected by bridges packets are sent from one LAN to another through intermediate bridges Since more than one path may exist between two LANs packets may have to be routed through multiple bridges Why is the spanning tree algorithm used for bridge routing For shortest path routing between LANs For avoiding loops in the routing paths For fault tolerance For minimizing collisions ,Routing,163 Consider the following statements about the routing protocols Routing Information Protocol RIP and Oprn Shortest Path First OSPF in an IPv4 network RIP uses distance vector routing RIP packets are sent using UDP OSPF packets are sent using TCP OSPF operation is based on link state routing Which of the above statements are CORRECT I and IV only I II and III only I II and IV only II III and IV only ,Routing,163 Consider a simple graph with unit edge costs Each node in the graph represents a router Each node maintains a routing table indicating the next hop router to be used to relay a packet to its destination and the cost of the path to the destination through that router Initially the routing table is empty The routing table is synchronously updated as follows In each updation interval three tasks are performed A node determines whether its neighbours in the graph are accessible If so it sets the tentative cost to each accessible neighbour as 1 Otherwise the cost is set to u221e From each accessible neighbour it gets the costs to relay to other nodes via that neighbour as the next hop Each node updates its routing table based on the information received in the previous two steps by choosing the minimum cost For the graph given above possible routing tables for various nodes after they have stabilized are shown in the following options Identify the correct table Table for node A A B B 1 C C 1 D B 3 E C 3 F C 4 Table for node C A A 1 B B 1 C D D 1 E E 1 F E 3 Table for node B A A 1 B C C 1 D D 1 E C 2 F D 2 Table for node D A B 3 B B 1 C C 1 D E E 1 F F 1 ,Routing,163 Consider a simple graph with unit edge costs Each node in the graph represents a router Each node maintains a routing table indicating the next hop router to be used to relay a packet to its destination and the cost of the path to the destination through that router Initially the routing table is empty The routing table is synchronously updated as follows In each updation interval three tasks are performed A node determines whether its neighbours in the graph are accessible If so it sets the tentative cost to each accessible neighbour as 1 Otherwise the cost is set to u221e From each accessible neighbour it gets the costs to relay to other nodes via that neighbour as the next hop Each node updates its routing table based on the information received in the previous two steps by choosing the minimum cost Continuing from the earlier problem suppose at some time t when the costs have stabilized node A goes down The cost from node F to node A at time t 100 is gt 100 but finite infty 3 gt 3 and leq 100 ,Routing,163 An IP router implementing Classless Inter domain Routing CIDR receives a packet with address 131 23 151 76 The router s routing table has the following entries Prefix Output Interface Identifier 131 16 0 0 12 3 131 28 0 0 14 5 131 19 0 0 16 2 131 22 0 0 15 1 The identifier of the output interface on which this packet will be forwarded is ______ ,Routing,163 A group of 15 routers are interconnected in a centralized complete binary tree with a router at each tree node Router i communicates with router j by sending a message to the root of the tree The root then sends the message back down to router j The mean number of hops per message assuming all possible router pairs are equally likely is 3 4 26 4 53 5 26 ,Routing,163 In a RSA cryptosystem a participant A uses two prime numbers p 13 and q 17 to generate here public and private keys If the public key of A is 35 then the private key of A is __________ ,Rsa Security Networks,164 Consider a database that has the relation schemas EMP EmpId EmpName DeptId and DEPT DeptName DeptId Note that the DeptId can be permitted to be NULL in the relation EMP Consider the following queries on the database expressed in tuple relational calculus t exists u in EMP t EmpName u EmpName wedge forall v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId v DeptId Which of the above queries are safe I and II only I and III only II and III only I II and III ,Safe Query,165 Consider a 128 imes 10 3 bits second satellite communication link with one way propagation delay of 150 milliseconds Selective retransmission repeat protocol is used on this link to send data with a frame size of 1 kilobyte Neglect the transmission time of acknowledgement The minimum number of bits required for the sequence number field to achieve 100 utilization is ________ ,Selective Repeat,166 The P and V operations on counting semaphores where s is a counting semaphore are defined as follows P s s s 1 If s lt 0 then wait V s s s 1 If s lt 0 then wake up process waiting on s Assume that P_b and V_b the wait and signal operations on binary semaphores are provided Two binary semaphores x_b and y_b are used to implement the semaphore operations P s and V s as follows P s P_b x_b ext s s 1 ext if s lt 0 ext V_b x_b ext P_b y_b ext else V_b x_b V s P_b x_b ext s s 1 ext if s lt 0 V_b y_b ext V_b x_b The initial values of x_b and y_b are respectively 0 and 0 0 and 1 1 and 0 1 and 1 ,Semaphore,167 Fill in the blanks Semaphore operations are atomic because they are implemented within the OS _________ ,Semaphore,167 Consider the blocked set semaphore where the signaling process awakens any one of the suspended process i e Wait S If S gt 0 then S leftarrow S 1 else suspend the execution of this process Signal S If there are processes that have been suspended on semaphore S then wake any one of them else S leftarrow S 1 Consider the following solution of mutual exclusion problem using blocked set semaphores s 1 cobegin P 1 P 2 P N coend Where the task body P i is begin while true do begin lt non critical section gt Wait S lt critical section gt Signal S end end Here N is the number of concurrent processors Which of the following is true The program fails to achieve mutual exclusion of critical regions The program achieves mutual exclusion but starvation freedom is ensured only for N leq 2 The program does not ensure mutual exclusion if N geq 3 The program achieves mutual exclusion but allows starvation for any N geq 2 The program achieves mutual exclusion and starvation freedom for any N geq 1 ,Semaphore,167 Consider a non negative counting semaphore S The operation P S decrements S and V S increments S During an execution 20 P S operations and 12 V S operations are issued in some order The largest initial value of S for which at least one P S operation will remain blocked is _______,Semaphore,167 The wait and signal operations of a monitor are implemented using semaphores as follows In the following x is a condition variable mutex is a semaphore initialized to 1 x_sem is a semaphore initialized to 0 x_count is the number of processes waiting on semaphore x_sem initially 0 next is a semaphore initialized to 0 next_count is the number of processes waiting on semaphore next initially 0 The body of each procedure that is visible outside the monitor is replaced with the following P mutex body of procedure if next_count gt 0 V next else V mutex Each occurrence of x wait is replaced with the following x_count x_count 1 if next_count gt 0 V next else V mutex E1 x_count x_count 1 Each occurrence of x signal is replaced with the following if x_count gt 0 next_count next_count 1 E2 P next next_count next_count 1 For correct implementation of the monitor statements E1 and E2 are respectively P x_sem V next V next P x_sem P next V x_sem P x_sem V x_sem ,Semaphore,167 Choose the correct alternatives more than one may be correct and write the corresponding letters only At a particular time of computation the value of a counting semaphore is 7 Then 20 P operations and 15 V operations were completed on this semaphore The resulting value of the semaphore is 42 2 7 12 ,Semaphore,167 How many bytes of data can be sent in 15 seconds over a serial link with baud rate of 9600 in asynchronous mode with odd parity and two stop bits in the frame 10 000 bytes 12 000 bytes 15 000 bytes 27 000 bytes ,Serial Communication,168 In serial communication employing 8 data bits a parity bit and 2 stop bits the minimum band rate required to sustain a transfer rate of 300 characters per second is 2400 band 19200 band 4800 band 1200 band ,Serial Communication,168 The number of subsets left 1 2 dots n right with odd cardinality is ___________,Sets,169 The number of elements in the power set P S of the set S phi 1 2 3 is 2 4 8 None of the above ,Sets,169 Out of a group of 21 persons 9 eat vegetables 10 eat fish and 7 eat eggs 5 persons eat all three How many persons eat at least two out of the three dishes ,Sets,169 Let S be an infinite set and S_1 dots S_n be sets such that S_1 cup S_2 cup dots cup S_n S Then at least one of the set S_i is a finite set not more than one of the set S_i can be finite at least one of the sets S_i is an infinite not more than one of the sets S_i can be infinite None of the above ,Sets,169 Let S be a set of n elements left 1 2 n right and G a graph with 2 n vertices each vertex corresponding to a distinct subset of S Two vertices are adjacent iff the symmetric difference of the corresponding sets has exactly 2 elements Note The symmetric difference of two sets R_ 1 and R_ 2 is defined as left R_ 1 setminus R_ 2 right cup left R_ 2 setminus R_ 1 right Every vertex in G has the same degree What is the degree of a vertex in G How many connected components does G have ,Sets,169 Let P S denotes the power set of set S Which of the following is always true P P S P S P S u2229 P P S u00d8 P S u2229 S P S S u2209 P S ,Sets,169 Let A be a set with n elements Let C be a collection of distinct subsets of A such that for any two subsets S_1 and S_2 in C either S_1 subset S_2 or S_2 subset S_1 What is the maximum cardinality of C n n 1 2 n 1 1 n ,Sets,169 Let A be a finite set of size n The number of elements in the power set of A imes A is 2 2 n 2 n 2 2 n 2 2 2 n None of the above ,Sets,169 Let A B and C be non empty sets and let X A B C and Y A C B C Which one of the following is TRUE X Y X u2282 Y Y u2282 X None of these ,Sets,169 Let A and B be sets and let A c and B c denote the complements of the sets A and B The set A B cup B A cup A cap B is equal to A cup B A c cup B c A cap B A c cap B c ,Sets,169 In a class of 200 students 125 students have taken Programming Language course 85 students have taken Data Structures course 65 students have taken Computer Organization course 50 students have taken both Programming Language and Data Structures 35 students have taken both Data Structures and Computer Organization 30 students have taken both Data Structures and Computer Organization 15 students have taken all the three courses How many students have not taken any of the three courses 15 20 25 30 ,Sets,169 Give a relational algebra expression using only the minimum number of operators from u222a u2212 which is equivalent to R u2229 S ,Sets,169 Every subset of a countable set is countable State whether the above statement is true or false with reason ,Sets,169 Consider the following statements S1 There exists infinite sets A B C such that A cap B cup C is finite S2 There exists two irrational numbers x and y such that x y is rational Which of the following is true about S1 and S2 Only S1 is correct Only S2 is correct Both S1 and S2 are correct None of S1 and S2 is correct ,Sets,169 The below figure shows four D type flip flops connnected as a shift register using an XOR gate The initial state and three subsequent states for three clock pulses are also given State Q_ A Q_ B Q_ C Q_ D Initial 1 1 1 1 After the first clock 0 1 1 1 After the second clock 0 0 1 1 After the third clock 0 0 0 1 The state Q_ A Q_ B Q_ C Q_ D after the fourth clock pulse is 0000 1111 1001 1000 ,Shift Registers,170 The maximum window size for data transmission using the selective reject protocol with n ext bit frame sequence numbers is 2 n 2 n 1 2 n 1 2 n 2 ,Sliding Window,171 The distance between two stations M and N is L kilometers All frames are K bits long The propagation delay per kilometer is t seconds Let R bits second be the channel capacity Assuming that the processing delay is negligible the ext minimum number of bits for the sequence number field in a frame for maximum utilization when the ext sliding window protocol is used is lceil log_2 frac 2LtR 2K K rceil lceil log_2 frac 2LtR K rceil lceil log_2 frac 2LtR K K rceil lceil log_2 frac 2LtR 2K 2K rceil ,Sliding Window,171 Suppose that the maximum transmit window size for a TCP connection is 12000 bytes Each packet consists of 2000 bytes At some point of time the connection is in slow start phase with a current transmit window of 4000 bytes Subsequently the transmitter receives two acknowledgements Assume that no packets are lost and there are no time outs What is the maximum possible value of the current transmit window 4000 bytes 8000 bytes 10000 bytes 12000 bytes ,Sliding Window,171 Suppose that it takes 1 unit of time to transmit a packet of fixed size on a communication link The link layer uses a window flow control protocol with a window size of N packets Each packet causes an ack or a nak to be generated by the receiver and ack nak transmission times are negligible Further the round trip time on the link is equal to N units Consider time i gt N If only acks have been received till time i no naks then the goodput evaluated at the transmitter at time i in packets per unit time is 1 dfrac N i dfrac i N i 1 1 e left frac i N right ,Sliding Window,171 Station A uses 32 byte packets to transmit messages to Station B using a sliding window protocol The round trip delay between A and B is 80 milliseconds and the bottleneck bandwidth on the path between A and B is 128 kbps What is the optimal window size that A should use 20 40 160 320 ,Sliding Window,171 Station A needs to send a message consisting of 9 packets to Station B using a sliding window window size 3 and go back n error control strategy All packets are ready and immediately available for transmission If every 5th packet that A transmits gets lost but no acks from B ever get lost then what is the number of packets that A will transmit for sending the message to B 12 14 16 18 ,Sliding Window,171 In a sliding window ARQ scheme the transmitter s window size is N and the receiver s window size is M The minimum number of distinct sequence numbers required to ensure correct operation of the ARQ scheme is min M N max M N M N MN ,Sliding Window,171 Host A is sending data to host B over a full duplex link A and B are using the sliding window protocol for flow control The send and receive window sizes are 5 packets each Data packets sent only from A to B are all 1000 bytes long and the transmission time for such a packet is 50 u03bcs Acknowledgement packets sent only from B to A are very small and require negligible transmission time The propagation delay over the link is 200 mu s What is the maximum achievable throughput in this communication 7 69 imes 10 6 Bps 11 11 imes 10 6 Bps 12 33 imes 10 6 Bps 15 00 imes 10 6 Bps ,Sliding Window,171 Frames of 1000 ext bits are sent over a 10 6 bps duplex link between two hosts The propagation time is 25ms Frames are to be transmitted into this link to maximally pack them in transit within the link Let I be the minimum number of bits I that will be required to represent the sequence numbers distinctly assuming that no time gap needs to be given between transmission of two frames Suppose that the sliding window protocol is used with the sender window size of 2 I where I is the numbers of bits as mentioned earlier and acknowledgements are always piggy backed After sending 2 I frames what is the minimum time the sender will have to wait before starting transmission of the next frame Identify the closest choice ignoring the frame processing time 16ms 18ms 20ms 22ms ,Sliding Window,171 Consider a selective repeat sliding window protocol that uses a frame size of 1 KB to send data on a 1 5 Mbps link with a one way latency of 50 msec To achieve a link utilization of 60 the minimum number of bits required to represent the sequence number field is ________ ,Sliding Window,171 Consider a network connecting two systems located 8000 kilometers apart The bandwidth of the network is 500 imes 10 6 bits per second The propagation speed of the media is 4 imes 10 6 meters per second It is need to design a Go Back N sliding window protocol for this network The average packet size is 10 7 bits The network is to be used to its full capacity Assume that processing delays at nodes are negligible Then the minimum size in bits of the sequence number field has to be ______ ,Sliding Window,171 A 20 Kbps satellite link has a propagation delay of 400 ms The transmitter employs the go back n ARQ scheme with n set to 10 Assuming that each frame is 100 bytes long what is the maximum data rate possible 5 Kbps 10 Kbps 15 Kbps 20 Kbps ,Sliding Window,171 A 1Mbps satellite link connects two ground stations The altitude of the satellite is 36 504 km and speed of the signal is 3 u00d7 108 m s What should be the packet size for a channel utilization of 25 for a satellite link using go back 127 sliding window proto u00adcol Assume that the acknowledgment packets are negligible in size and that there are no errors during communication 120 bytes 60 bytes 240 bytes 90 bytes ,Sliding Window,171 Frames of 1000 bits are sent over a 10 6 bps duplex link between two hosts The propagation time is 25ms Frames are to be transmitted into this link to maximally pack them in transit within the link What is the minimum number of bits I that will be required to represent the sequence numbers distinctly Assume that no time gap needs to be given between transmission of two frames I 2 I 3 I 4 I 5 ,Sliding Window,171 A client process P needs to make a TCP connection to a server process S Consider the following situation the server process S executes a ext socket a ext bind and a ext listen system call in that order following which it is preempted Subsequently the client process P executes a ext socket system call followed by ext connect system call to connect to the server process S The server process has not executed any ext accept system call Which one of the following events could take place ext connect system call returns successfully ext connect system call blocks ext connect system call returns an error ext connect system call results in a core dump ,Sockets,172 Identify the correct order in which a server process must invoke the function calls accept bind listen and recv according to UNIX socket API listen accept bind recv bind listen accept recv bind accept listen recv accept listen bind recv ,Sockets,172 The employee information in a company is stored in the relation Employee name sex salary deptName Consider the following SQL query Select deptName From Employee Where sex u2018M u2019 Group by deptName Having avg salary gt select avg salary from Employee It returns the names of the department in which the average salary is more than the average salary in the company the average salary of male employees is more than the average salary of all male employees in the company the average salary of male male employees is more than the average salary of employees in same the department the average salary of male employees is more than the average salary in the company ,Sql,173 Suppose a database consist of the following relations SUPPLIER SCODE SNAME CITY PART PCODE PNAME PDESC CITY PROJECTS PRCODE PRNAME PRCITY SPPR SCODE PCODE PRCODE QTY Write SQL programs corresponding to the following queries Print PCODE values for parts supplied to any project in DEHLI by a supplier in DELHI Print all triples lt CITY PCODE CITY gt such that a supplier in first city supplies the specified part to a project in the second city but do not print the triples in which the two CITY values are same ,Sql,173 In SQL relations can contain null values and comparisons with null values are treated as unknown Suppose all comparisons with a null value are treated as false Which of the following pairs is not equivalent x 5 quad not not x 5 x 5 quad x gt 4 and x lt 6 where x is an integer x u2260 5 quad not x 5 none of the above ,Sql,173 In an inventory management system implemented at a trading corporation there are several tables designed to hold all the information Amongst these the following two tables hold information on which items are supplied by which suppliers and which warehouse keeps which items along with the stock level of these items Supply supplierid itemcode Inventory itemcode warehouse stocklevel For a specific information required by the management following SQL query has been written Select distinct STMP supplierid From Supply as STMP Where not unique Select ITMP supplierid From Inventory Supply as ITMP Where STMP supplierid ITMP supplierid And ITMP itemcode Inventory itemcode And Inventory warehouse Nagpur For the warehouse at Nagpur this query will find all suppliers who do not supply any item supply exactly one item supply one or more items supply two or more items ,Sql,173 Given relations r w x and s y z the result of select distinct w x from r s is guaranteed to be same as r provided r has no duplicates and s is non empty r and s have no duplicates s has no duplicates and r is non empty r and s have the same number of tuples ,Sql,173 Consider two tables in a relational database with columns and rows as follows Table Student Roll_no Name Dept_id 1 ABC 1 2 DEF 1 3 GHI 2 4 JKL 3 Table Department Dept_id Dept_name 1 A 2 B 3 C Roll_no is the primary key of the Student table Dept_id is the primary key of the Department table and Student Dept_id is a foreign key from Department Dept_id What will happen if we try to execute the following two SQL statements update Student set Dept_id Null where Roll_on 1 update Department set Dept_id Null where Dept_id 1 Both i and ii will fail i will fail but ii will succeed i will succeed but ii will fail Both i and ii will succeed ,Sql,173 Consider the set of relations shown below and the SQL query that follows Students Roll_number Name Date_of_birth Courses Course_number Course_name Instructor Grades Roll_number Course_number Grade Select distinct Name from Students Courses Grades where Students Roll_number Grades Roll_number and Courses Instructor Korth and Courses Course_number Grades Course_number and Grades Grade A Which of the following sets is computed by the above query Names of students who have got an A grade in all courses taught by Korth Names of students who have got an A grade in all courses Names of students who have got an A grade in at least one of the courses taught by Korth None of the above ,Sql,173 Consider the set of relations EMP Employee no Dept no Employee name Salary DEPT Dept no Dept name Location Write an SQL query to Find all employees names who work in departments located at u2018Calcutta u2019 and whose salary is greater than Rs 50 000 ,Sql,173 Consider the following relational database employees eno ename address basic salary projects pno pname nos of staffs allotted working pno eno pjob The queries regarding data in the above database are formulated below in SQL Describe in ENGLISH sentences the two queries that have been posted SELECT ename FROM employees WHERE eno IN SELECT eno FROM working GROUP BY eno HAVING COUNT SELECT COUNT FROM projects SELECT pname FROM projects WHERE pno IN SELECT pno FROM projects MINUS SELECT DISTINCT pno FROM working ,Sql,173 Consider a relation geq which represents greater than or equal to that is x y in geq only if y geq x create table geq ib integer not null ub integer not null primary key ib foreign key ub references geq on delete cascade Which of the following is possible if tuple x y is deleted A tuple z w with z gt y is deleted A tuple z w with z gt x is deleted A tuple z w with w lt x is deleted The deletion of x y is prohibited ,Sql,173 Consider a relation examinee regno name score where regno is the primary key to score is a real number Write a relational algebra using Pi sigma rho imes to find the list of names which appear more than once in examinee ,Sql,173 A table T1 in a relational database has the following rows and columns roll no marks 1 10 2 20 3 30 4 Null The following sequence of SQL statements was successfully executed on table T1 Update T1 set marks marks 5 Select avg marks from T1 What is the output of the select statement 18 75 20 25 Null ,Sql,173 A relational database contains two tables student and department in which student table has columns roll_no name and dept_id and department table has columns dept_id and dept_name The following insert statements were executed successfully to populate the empty tables Insert into department values 1 Mathematics Insert into department values 2 Physics Insert into student values l Navin 1 Insert into student values 2 Mukesh 2 Insert into student values 3 Gita 1 How many rows and columns will be retrieved by the following SQL statement Select from student department 0 row and 4 columns 3 rows and 4 columns 3 rows and 5 columns 6 rows and 5 columns ,Sql,173 The relation book title price contains the titles and prices of different books Assuming that no two books have the same price what does the following SQL query list select title from book as B where select count from book as T where T price gt B price lt 5 Titles of the four most expensive books Title of the fifth most inexpensive book Title of the fifth most expensive book Titles of the five most expensive books ,Sql,173 The result evaluating the postfix expression 10 5 60 6 8 is 284 213 142 71 ,Stack,174 The postfix expression for the infix expression A B C D F D E is AB CD F D E ABCD F DE A B CD F DE A BCD F DE ,Stack,174 The following postfix expression with single digit operands is evaluated using a stack 8 2 3 hat 2 3 5 1 Note that hat is the exponentiation operator The top two elements of the stack after the first is evaluated are 6 1 5 7 3 2 1 5 ,Stack,174 The best data structure to check whether an arithmetic expression has balanced parentheses is a queue stack tree list ,Stack,174 Suppose a stack implementation supports in addition to PUSH and POP an operation REVERSE which reverses the order of the elements on the stack To implement a queue using the above stack implementation show how to implement ENQUEUE using a single operation and DEQUEUE using a sequence of 3 operations The following post fix expression containing single digit operands and arithmetic operators and is evaluated using a stack 5 2 3 4 5 2 Show the contents of the stack After evaluating 5 2 3 4 After evaluating 5 2 3 4 5 2 At the end of evaluation ,Stack,174 Suppose a stack implementation supports an instruction REVERSE which reverses the order of elements on the stack in addition to the PUSH and POP instructions Which one of the following statements is TRUE with respect to this modified stack A queue cannot be implemented using this stack A queue can be implemented where ENQUEUE takes a single instruction and DEQUEUE takes a sequence of two instructions A queue can be implemented where ENQUEUE takes a sequence of three instructions and DEQUEUE takes a single instruction A queue can be implemented where both ENQUEUE and DEQUEUE take a single instruction each ,Stack,174 Let S be a stack of size n geq1 Starting with the empty stack suppose we push the first n natural numbers in sequence and then perform n pop operations Assume that Push and Pop operations take X seconds each and Y seconds elapse between the end of one such stack operation and the start of the next operation For m geq1 define the stack life of m as the time elapsed from the end of Push m to the start of the pop operation that removes m from S The average stack life of an element of this stack is n X Y 3Y 2X n X Y X Y 2X ,Stack,174 Consider the following C program include lt stdio h gt define EOF 1 void push int push the argument on the stack int pop void pop the top of the stack void flagError int main int c m n r while c getchar EOF if isdigit c push c else if c c m pop n pop r c n m n m push r else if c flagError printf c pop What is the output of the program for the following input 5 2 3 3 2 15 25 30 150 ,Stack,174 Choose the correct alternatives more than one may be correct and write the corresponding letters only The following sequence of operations is performed on a stack PUSH 10 PUSH 20 POP PUSH 10 PUSH 20 POP POP POP PUSH 20 POP The sequence of values popped out is 20 10 20 10 20 20 20 10 10 20 10 20 20 10 20 20 20 10 20 10 ,Stack,174 Assume that the operators imes are left associative and hat is right associative The order of precedence from highest to lowest is hat imes The postfix expression corresponding to the infix expression a b imes c d hat e hat f is abc imes def hat hat abc imes de hat f hat ab c imes d e hat f hat a imes bc hat hat def ,Stack,174 A single array A 1 MAXSIZE is used to implement two stacks The two stacks grow from opposite ends of the array Variables top1 and top2 top lt top 2 point to the location of the topmost element in each of the stacks If the space is to be used efficiently the condition for u201cstack full u201d is top1 MAXSIZE 2 and top2 MAXSIZE 2 1 top1 top2 MAXSIZE top1 MAXSIZE 2 or top2 MAXSIZE top1 top2 1 ,Stack,174 A program attempts to generate as many permutations as possible of the string abcd by pushing the characters a b c d in the same order onto a stack but it may pop off the top character at any time Which one of the following strings CANNOT be generated using this program abcd dcba cbad cabd ,Stack,174 A function f defined on stacks of integers satisfies the following properties f u2205 0 and f push S i max f S 0 i for all stacks S and integers i If a stack S contains the integers 2 3 2 1 2 in order from bottom to top what is f S 6 4 3 2 ,Stack,174 Consider the C program below include lt stdio h gt int A stkTop int stkFunc int opcode int val static int size 0 stkTop 0 switch opcode case 1 size val break case 0 if stkTop lt size A stkTop val break default if stkTop return A stkTop return 1 int main int B 20 A B stkTop 1 stkFunc 1 10 stkFunc 0 5 stkFunc 0 10 printf d stkFunc 1 0 stkFunc 1 0 The value printed by the above program is ________ ,Stack,174 Based on the given statements select the most appropriate option to solve the given question If two floors in a certain building are 9 feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building Statements I Each step is 3 4 foot high II Each step is 1 foot wide Statements I alone is sufficient but statement II alone is not sufficient Statements II alone is sufficient but statement I alone is not sufficient Both statements together are sufficient but neither statement alone is sufficient Statements I and II together are not sufficient ,Statement Sufficiency,175 Consider a Boolean function f w x y z Suppose that exactly one of its inputs is allowed to change at a time If the function happens to be true for two input vectors i_ 1 left langle w_ 1 x_ 1 y_ 1 z_ 1 right rangle and i_ 2 left langle w_ 2 x_ 2 y_ 2 z_ 2 right rangle we would like the function to remain true as the input changes from i_ 1 to i_ 2 i_ 1 and i_ 2 differ in exactly one bit position without becoming false momentarily Let f w x y z sum 5 7 11 12 13 15 Which of the following cube covers of f will ensure that the required property is satisfied overline w xz wx overline y x overline y z xyz wyz wxy overline w xz wyz wx overline y overline z xz w overline x yz wx overline y wyz wxz overline w xz x overline y z xyz ,Static Hazard,176 The values of parameters for the Stop and Wait ARQ protocol are as given below Bit rate of the transmission channel 1 Mbps Propagation delay from sender to receiver 0 75 ms Time to process a frame 0 25 ms Number of bytes in the information frame 1980 Number of bytes in the acknowledge frame 20 Number of overhead bytes in the information frame 20 Assume there are no transmission errors Then the transmission efficiency expressed in percentage of the Stop and Wait ARQ protocol for the above parameters is _____________ correct to 2 decimal places ,Stop And Wait,177 Suppose that the stop and wait protocol is used on a link with a bit rate of 64 kilobits per second and 20 milliseconds propagation delay Assume that the transmission time for the acknowledgement and the processing time at nodes are negligible Then the minimum frame size in bytes to achieve a link utilization of at least 50 is_________________ ,Stop And Wait,177 On a wireless link the probability of packet error is 0 2 A stop and wait protocol is used to transfer data across the link The channel condition is assumed to be independent from transmission to transmission What is the average number of transmission attempts required to transfer 100 packets 100 125 150 200 ,Stop And Wait,177 A sender uses the Stop and Wait ARQ protocol for reliable transmission of frames Frames are of size 1000 bytes and the transmission rate at the sender is 80 Kbps 1 Kbps 1000 bits second Size of an acknowledgement is 100 bytes and the transmission rate at the receiver is 8 Kbps The one way propagation delay is 100 milliseconds Assuming no frame is lost the sender throughout is ________ bytes second ,Stop And Wait,177 Consider the following relations A B and C A Id Name Age 12 Arun 60 15 Shreya 24 99 Rohit 11 B Id Name Age 15 Shreya 24 25 Hari 40 98 Rohit 20 99 Rohit 11 C Id Phone Area 10 2200 02 99 2100 01 How many tuples does the result of the following SQL query contain SELECT A Id FROM A WHERE A Age gt ALL SELECT B Age FROM B WHERE B Name lsquo Arun rsquo 4 3 0 1 ,Sub Queries,178 Consider the following relational schema ext Suppliers underline ext sid integer ext sname string city string street string ext Parts underline ext pid integer ext pname string color string ext Catalog underline ext sid integer pid integer ext cost real Consider the following relational query on the above database SELECT S sname FROM Suppliers S WHERE S sid NOT IN SELECT C sid FROM Catalog C WHERE C pid NOT IN SELECT P pid FROM Parts P WHERE P color lt gt blue Assume that relations corresponding to the above schema are not empty Which one of the following is the correct interpretation of the above query Find the names of all suppliers who have supplied a non blue part Find the names of all suppliers who have not supplied a non blue part Find the names of all suppliers who have supplied only non blue part Find the names of all suppliers who have not supplied only blue parts ,Sub Queries,178 Two computers C1 and C2 are configured as follows C1 has IP address 203 197 2 53 and netmask 255 255 128 0 C2 has IP address 203 197 75 201 and netmask 255 255 192 0 Which one of the following statements is true C1 and C2 both assume they are on the same network C2 assumes C1 is on same network but C1 assumes C2 is on a different network C1 assumes C2 is on same network but C2 assumes C1 is on a different network C1 and C2 both assume they are on different networks ,Subnetting,179 The subnet mask for a particular network is 255 255 31 0 Which of the following pairs of ext IP addresses could belong to this network 172 57 88 62 and 172 56 87 23 10 35 28 2 and 10 35 29 4 191 203 31 87 and 191 234 31 88 128 8 129 43 and 128 8 161 55 ,Subnetting,179 The routing table of a router is shown below Destination Subnet Mask Interface 128 75 43 0 255 255 255 0 Eth0 128 75 43 0 255 255 255 128 Eth1 192 12 17 5 255 255 255 255 Eth3 Default Eth2 On which interface will the router forward packets addressed to destinations 128 75 43 16 and 192 12 17 10 respectively Eth1 and Eth2 Eth0 and Eth2 Eth0 and Eth3 Eth1 and Eth3 ,Subnetting,179 The address of a class B host is to be split into subnets with a 6 bit subnet number What is the maximum number of subnets and the maximum number of hosts in each subnet 62 subnets and 262142 hosts 64 subnets and 262142 hosts 62 subnets and 1022 hosts 64 subnets and 1024 hosts ,Subnetting,179 Suppose computers A and B have IP addresses 10 105 1 113 and 10 105 1 91 respectively and they both use same netmask N Which of the values of N given below should not be used if A and B should belong to the same network 255 255 255 0 255 255 255 128 255 255 255 192 255 255 255 224 ,Subnetting,179 In the network 200 10 11 144 27 the fourth octet in decimal of the last IP address of the network which can be assigned to a host is _____ ,Subnetting,179 If a class B network on the Internet has a subnet mask of 255 255 248 0 what is the maximum number of hosts per subnet 1022 1023 2046 2047 ,Subnetting,179 Host X has IP address 192 168 1 97 and is connected through two routers R1 and R2 to an u00adother host Y with IP address 192 168 1 80 Router R1 has IP addresses 192 168 1 135 and 192 168 1 110 R2 has IP addresses 192 168 1 67 and 192 168 1 155 The netmask used in the network is 255 255 255 224 Which IP address should X configure its gateway as 192 168 1 67 192 168 1 110 192 168 1 135 192 168 1 155 ,Subnetting,179 Host X has IP address 192 168 1 97 and is connected through two routers R1 and R2 to an u00adother host Y with IP address 192 168 1 80 Router R1 has IP addresses 192 168 1 135 and 192 168 1 110 R2 has IP addresses 192 168 1 67 and 192 168 1 155 The netmask used in the network is 255 255 255 224 Given the information above how many distinct subnets are guaranteed to already exist in the network 1 2 3 6 ,Subnetting,179 Consider the following routing table at an IP router Network No Net Mask Next Hop 128 96 170 0 255 255 254 0 Interface 0 128 96 168 0 255 255 254 0 Interface 1 128 96 166 0 255 255 254 0 R2 128 96 164 0 255 255 252 0 R3 0 0 0 0 Default R4 For each IP address in Group I Identify the correct choice of the next hop from Group II using the entries from the routing table above Group I Group II i 128 96 171 92 a Interface 0 ii 128 96 167 151 b Interface 1 iii 128 96 163 151 c R2 iv 128 96 164 121 d R3 e R4 i a ii c iii e iv d i a ii d iii b iv e i b ii c iii d iv e i b ii c iii e iv d ,Subnetting,179 An organization has a class B network and wishes to form subnets for 64 departments The subnet mask would be 255 255 0 0 255 255 64 0 255 255 128 0 255 255 252 0 ,Subnetting,179 An Internet Service Provider ISP has the following chunk of CIDR based IP addresses available with it 245 248 128 0 20 The ISP wants to give half of this chunk of addresses to Organization A and a quarter to Organization B while retaining the remaining with itself Which of the following is a valid allocation of addresses to A and B A 245 248 136 0 21 ext and 245 248 128 0 22 B 245 248 128 0 21 ext and u00a0245 248 128 0 22 C 245 248 132 0 22 ext and u00a0245 248 132 0 21 D 245 248 136 0 24 ext and u00a0245 248 132 0 21 ,Subnetting,179 A subnetted Class B network has the following broadcase address 144 16 95 255 Its subnet mask is necessarily 255 255 224 0 is necessarily 255 255 240 0 is necessarily 255 255 248 0 could be any one of 255 255 224 0 255 255 240 0 255 255 248 0 ,Subnetting,179 A subnet has been assigned a subnet mask of 255 255 255 192 What is the maximum number of hosts that can belong to this subnet 14 30 62 126 ,Subnetting,179 A company has a class C network address of 204 204 204 0 It wishes to have three subnets one with 100 hosts and two with 50 hosts each Which one of the following options represents a feasible set of subnet address subnet mask pairs 204 204 204 128 255 255 255 192 204 204 204 0 255 255 255 128 204 204 204 64 255 255 255 128 204 204 204 0 255 255 255 192 204 204 204 192 255 255 255 128 204 204 204 64 255 255 255 128 204 204 204 128 255 255 255 128 204 204 204 192 255 255 255 192 204 204 204 224 255 255 255 192 204 204 204 128 255 255 255 128 204 204 204 64 255 255 255 192 204 204 204 0 255 255 255 192 ,Subnetting,179 Use the patterns given to prove that sum limits_ i 0 n 1 2i 1 n 2 You are not permitted to employ induction Use the result obtained in a to prove that sum limits_ i 1 n i frac n n 1 2 ,Summation,180 Let P sum_ substack 1 le i le 2k i odd i and Q sum_ substack 1 le i le 2k i even i where k is a positive integer Then P Q k P Q k P Q P Q 2k ,Summation,180 sum limits_ x 1 99 frac 1 x x 1 __________________ ,Summation,180 Choose the correct alternatives more than one may be correct and write the corresponding letters only Advantage of synchronous sequential circuits over asynchronous ones is faster operation ease of avoiding problems due to hazards lower hardware requirement better noise immunity none of the above ,Synchronous Asynchronous Circuits,181 Consider the circuit given below with initial state Q_0 1 Q_1 Q_2 0 The state of the circuit is given by the value 4Q_2 2Q_1 Q_0 Which one of the following is correct state sequence of the circuit 1 3 4 6 7 5 2 1 2 5 3 7 6 4 1 2 7 3 5 6 4 1 6 5 7 2 3 4 ,Synchronous Circuit,182 Design a synchronous counter to go through the following states 1 4 2 3 1 4 2 3 1 4 dots ,Synchronous Counter,183 System calls are usually invoked by using a software interrupt polling an indirect jump a privileged instruction ,System Calls,184 What values of x y and z satisfy the following system of linear equations begin bmatrix 1 amp 2 amp 3 1 amp 3 amp 4 2 amp 2 amp 3 end bmatrix begin bmatrix x y z end bmatrix begin bmatrix 6 8 12 end bmatrix x 6 y 3 z 2 x 12 y 3 z 4 x 6 y 6 z 4 x 12 y 3 z 0 ,System Of Equations,185 The following system of equations x_1 x_2 2x_3 1 x_1 2x_2 3x_3 2 x_1 4x_2 u03b1x_3 4 has a unique solution The only possible value s for u03b1 is are 0 either 0 or 1 one of 0 1 or 1 any real number ,System Of Equations,185 Let c_ 1 c_ n be scalars not all zero such that sum_ i 1 n c_ i a_ i 0 where a_ i are column vectors in R n Consider the set of linear equations Ax b where A left a_ 1 a_ n right and b sum_ i 1 n a_ i The set of equations has a unique solution at x J_ n where J_ n denotes a n dimensional vector of all 1 no solution infinitely many solutions finitely many solutions ,System Of Equations,185 If the following system has non trivial solution u00a0 px qy rz 0 qx ry pz 0 rx py qz 0 then which one of the following options is TRUE u00a0 p q r 0 ext or p q r p q r 0 ext or p q r p q r 0 ext or p q r p q r 0 ext or p q r ,System Of Equations,185 How many solutions does the following system of linear equations have x 5y 1 x y 2 x 3y 3 infinitely many two distinct solutions unique none ,System Of Equations,185 Consider the system each consisting of m linear equations in n variables If m lt n then all such systems have a solution If m gt n then none of these systems has a solution If m n then there exists a system which has a solution Which one of the following is CORRECT I II and III are true Only II and III are true Only III is true None of them is true ,System Of Equations,185 Consider the following system of linear equations left begin array ccc 2 amp 1 amp 4 4 amp 3 amp 12 1 amp 2 amp 8 end array right left begin array ccc x y z end array right left begin array ccc alpha 5 7 end array right Notice that the second and the third columns of the coefficient matrix are linearly dependent For how many values of alpha does this system of equations have infinitely many solutions 0 1 2 3 ,System Of Equations,185 Consider the following system of linear equations 2x_1 x_2 3x_3 1 3x_1 2x_2 5x_3 2 x_1 4x_2 x_3 3 The system of equations has no solution a unique solution more than one but a finite number of solutions an infinite number of solutions ,System Of Equations,185 Consider the following system of equations 3x 2y 1 4x 7z 1 x y z 3 x 2y 7z 0 The number of solutions for this system is ______________,System Of Equations,185 Let Ax b be a system of linear equations where A is an m imes n matrix and b is a m imes 1 column vector and X is an n imes1 column vector of unknowns Which of the following is false The system has a solution if and only if both A and the augmented matrix Ab have the same rank If m lt n and b is the zero vector then the system has infinitely many solutions If m n and b is a non zero vector then the system has a unique solution The system will have only a trivial solution when m n b is the zero vector and ext rank A n ,System Of Equations,185 Consider the following set of equations x 2y 5 4x 8y 12 3x 6y 3z 15 This set has unique solution has no solution has finite number of solutions has infinite number of solutions ,System Of Equations,185 The three way handshake for TCP connection establishment is shown below Which of the following statements are TRUE S1 Loss of SYN ACK from the server will not establish a connection S2 Loss of ACK from the client cannot establish the connection S3 The server moves LISTEN u2192 SYN_RCVD u2192 SYN_SENT u2192 ESTABLISHED in the state machine on no packet loss S4 The server moves LISTEN u2192 SYN_RCVD u2192 ESTABLISHED in the state machine on no packet loss S 2 and S 3 only S 1 and S 4 only S 1 and S 3 only S 2 and S 4 only ,Tcp,186 In TCP a unique sequence number is assigned to each byte word segment message ,Tcp,186 Identify the correct sequence in which the following packets are transmitted on the network by a host when a browser requests a webpage from a remote server assuming that the host has just been restarted HTTP GET request DNS query TCP SYN DNS query HTTP GET request TCP SYN DNS query TCP SYN HTTP GET request TCP SYN DNS query HTTP GET request ,Tcp,186 Consider the following statements about the timeout value used in TCP The timeout value is set to the RTT Round Trip Time measured during TCP connection establishment for the entire duration of the connection Appropriate RTT estimation algorithm is used to set the timeout value of a TCP connection Timeout value is set to twice the propagation delay from the sender to the receiver Which of the following choices hold i is false but ii and iii are true i and iii are false but ii is title i and ii are false but iii is true i ii and iii are false ,Tcp,186 Consider a TCP connection in a state where there are no outstanding ACK s The sender sends two segments back to back The sequence numbers of the first and second segments are 230 and 290 respectively The first segment was lost but the second segment was received correctly by the receiver Let X be the amount of data carried in the first segment in bytes and Y be the ACK number sent by the receiver The values of X and Y in that order are 60 and 290 230 and 291 60 and 231 60 and 230 ,Tcp,186 Consider a TCP client and a TCP server running on two different machines After completing data transfer the TCP client calls close to terminate the connection and a FIN segment is sent to the TCP server Server side TCP responds by sending an ACK which is received by the client side TCP As per the TCP connection state diagram RFC 793 in which state does the client side TCP connection wait for the FIN from the server side TCP LAST ACK TIME WAIT FIN WAIT 1 FIN WAIT 2 ,Tcp,186 Assume that the bandwidth for a TCP connection is 1048560 bits sec Let alpha be the value of RTT in milliseconds rounded off to the nearest integer after which the TCP window scale option is needed Let beta be the maximum possible window size with window scale option Then the values of alpha and beta are 63 milliseconds 65535 imes 2 14 63 milliseconds 65535 imes 2 16 500 milliseconds 65535 imes 2 14 500 milliseconds 65535 imes 2 16 ,Tcp,186 Suppose two hosts use a TCP connection to transfer a large file Which of the following statements is are FALSE with respect to the TCP connection If the sequence number of a segment is m then the sequence number of the subsequent segment is always m 1 If the estimated round trip time at any given point of time is t sec the value of the retransmission timeout is always set to greater than or equal to t sec The size of the advertised window never changes during the course of the TCP connection The number of unacknowledged bytes at the sender is always less than or equal to the advertised window III only I and III only I and IV only II and IV only ,Tcp,186 Consider the following statements TCP connections are full duplex TCP has no option for selective acknowledgement TCP connections are message streams Only I is correct Only I and III are correct Only II and III are correct All of I II and III are correct ,Tcp,186 After Rajendra Chola returned from his voyage to Indonesia he ________ to visit the temple in Thanjavur was wishing is wishing wished had wished ,Tenses,187 Threads of a process share global variables but not heap heap but not global variables neither global variables nor heap both heap and global variables ,Threads,188 Consider the following statements with respect to user level threads and kernel supported threads context switch is faster with kernel supported threads for user level threads a system call can block the entire process Kernel supported threads can be scheduled independently User level threads are transparent to the kernel Which of the above statements are true II III and IV only II and III only I and III only I and II only ,Threads,188 Consider the following statements about user level threads and kernel level threads Which one of the following statements is FALSE Context switch time is longer for kernel level threads than for user level threads User level threads do not need any hardware support Related kernel level threads can be scheduled on different processors in a multi processor system Blocking one kernel level thread blocks all related threads ,Threads,188 A thread is usually defined as a light weight process because an Operating System OS maintains smaller data structure for a thread than for a process In relation to this which of the following statement is correct OS maintains only scheduling and accounting information for each thread OS maintains only CPU registers for each thread OS does not maintain virtual memory state for each thread OS does not maintain a separate stack for each thread ,Threads,188 In a database system unique timestamps are assigned to each transaction using Lamport s logical clock Let TS T_ 1 and TS T_ 2 be the timestamps of transactions T_ 1 and T_ 2 respectively Besides T_ 1 holds a lock on the resource R and T_ 2 has requested a conflicting lock on the same resource R The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp if TS T_ 2 lt TS T_ 1 then T_ 1 is killed else T_ 2 waits Assume any transaction that is not killed terminates eventually Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks The database system is both deadlock free and starvation free The database system is deadlock free but not starvation free The database system is starvation free but not deadlock free The database system is neither deadlock free nor starvation free ,Timestamp Ordering,189 For a host machine that uses the token bucket algorithm for congestion control the token bucket has a capacity of 1 mega byte and the maximum output rate is 20 mega bytes per second Tokens arrive at a rate to sustain output at a rate of 10 mega bytes per second The token bucket is currently full and the machine needs to send 12 mega bytes of data The minimum time required to transmit the data is _____________ seconds ,Token Bucket,190 A computer on a 10 Mbps network is regulated by a token bucket The token bucket is filled at a rate of 2 Mbps It is initially filled to capacity with 16 Megabits What is the maximum duration for which the computer can transmit at the full 10 Mbps 1 6 seconds 2 seconds 5 seconds 8 seconds ,Token Bucket,190 Which level of locking provides the highest degree of concurrency in a relational database Page Table Row Page table and row level locking allow the same degree of concurrency ,Transaction And Concurrency,191 In a data flow diagram the segment shown below is identified as having transaction flow characteristics with p2 identified as the transaction center A first level architectural design of this segment will result in a set of process modules with an associated invocation sequence The most appropriate architecture is p1 invokes p2 p2 invokes either p3 or p4 or p5 p2 invokes p1 and then invokes p3 or p4 or p5 A new module Tc is defined to control the transaction flow This module Tc first invokes pl and then invokes p2 p2 in turn invokes p3 or p4 or p5 A new module Tc is defined to control the transaction flow This module Tc invokes p2 p2 invokes p1 and then invokes p3 or p4 or p5 ,Transactions,192 For the schedule given below which of the following is correct 1 Read A 2 Read B 3 Write A 4 Read A 5 Write A 6 Write B 7 Read B 8 Write B This schedule is serializable and can occur in a scheme using 2PL protocol This schedule is serializable but cannot occur in a scheme using 2PL protocol This schedule is not serializable but can occur in a scheme using 2PL protocol This schedule is not serializable and cannot occur in a scheme using 2PL protocol ,Transactions,192 Consider two transactions T_1 and T_2 and four schedules S_1 S_2 S_3 S_4 of T_1 and T_2 as given below T_1 R_1 x W_1 x W_1 y T_2 R_2 x R_2 y W_2 y S_1 R_1 x R_2 x R_2 y W_1 x W_1 y W_2 y S_2 R_1 x R_2 x R_2 y W_1 x W_2 y W_1 y S_3 R_1 x W_1 x R_2 x W_1 y R_2 y W_2 y S_4 R_2 x R_2 y R_1 x W_1 x W_1 y W_2 y Which of the above schedules are conflict serializable S_1 ext and S_2 S_2 ext and S_3 S_3 only S_4 only ,Transactions,192 Consider three data items D1 D2 and D3 and the following execution schedule of transactions T1 T2 and T3 In the diagram R D and W D denote the actions reading and writing the data item D respectively Which of the following statements is correct The schedule is serializable as T2 T3 T1 The schedule is serializable as T2 T1 T3 The schedule is serializable as T3 T2 T1 The schedule is not serializable ,Transactions,192 Consider the following two transactions T1 and T2 T1 read A T2 read B read B read A if A 0 then B u2190 B 1 if B u2260 0 then A u2190 A 1 write B write A Which of the following schemes using shared and exclusive locks satisfy the requirements for strict two phase locking for the above transactions S1 lock S A S2 lock S B read A read B lock S B lock S A read B read A if A 0 if B u2260 0 then B u2190 B 1 then A u2190 A 1 write B write A commit commit unlock A unlock B unlock B unlock A S1 lock X A S2 lock X B read A read B lock X B lock X A read B read A if A 0 if B u2260 0 then B u2190 B 1 then A u2190 A 1 write B write A unlock A unlock A commit commit unlock B unlock A S1 lock S A S2 lock S B read A read B lock X B lock X A read B read A if A 0 if B u2260 0 then B u2190 B 1 then A u2190 A 1 write B write A unlock A unlock B commit commit unlock B unlock A S1 lock S A S2 lock S B read A read B lock X B lock X A read B read A if A 0 if B u2260 0 then B u2190 B 1 then A u2190 A 1 write B write A unlock A unlock A unlock B unlock B commit commit ,Transactions,192 Consider the following three schedules of transactions T1 T2 and T3 Notation In the following NYO represents the action Y R for read W for write performed by transac u00adtion N on object O S1 2RA 2WA 3RC 2WB 3WA 3WC 1RA 1RB 1WA 1WB S2 3RC 2RA 2WA 2WB 3WA 1RA 1RB 1WA 1WB 3WC S3 2RZ 3RC 3WA 2WA 2WB 3WC 1RA 1RB 1WA 1WB Which of the following statements is TRUE S1 S2 and S3 are all conflict equivalent to each other No two of S1 S2 and S3 are conflict equivalent to each other S2 is conflict equivalent to S3 but not to S1 S1 is conflict equivalent to S2 but not to S3 ,Transactions,192 Consider the following schedules involving two transactions Which one of the following statements is TRUE S_1 r_1 X r_1 Y r_2 X r_2 Y w_2 Y w_1 X S_2 r_1 X r_2 X r_2 Y w_2 Y r_1 Y w_1 X Both S_1 and S_2 are conflict serializable S_1 is conflict serializable and S_2 is not conflict serializable S_1 is not conflict serializable and S_2 is conflict serializable Both S_1 and S_2 are not conflict serializable ,Transactions,192 Consider the following schedule S of transactions T1 and T2 T1 T2 Read A A A 10 Read A Temp 0 2 A Write A Read B Write A Read B B B 10 Write B B B Temp Write B Which of the following is TRUE about the schedule S S is serializable only as T1 T2 S is serializable only as T2 T1 S is serializable both as T1 T2 and T2 T1 S is serializable either as T1 or as T2 ,Transactions,192 Consider the following log sequence of two transactions on a bank account with initial balance 12000 that transfer 2000 to a mortgage payment and then apply a 5 interest T1 start T1 B old 1200 new 10000 T1 M old 0 new 2000 T1 commit T2 start T2 B old 10000 new 10500 T2 commit Suppose the database system crashes just before log record 7 is written When the system is restarted which one statement is true of the recovery procedure We must redo log record 6 to set B to 10500 We must undo log record 6 to set B to 10000 and then redo log records 2 and 3 We need not redo log records 2 and 3 because transaction T1 has committed We can apply redo and undo operations in arbitrary order because they are idempotent ,Transactions,192 Amongst the ACID properties of a transaction the Durability property requires that the changes made to the database by a successful transaction persist Except in case of an Operating System crash Except in case of a Disk crash Except in case of a power failure Always even if there is a failure of any kind ,Transactions,192 A company maintains records of sales made by its salespersons and pays them commission based on each individual s total sales made in a year This data is maintained in a table with following schema salesinfo salespersonid totalsales commission In a certain year due to better business results the company decides to further reward its salespersons by enhancing the commission paid to them as per the following formula If commission lt 50000 enhance it by 2 If 50000 lt commission lt 100000 enhance it by 4 If commission gt 100000 enhance it by 6 The IT staff has written three different SQL scripts to calculate enhancement for each slab each of these scripts is to run as a separate transaction as follows T1 Update salesinfo Set commission commission 1 02 Where commission lt 50000 T2 Update salesinfo Set commission commission 1 04 Where commission gt 50000 and commission is lt 100000 T3 Update salesinfo Set commission commission 1 06 Where commission gt 100000 Which of the following options of running these transactions will update the commission of all salespersons correctly Execute T1 followed by T2 followed by T3 Execute T2 followed by T3 T1 running concurrently throughout Execute T3 followed by T2 T1 running concurrently throughout Execute T3 followed by T2 followed by T1 ,Transactions,192 Which one of the following is NOT a part of the ACID properties of database transactions Atomicity Consistency Isolation Deadlock freedom ,Transactions,192 Which of the following scenarios may lead to an irrecoverable error in a database system A transaction writes a data item after it is read by an uncommitted transaction A transaction reads a data item after it is read by an uncommitted transaction A transaction reads a data item after it is written by a committed transaction A transaction reads a data item after it is written by an uncommitted transaction ,Transactions,192 Consider the following two phase locking protocol Suppose a transaction T accesses for read or write operations a certain set of objects O_1 O_k This is done in the following manner ext Step 1 T acquires exclusive locks to O_1 O_k in increasing order of their addresses ext Step 2 The required operations are performed ext Step 3 All locks are released This protocol will guarantee serializability and deadlock freedom guarantee neither serializability nor deadlock freedom guarantee serializability but not deadlock freedom guarantee deadlock freedom but not serializability ,Transactions,192 Fig 7 shows a B tree where only key values are indicated in the records Each block can hold upto three records A record with a key value 34 is inserted into the B tree Obtain the modified B tree after insertion ,Tree,193 The number of leaf nodes in a rooted tree of n nodes with each node having 0 or 3 children is frac n 2 frac n 1 3 frac n 1 2 frac 2n 1 3 ,Trees,194 Level order traversal of a rooted tree can be done by starting from the root and performing preorder traversal in order traversal depth first search breadth first search ,Trees,194 Let G V E be a graph Define xi G sum limits_d i_d d where i_d is the number of vertices of degree d in G If S and T are two different trees with xi S xi T then mid S mid 2 mid T mid mid S mid mid T mid 1 mid S mid mid T mid mid S mid mid T mid 1 ,Trees,194 In a complete k ary tree every internal node has exactly k children The number of leaves in such a tree with n internal node is nk n 1 k 1 n k 1 1 n k 1 ,Trees,194 Consider the pseudocode given below The function DoSomething takes as argument a pointer to the root of an arbitrary tree represented by the leftMostChild rightSibling representation Each node of the tree is of type treeNode ypedef struct treeNode treeptr struct treeNode treeptr leftMostChild rightSibling int DoSomething treeptr tree int value 0 if tree NULL if tree gt leftMostChild NULL value 1 else value DoSomething tree gt leftMostChild value value DoSomething tree gt rightSibling return value When the pointer to the root of a tree is passed as the argument to DoSomething the value returned by the function corresponds to the number of internal nodes in the tree height of the tree number of nodes without a right sibling in the tree number of leaf nodes in the tree ,Trees,194 Consider the following rooted tree with the vertex labeled P as the root The order in which the nodes are visited during an in order traversal of the tree is SQPTRWUV SQPTUWRV SQPTWUVR SQPTRUWV ,Trees,194 Consider the following 2 3 4 tree i e B tree with a minimum degree of two in which each data item is a letter The usual alphabetical ordering of letters is used in constructing the tree What is the result of inserting G in the above tree None of the above ,Trees,194 Consider all possible trees with n nodes Let k be the number of nodes with degree greater than 1 in a given tree What is the maximum possible value of k ,Trees,194 Choose the correct alternatives more than one may be correct and write the corresponding letters only A 2 3 tree is such that All internal nodes have either 2 or 3 children All paths from root to the leaves have the same length The number of internal nodes of a 2 3 tree having 9 leaves could be 4 5 6 7 ,Trees,194 A complete n ary tree is one in which every node has 0 or n sons If x is the number of internal nodes of a complete n ary tree the number of leaves in it is given by x n 1 1 xn 1 xn 1 x n 1 ,Trees,194 A complete n ary tree is a tree in which each node has n children or no children Let I be the number of internal nodes and L be the number of leaves in a complete n ary tree If L 41 and I 10 what is the value of n 3 4 5 6 ,Trees,194 A 3 ext ary tree is a tree in which every internal node has exactly three children Use induction to prove that the number of leaves in a 3 ext ary tree with n internal nodes is 2 n 1 ,Trees,194 Derive a recurrence relation for the size of the smallest AVL tree with height h What is the size of the smallest AVL tree with height 8 ,Trees,194 The aim of the following question is to prove that the language M M is the code of the Turing Machine which irrespective of the input halts and outputs a 1 is undecidable This is to be done by reducing from the language M x M halts on x which is known to be undecidable In parts a and b describe the 2 main steps in the construction of M In part c describe the key property which relates the behaviour of M on its input w to the behaviour of M on x On input w what is the first step that M must make On input w based on the outcome of the first step what is the second step M must make What key property relates the behaviour of M on w to the behaviour of M on x ,Turing Machine,195 Let langle M rangle be the encoding of a Turing machine as a string over Sigma left 0 1 right Let L left langle M rangle mid M ext is a Turing machine ext that accepts a string of length 2014 right Then L is decidable and recursively enumerable undecidable but recursively enumerable undecidable and not recursively enumerable decidable but not recursively enumerable ,Turing Machine,195 Let a decision problem X be defined as follows X Given a Turing machine M over Sigma and any word w in Sigma does M loop forever on w You may assume that the halting problem of Turing machine is undecidable but partially decidable Show that X is undecidable Show that X is not even partially decidable ,Turing Machine,195 Define languages L_0 and L_1 as follows L_0 langle M w 0 rangle mid M ext halts on w L_1 langle M w 1 rangle mid M ext does not halts on w Here langle M w i rangle is a triplet whose first component M is an encoding of a Turing Machine second component w is a string and third component i is a bit Let L L_0 u222a L_1 Which of the following is true L is recursively enumerable but L is not L is recursively enumerable but L is not Both L and L are recursive Neither L nor L is recursively enumerable ,Turing Machine,195 Consider the following languages L_ 1 left left langle M right rangle mid M ext takes at least 2016 steps on some input right L_ 2 left left langle M right rangle mid M ext takes at least 2016 steps on all inputs right and L_ 3 left left langle M right rangle mid M ext accepts epsilon right where for each Turing machine M left langle M right rangle denotes a specific encoding of M Which one of the following is TRUE L_ 1 is recursive and L_ 2 L_ 3 are not recursive L_ 2 is recursive and L_ 1 L_ 3 are not recursive L_ 1 L_ 2 are recursive and L_ 3 is not recursive L_ 1 L_ 2 L_ 3 are recursive ,Turing Machine,195 A single tape Turing Machine M has two states q0 and q1 of which q0 is the starting state The tape alphabet of M is 0 1 B and its input alphabet is 0 1 The symbol B is the blank symbol used to indicate end of an input string The transition function of M is described in the following table 0 1 B q0 q1 1 R q1 1 R Halt q1 q1 1 R q0 1 L q0 B L The table is interpreted as illustrated below The entry q1 1 R in row q0 and column 1 signifies that if M is in state q0 and reads 1 on the current page square then it writes 1 on the same tape square moves its tape head one position to the right and transitions to state q1 Which of the following statements is true about M M does not halt on any string in 0 1 M does not halt on any string in 00 1 M halts on all strings ending in a 0 M halts on all strings ending in a 1 ,Turing Machine,195 L_1 is a recursively enumerable language over Sigma An algorithm A effectively enumerates its words as omega_1 omega_2 omega_3 dots Define another language L_2 over Sigma cup left ext right as left w_i ext w_j mid w_i w_j in L_1 i lt j right Here is new symbol Consider the following assertions S_1 L_1 is recursive implies L_2 is recursive S_2 L_2 is recursive implies L_1 is recursive Which of the following statements is true Both S_1 and S_2 are true S_1 is true but S_2 is not necessarily true S_2 is true but S_1 is not necessarily true Neither is necessarily true ,Turing Machine,195 The transport layer protocols used for real time multimedia file transfer DNS and email respectively are A TCP UDP UDP and TCP B UDP TCP TCP and UDP C UDP TCP UDP and TCP D TCP UDP TCP and UDP,Udp,196 Packets of the same session may be routed through different paths in TCP but not UDP TCP and UDP UDP but not TCP Neither TCP nor UDP ,Udp,196 Consider socket API on a Linux machine that supports connected UDP sockets A connected UDP socket is a UDP socket on which connect function has already been called Which of the following statements is are CORRECT A connected UDP socket can be used to communicate with multiple peers simultaneously A process can successfully call connect function again for an already connected UDP socket I only II only Both I and II Neither I nor II ,Udp,196 A program on machine X attempts to open a UDP connection to port 5376 on a machine Y and a TCP connection to port 8632 on machine Z However there are no applications listening at the corresponding ports on Y and Z An ICMP Port Unreachable error will be generated by Y but not Z Z but not Y Neither Y nor Z Both Y and Z ,Udp,196 Suppose you break a stick of unit length at a point chosen uniformly at random Then the expected length of the shorter stick is ________ ,Uniform Distribution,197 Consider a selection of the form sigma_ A leq 100 r where r is a relation with 1000 tuples Assume that the attribute values for A among the tuples are uniformly distributed in the interval 0 500 Which one of the following options is the best estimate of the number of tuples returned by the given selection query 50 100 150 200 ,Uniform Distribution,197 A point is randomly selected with uniform probability in the X Y plane within the rectangle with corners at 0 0 1 0 1 2 and 0 2 If p is the length of the position vector of the point the expected value of p 2 is left dfrac 2 3 right quad 1 left dfrac 4 3 right left dfrac 5 3 right ,Uniform Distribution,197 A user level process in Unix traps the signal sent on a Ctrl C input and has a signal handling routine that saves appropriate files before terminating the process When a Ctrl C input is given to this process what is the mode in which the signal handling routine executes User mode Kernel mode Superuser mode Privileged mode ,User Modes,198 Let u and v be two vectors in R2 whose Euclidean norms satisfy left u right 2 left v right What is the value of alpha such that w u alpha v bisects the angle between u and v 2 frac 1 2 1 frac 1 2 ,Vector Space,199 If V_1 and V_2 are 4 dimensional subspaces of a 6 dimensional vector space V then the smallest possible dimension of V_1 cap V_2 is _____ ,Vector Space,199 Consider the set of column vectors defined by X left x in R 3 mid x_1 x_2 x_3 0 ext where x T left x_1 x_2 x_3 right T right Which of the following is TRUE left left 1 1 0 right T left 1 0 1 right T right is a basis for the subspace X left left 1 1 0 right T left 1 0 1 right T right is a linearly independent set but it does not span X and therefore is not a basis of X X is not a subspace of R 3 None of the above ,Vector Space,199 Alexander turned his attention towards India since he had conquered Persia Which one of the statements below is logically valid and can be inferred from the above sentence Alexander would not have turned his attention towards India had he not conquered Persia Alexander was not ready to rest on his laurels and wanted to march to India Alexander was not completely in control of his army and could command it to move towards India Since Alexander s kingdom extended to Indian borders after the conquest of Persia he was keen to move further ,Verbal Reasoning,200 u201cWe lived in a culture that denied any merit to literary works considering them important only when they were handmaidens to something seemingly more urgent u2013 namely ideology This was a country where all gestures even the most private were interpreted in political terms u201d The author u2019s belief that ideology is not as important as literature is revealed by the word u2018culture u2019 u2018seemingly u2019 u2018urgent u2019 u2018political u2019 ,Verbal Reasoning,200 Let G be a simple graph with 20 vertices and 100 edges The size of the minimum vertex cover of G is 8 Then the size of the maximum independent set of G is 12 8 less than 8 more than 12 ,Vertex Cover,201 For the IEEE 802 11 MAC protocol for wireless communication which of the following statements is are TRUE I At least three non overlapping channels are available for transmissions II The RTS CTS mechanism is used for collision detection III Unicast frames are ACKed All I II and III I and III only II and III only II only ,Wifi,202 Select the pair of best expresses a relationship similar to that expressed in the pair Children Pediatrician Adult Orthopaedist Females Gynaecologist Kidney Nephrologist Skin Dermatologist ,Word Pairs,203 A transporter receives the same number of orders each day Currently he has some pending orders backlog to be shipped If he uses 7 trucks then at the end of the 4th day he can clear all the orders Alternatively if he uses only 3 trucks then all the orders are cleared at the end of the 10th day What is the minimum number of trucks required so that there will be no pending order at the end of 5th day A 4 B 5 C 6 D 7,Work Time,204 In the working set strategy which of the following is done by the operating system to prevent thrashing It initiates another process if there are enough extra frames It selects a process to suspend if the sum of the sizes of the working sets exceeds the total number of available frames I only II only Neither I nor II Both I and II ,Working Set,205 What happens when a bit string is XORed with itself n times as shown left B oplus B oplus B oplus B dots n ext times right complements when n is even complements when n is odd divides by 2 n always remains unchanged when n is even ,Xor,206 If x is real and mid x 2 2x 3 mid 11 then possible values of mid x 3 x 2 x mid include 2 4 2 14 4 52 14 52 ,Absolute Value,0 The expression large frac x y x y 2 is equal to The maximum of x and y The minimum of x and y 1 None of the above ,Absolute Value,0 If x is real and mid x 2 2x 3 mid 11 then possible values of mid x 3 x 2 x mid include 2 4 2 14 4 52 14 52 ,Absolute Value,0 The expression large frac x y x y 2 is equal to The maximum of x and y The minimum of x and y 1 None of the above ,Absolute Value,0 The expression large frac x y x y 2 is equal to The maximum of x and y The minimum of x and y 1 None of the above ,Absolute Value,0 If x is real and mid x 2 2x 3 mid 11 then possible values of mid x 3 x 2 x mid include 2 4 2 14 4 52 14 52 ,Absolute Value,0 If mid 4X 7 mid 5 then the values of 2 mid X mid mid X mid is quad 2 left dfrac 1 3 right left dfrac 1 2 right 3 left dfrac 3 2 right 9 left dfrac 2 3 right 9 ,Absolute Value,0 If mid 4X 7 mid 5 then the values of 2 mid X mid mid X mid is quad 2 left dfrac 1 3 right left dfrac 1 2 right 3 left dfrac 3 2 right 9 left dfrac 2 3 right 9 ,Absolute Value,0 If mid 4X 7 mid 5 then the values of 2 mid X mid mid X mid is quad 2 left dfrac 1 3 right left dfrac 1 2 right 3 left dfrac 3 2 right 9 left dfrac 2 3 right 9 ,Absolute Value,0 If x is real and mid x 2 2x 3 mid 11 then possible values of mid x 3 x 2 x mid include 2 4 2 14 4 52 14 52 ,Absolute Value,0 If mid 4X 7 mid 5 then the values of 2 mid X mid mid X mid is quad 2 left dfrac 1 3 right left dfrac 1 2 right 3 left dfrac 3 2 right 9 left dfrac 2 3 right 9 ,Absolute Value,0 The expression large frac x y x y 2 is equal to The maximum of x and y The minimum of x and y 1 None of the above ,Absolute Value,0 An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above ,Abstract Data Type,1 An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above ,Abstract Data Type,1 An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above ,Abstract Data Type,1 An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above ,Abstract Data Type,1 An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above ,Abstract Data Type,1 An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above ,Abstract Data Type,1 An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above ,Abstract Data Type,1 An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above ,Abstract Data Type,1 An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above ,Abstract Data Type,1 An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above ,Abstract Data Type,1 An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above ,Abstract Data Type,1 An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above ,Abstract Data Type,1 An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above ,Abstract Data Type,1 An Abstract Data Type ADT is same as an abstract class a data type that cannot be instantiated a data type for which only the operations defined on it can be used but none else all of the above ,Abstract Data Type,1 Consider the ALU shown below If the operands are in 2 u2019s complement representation which of the following operations can be performed by suitably setting the control lines K and C_0 only and u2013 denote addition and subtraction respectively A B and A u2013 B but not A 1 A B and A 1 but not A u2013 B A B but not A u2013 B or A 1 A B and A u2013 B and A 1 ,Adder,2 Consider an eight bit ripple carry adder for computing the sum of A and B where A and B are integers represented in 2 s complement form If the decimal value of A is one the decimal value of B that leads to the longest latency for the sum to stabilize is ___________,Adder,2 Fill in the blanks In the two bit full adder subtractor unit shown in below figure when the switch is in position 2 ___________ using _________ arithmetic ,Adder,2 The number of full and half adders required to add 16 bit numbers is 8 half adders 8 full adders 1 half adder 15 full adders 16 half adders 0 full adders 4 half adders 12 full adders ,Adder,2 A 4 bit carry look ahead adder which adds two 4 bit numbers is designed using AND OR NOT NAND NOR gates only Assuming that all the inputs are available in both complemented and uncomplemented forms and the delay of each gate is one time unit what is the overall propagation delay of the adder Assume that the carry network has been implemented using two level AND OR logic 4 time units 6 time units 10 time units 12 time units ,Adder,2 Consider a carry look ahead adder for adding two n bit integers built using gates of fan in at most two The time to perform addition using this adder is Theta 1 Theta log n Theta sqrt n Theta n ,Adder,2 The number of full and half adders required to add 16 bit numbers is 8 half adders 8 full adders 1 half adder 15 full adders 16 half adders 0 full adders 4 half adders 12 full adders ,Adder,2 A 4 bit carry look ahead adder which adds two 4 bit numbers is designed using AND OR NOT NAND NOR gates only Assuming that all the inputs are available in both complemented and uncomplemented forms and the delay of each gate is one time unit what is the overall propagation delay of the adder Assume that the carry network has been implemented using two level AND OR logic 4 time units 6 time units 10 time units 12 time units ,Adder,2 Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable ,Aliasing,3 Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable ,Aliasing,3 Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable ,Aliasing,3 Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable ,Aliasing,3 Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable ,Aliasing,3 Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable ,Aliasing,3 Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable ,Aliasing,3 Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable ,Aliasing,3 Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable ,Aliasing,3 Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable ,Aliasing,3 Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable ,Aliasing,3 Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable ,Aliasing,3 Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable ,Aliasing,3 Aliasing in the context of programming languages refers to multiple variables having the same memory location multiple variables having the same value multiple variables having the same identifier multiple uses of the same variable ,Aliasing,3 The maximum gate delay for any output to appear in an array multiplier for multiplying two n bit numbers is O n 2 O n O log n O 1 ,Array Multiplier,4 The maximum gate delay for any output to appear in an array multiplier for multiplying two n bit numbers is O n 2 O n O log n O 1 ,Array Multiplier,4 Consider an array multiplier for multiplying two n bit numbers If each gate in the circuit has a unit delay the total delay of the multiplier is Theta 1 Theta log n Theta n Theta n 2 ,Array Multiplier,4 The maximum gate delay for any output to appear in an array multiplier for multiplying two n bit numbers is O n 2 O n O log n O 1 ,Array Multiplier,4 Consider an array multiplier for multiplying two n bit numbers If each gate in the circuit has a unit delay the total delay of the multiplier is Theta 1 Theta log n Theta n Theta n 2 ,Array Multiplier,4 Consider an array multiplier for multiplying two n bit numbers If each gate in the circuit has a unit delay the total delay of the multiplier is Theta 1 Theta log n Theta n Theta n 2 ,Array Multiplier,4 Consider an array multiplier for multiplying two n bit numbers If each gate in the circuit has a unit delay the total delay of the multiplier is Theta 1 Theta log n Theta n Theta n 2 ,Array Multiplier,4 Consider an array multiplier for multiplying two n bit numbers If each gate in the circuit has a unit delay the total delay of the multiplier is Theta 1 Theta log n Theta n Theta n 2 ,Array Multiplier,4 Consider an array multiplier for multiplying two n bit numbers If each gate in the circuit has a unit delay the total delay of the multiplier is Theta 1 Theta log n Theta n Theta n 2 ,Array Multiplier,4 Consider an array multiplier for multiplying two n bit numbers If each gate in the circuit has a unit delay the total delay of the multiplier is Theta 1 Theta log n Theta n Theta n 2 ,Array Multiplier,4 Consider an array multiplier for multiplying two n bit numbers If each gate in the circuit has a unit delay the total delay of the multiplier is Theta 1 Theta log n Theta n Theta n 2 ,Array Multiplier,4 Consider an array multiplier for multiplying two n bit numbers If each gate in the circuit has a unit delay the total delay of the multiplier is Theta 1 Theta log n Theta n Theta n 2 ,Array Multiplier,4 The maximum gate delay for any output to appear in an array multiplier for multiplying two n bit numbers is O n 2 O n O log n O 1 ,Array Multiplier,4 An n imes n array v is defined as follows v left i j right i j for all i j i leq n 1 leq j leq n The sum of the elements of the array v is 0 n 1 n 2 3n 2 n 2 frac left n 1 right 2 ,Arrays,5 A program P reads in 500 integers in the range 0 100 representing the scores of 500 students It then prints the frequency of each score above 50 What would be the best way for P to store the frequencies An array of 50 numbers An array of 100 numbers An array of 500 numbers A dynamically allocated array of 550 numbers ,Arrays,5 The procedure given below is required to find and replace certain characters inside an input character string supplied in array A The characters to be replaced are supplied in array oldc while their respective replacement characters are supplied in array newc Array A has a fixed length of five characters while arrays oldc and newc contain three characters each However the procedure is flawed void find_and_replace char A char oldc char newc for int i 0 i lt 5 i for int j 0 j lt 3 j if A i oldc j A i newc j The procedure is tested with the following four test cases oldc u201cabc u201d newc u201cdab u201d oldc u201ccde u201d newc u201cbcd u201d oldc u201cbca u201d newc u201ccda u201d oldc u201cabc u201d newc u201cbac u201d If array A is made to hold the string u201c abcde u201d which of the above four test cases will be successful in exposing the flaw in this procedure None 2 only 3 and 4 only 4 only ,Arrays,5 A B tree index is to be built on the Name attribute of the relation STUDENT Assume that all the student names are of length 8 bytes disk blocks are of size 512 bytes and index pointers are of size 4 bytes Given the scenario what would be the best choice of the degree i e number of pointers per node of the B tree 16 42 43 44 ,B Tree,6 Suppose a fair six sided die is rolled once If the value on the die is 1 2 or 3 the die is rolled a second time What is the probability that the sum total of values that turn up is at least 6 dfrac 10 21 dfrac 5 12 dfrac 2 3 dfrac 1 6 ,Bayes Theorem,7 An automobile plant contracted to buy shock absorbers from two suppliers X and Y X supplies 60 and Y supplies 40 of the shock absorbers All shock absorbers are subjected to a quality test The ones that pass the quality test are considered reliable Of X u2019s shock absorbers 96 are reliable Of Y u2019s shock absorbers 72 are reliable The probability that a randomly chosen shock absorber which is found to be reliable is made by Y is A 0 288 B 0 334 C 0 667 D 0 720,Bayes Theorem,7 Suppose a fair six sided die is rolled once If the value on the die is 1 2 or 3 the die is rolled a second time What is the probability that the sum total of values that turn up is at least 6 dfrac 10 21 dfrac 5 12 dfrac 2 3 dfrac 1 6 ,Bayes Theorem,7 An automobile plant contracted to buy shock absorbers from two suppliers X and Y X supplies 60 and Y supplies 40 of the shock absorbers All shock absorbers are subjected to a quality test The ones that pass the quality test are considered reliable Of X u2019s shock absorbers 96 are reliable Of Y u2019s shock absorbers 72 are reliable The probability that a randomly chosen shock absorber which is found to be reliable is made by Y is A 0 288 B 0 334 C 0 667 D 0 720,Bayes Theorem,7 Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1 blue ball A ball is selected as follows i select a box ii choose a ball from the selected box such that each ball in the box is equally likely to be chosen The probabilities of selecting boxes P and Q are dfrac 1 3 and dfrac 2 3 respectively Given that a ball selected in the above process is a red ball the probability that it came from the box P is dfrac 4 19 dfrac 5 19 dfrac 2 9 dfrac 19 30 ,Bayes Theorem,7 Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1 blue ball A ball is selected as follows i select a box ii choose a ball from the selected box such that each ball in the box is equally likely to be chosen The probabilities of selecting boxes P and Q are dfrac 1 3 and dfrac 2 3 respectively Given that a ball selected in the above process is a red ball the probability that it came from the box P is dfrac 4 19 dfrac 5 19 dfrac 2 9 dfrac 19 30 ,Bayes Theorem,7 Suppose a fair six sided die is rolled once If the value on the die is 1 2 or 3 the die is rolled a second time What is the probability that the sum total of values that turn up is at least 6 dfrac 10 21 dfrac 5 12 dfrac 2 3 dfrac 1 6 ,Bayes Theorem,7 An automobile plant contracted to buy shock absorbers from two suppliers X and Y X supplies 60 and Y supplies 40 of the shock absorbers All shock absorbers are subjected to a quality test The ones that pass the quality test are considered reliable Of X u2019s shock absorbers 96 are reliable Of Y u2019s shock absorbers 72 are reliable The probability that a randomly chosen shock absorber which is found to be reliable is made by Y is A 0 288 B 0 334 C 0 667 D 0 720,Bayes Theorem,7 Suppose a fair six sided die is rolled once If the value on the die is 1 2 or 3 the die is rolled a second time What is the probability that the sum total of values that turn up is at least 6 dfrac 10 21 dfrac 5 12 dfrac 2 3 dfrac 1 6 ,Bayes Theorem,7 Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1 blue ball A ball is selected as follows i select a box ii choose a ball from the selected box such that each ball in the box is equally likely to be chosen The probabilities of selecting boxes P and Q are dfrac 1 3 and dfrac 2 3 respectively Given that a ball selected in the above process is a red ball the probability that it came from the box P is dfrac 4 19 dfrac 5 19 dfrac 2 9 dfrac 19 30 ,Bayes Theorem,7 Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1 blue ball A ball is selected as follows i select a box ii choose a ball from the selected box such that each ball in the box is equally likely to be chosen The probabilities of selecting boxes P and Q are dfrac 1 3 and dfrac 2 3 respectively Given that a ball selected in the above process is a red ball the probability that it came from the box P is dfrac 4 19 dfrac 5 19 dfrac 2 9 dfrac 19 30 ,Bayes Theorem,7 An automobile plant contracted to buy shock absorbers from two suppliers X and Y X supplies 60 and Y supplies 40 of the shock absorbers All shock absorbers are subjected to a quality test The ones that pass the quality test are considered reliable Of X u2019s shock absorbers 96 are reliable Of Y u2019s shock absorbers 72 are reliable The probability that a randomly chosen shock absorber which is found to be reliable is made by Y is A 0 288 B 0 334 C 0 667 D 0 720,Bayes Theorem,7 A binary operation oplus on a set of integers is defined as x oplus y x 2 y 2 Which one of the following statements is TRUE about oplus A Commutative but not associative B Both commutative and associative C Associative but not commutative D Neither commutative nor associative,Binary Operation,8 The number of possible commutative binary operations that can be defined on a set of n elements for a given n is ___________ ,Binary Operation,8 On the set N of non negative integers the binary operation ______ is associative and non commutative ,Binary Operation,8 The number of possible commutative binary operations that can be defined on a set of n elements for a given n is ___________ ,Binary Operation,8 The number of possible commutative binary operations that can be defined on a set of n elements for a given n is ___________ ,Binary Operation,8 A binary operation oplus on a set of integers is defined as x oplus y x 2 y 2 Which one of the following statements is TRUE about oplus A Commutative but not associative B Both commutative and associative C Associative but not commutative D Neither commutative nor associative,Binary Operation,8 The binary operator u2260 is defined by the following truth table p q p u2260 q 0 0 0 0 1 1 1 0 1 1 1 0 Which one of the following is true about the binary operator u2260 Both commutative and associative Commutative but not associative Not commutative but associative Neither commutative nor associative ,Binary Operation,8 Suppose that we have numbers between 1 and 100 in a binary search tree and want to search for the number 55 Which of the following sequences CANNOT be the sequence of nodes examined 10 75 64 43 60 57 55 90 12 68 34 62 45 55 9 85 47 68 43 57 55 79 14 72 56 16 53 55 ,Binary Search Tree,9 A Binary Search Tree BST stores values in the range 37 to 573 Consider the following sequence of keys 81 537 102 439 285 376 305 52 97 121 195 242 381 472 142 248 520 386 345 270 307 550 149 507 395 463 402 270 Suppose the BST has been unsuccessfully searched for key 273 Which all of the above sequences list nodes in the order in which we could have encountered them in the search II and III only I and III only III and IV only III only ,Binary Search Tree,9 For each element in a set of size 2n an unbiased coin is tossed The 2n coin tosses are independent An element is chosen if the corresponding coin toss was a head The probability that exactly n elements are chosen is frac 2n mathrm C _n 4 n frac 2n mathrm C _n 2 n frac 1 2n mathrm C _n frac 1 2 ,Binomial Distribution,11 An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same Assuming that the trials are independent the expected number of tosses is 3 4 5 6 ,Binomial Distribution,11 For each element in a set of size 2n an unbiased coin is tossed The 2n coin tosses are independent An element is chosen if the corresponding coin toss was a head The probability that exactly n elements are chosen is frac 2n mathrm C _n 4 n frac 2n mathrm C _n 2 n frac 1 2n mathrm C _n frac 1 2 ,Binomial Distribution,11 An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same Assuming that the trials are independent the expected number of tosses is 3 4 5 6 ,Binomial Distribution,11 A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail respectively The probability that two such randomly generated strings are not identical is frac 1 2 n 1 frac 1 n frac 1 n 1 frac 1 2 n ,Binomial Distribution,11 A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail respectively The probability that two such randomly generated strings are not identical is frac 1 2 n 1 frac 1 n frac 1 n 1 frac 1 2 n ,Binomial Distribution,11 An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same Assuming that the trials are independent the expected number of tosses is 3 4 5 6 ,Binomial Distribution,11 For each element in a set of size 2n an unbiased coin is tossed The 2n coin tosses are independent An element is chosen if the corresponding coin toss was a head The probability that exactly n elements are chosen is frac 2n mathrm C _n 4 n frac 2n mathrm C _n 2 n frac 1 2n mathrm C _n frac 1 2 ,Binomial Distribution,11 When a coin is tossed the probability of getting a Head is p 0 lt p lt 1 Let N be the random variable denoting the number of tosses till the first Head appears including the toss where the Head appears Assuming that successive tosses are independent the expected value of N is dfrac 1 p dfrac 1 1 p dfrac 1 p 2 dfrac 1 1 p 2 ,Binomial Distribution,11 When a coin is tossed the probability of getting a Head is p 0 lt p lt 1 Let N be the random variable denoting the number of tosses till the first Head appears including the toss where the Head appears Assuming that successive tosses are independent the expected value of N is dfrac 1 p dfrac 1 1 p dfrac 1 p 2 dfrac 1 1 p 2 ,Binomial Distribution,11 For each element in a set of size 2n an unbiased coin is tossed The 2n coin tosses are independent An element is chosen if the corresponding coin toss was a head The probability that exactly n elements are chosen is frac 2n mathrm C _n 4 n frac 2n mathrm C _n 2 n frac 1 2n mathrm C _n frac 1 2 ,Binomial Distribution,11 Let x_ 1 u2295 x_ 2 u2295 x_ 3 u2295 x_ 4 0 where x_ 1 x_ 2 x_ 3 x_ 4 are Boolean variables and u2295 is the XOR operator Which one of the following must always be TRUE x_ 1 x_ 2 x_ 3 x_ 4 0 x_ 1 x_ 3 x_ 2 0 bar x _ 1 u2295 bar x _ 3 bar x _ 2 u2295 bar x _ 4 x_ 1 x_ 2 x_ 3 x_ 4 0 ,Boolean Algebra,12 For x in 0 1 let lnot x denote the negation of x that is lnot x begin cases 1 amp mbox iff x 0 0 amp mbox iff x 1 end cases If x in 0 1 n then lnot x denotes the component wise negation of x that is lnot x _i biggl lnot x_i mid i in 1 n biggr Consider a circuit C computing a function f 0 1 n o 0 1 using AND land OR lor and NOT lnot gates Let D be the circuit obtained from C by replacing each AND gate by an OR gate and replacing each OR gate by an AND Suppose D computes the function g Which of the following is true for all inputs x g x lnot f x g x f x land f lnot x g x f x lor f lnot x g x lnot f lnot x None of the above ,Boolean Algebra,12 Let x_ 1 u2295 x_ 2 u2295 x_ 3 u2295 x_ 4 0 where x_ 1 x_ 2 x_ 3 x_ 4 are Boolean variables and u2295 is the XOR operator Which one of the following must always be TRUE x_ 1 x_ 2 x_ 3 x_ 4 0 x_ 1 x_ 3 x_ 2 0 bar x _ 1 u2295 bar x _ 3 bar x _ 2 u2295 bar x _ 4 x_ 1 x_ 2 x_ 3 x_ 4 0 ,Boolean Algebra,12 The simultaneous equations on the Boolean variables x y z and w x y z 1 xy 0 xz w 1 xy bar z bar w 0 have the following solution for x y z and w respectively 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 ,Boolean Algebra,12 For x in 0 1 let lnot x denote the negation of x that is lnot x begin cases 1 amp mbox iff x 0 0 amp mbox iff x 1 end cases If x in 0 1 n then lnot x denotes the component wise negation of x that is lnot x _i biggl lnot x_i mid i in 1 n biggr Consider a circuit C computing a function f 0 1 n o 0 1 using AND land OR lor and NOT lnot gates Let D be the circuit obtained from C by replacing each AND gate by an OR gate and replacing each OR gate by an AND Suppose D computes the function g Which of the following is true for all inputs x g x lnot f x g x f x land f lnot x g x f x lor f lnot x g x lnot f lnot x None of the above ,Boolean Algebra,12 For x in 0 1 let lnot x denote the negation of x that is lnot x begin cases 1 amp mbox iff x 0 0 amp mbox iff x 1 end cases If x in 0 1 n then lnot x denotes the component wise negation of x that is lnot x _i biggl lnot x_i mid i in 1 n biggr Consider a circuit C computing a function f 0 1 n o 0 1 using AND land OR lor and NOT lnot gates Let D be the circuit obtained from C by replacing each AND gate by an OR gate and replacing each OR gate by an AND Suppose D computes the function g Which of the following is true for all inputs x g x lnot f x g x f x land f lnot x g x f x lor f lnot x g x lnot f lnot x None of the above ,Boolean Algebra,12 The total number of Boolean functions which can be realised with four variables is 4 17 256 65 536 ,Boolean Algebra,12 For x in 0 1 let lnot x denote the negation of x that is lnot x begin cases 1 amp mbox iff x 0 0 amp mbox iff x 1 end cases If x in 0 1 n then lnot x denotes the component wise negation of x that is lnot x _i biggl lnot x_i mid i in 1 n biggr Consider a circuit C computing a function f 0 1 n o 0 1 using AND land OR lor and NOT lnot gates Let D be the circuit obtained from C by replacing each AND gate by an OR gate and replacing each OR gate by an AND Suppose D computes the function g Which of the following is true for all inputs x g x lnot f x g x f x land f lnot x g x f x lor f lnot x g x lnot f lnot x None of the above ,Boolean Algebra,12 The simultaneous equations on the Boolean variables x y z and w x y z 1 xy 0 xz w 1 xy bar z bar w 0 have the following solution for x y z and w respectively 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 ,Boolean Algebra,12 The total number of Boolean functions which can be realised with four variables is 4 17 256 65 536 ,Boolean Algebra,12 The simultaneous equations on the Boolean variables x y z and w x y z 1 xy 0 xz w 1 xy bar z bar w 0 have the following solution for x y z and w respectively 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 ,Boolean Algebra,12 What values of A B C and D satisfy the following simultaneous Boolean equations overline A AB 0 AB AC AB A overline C CD overline C D A 1 B 0 C 0 D 1 A 1 B 1 C 0 D 0 A 1 B 0 C 1 D 1 A 1 B 0 C 0 D 0 ,Boolean Expressions,13 Choose the correct alternatives more than one may be correct and write the corresponding letters only The operation which is commutative but not associative is AND OR EX OR NAND ,Boolean Operations,14 Choose the correct alternatives more than one may be correct and write the corresponding letters only The operation which is commutative but not associative is AND OR EX OR NAND ,Boolean Operations,14 Choose the correct alternatives more than one may be correct and write the corresponding letters only The operation which is commutative but not associative is AND OR EX OR NAND ,Boolean Operations,14 Choose the correct alternatives more than one may be correct and write the corresponding letters only The operation which is commutative but not associative is AND OR EX OR NAND ,Boolean Operations,14 Choose the correct alternatives more than one may be correct and write the corresponding letters only The operation which is commutative but not associative is AND OR EX OR NAND ,Boolean Operations,14 Choose the correct alternatives more than one may be correct and write the corresponding letters only The operation which is commutative but not associative is AND OR EX OR NAND ,Boolean Operations,14 Choose the correct alternatives more than one may be correct and write the corresponding letters only The operation which is commutative but not associative is AND OR EX OR NAND ,Boolean Operations,14 Choose the correct alternatives more than one may be correct and write the corresponding letters only The operation which is commutative but not associative is AND OR EX OR NAND ,Boolean Operations,14 Choose the correct alternatives more than one may be correct and write the corresponding letters only The operation which is commutative but not associative is AND OR EX OR NAND ,Boolean Operations,14 Choose the correct alternatives more than one may be correct and write the corresponding letters only The operation which is commutative but not associative is AND OR EX OR NAND ,Boolean Operations,14 Choose the correct alternatives more than one may be correct and write the corresponding letters only The operation which is commutative but not associative is AND OR EX OR NAND ,Boolean Operations,14 Choose the correct alternatives more than one may be correct and write the corresponding letters only The operation which is commutative but not associative is AND OR EX OR NAND ,Boolean Operations,14 Choose the correct alternatives more than one may be correct and write the corresponding letters only The operation which is commutative but not associative is AND OR EX OR NAND ,Boolean Operations,14 Choose the correct alternatives more than one may be correct and write the corresponding letters only The operation which is commutative but not associative is AND OR EX OR NAND ,Boolean Operations,14 When multiplicand Y is multiplied by multiplier X x_ n 1 x_ n 2 dots x_0 using bit pair recoding in Booth s algorithm partial products are generated according to the following table Row xi 1 xi xi 1 Partial Product 1 0 0 0 0 2 0 0 1 Y 3 0 1 0 Y 4 0 1 1 2Y 5 1 0 0 6 1 0 1 Y 7 1 1 0 Y 8 1 1 1 The partial products for rows 5 and 8 are 2Y and Y 2Y and 2Y 2Y and 0 0 and Y ,Booth Recoding,15 When multiplicand Y is multiplied by multiplier X x_ n 1 x_ n 2 dots x_0 using bit pair recoding in Booth s algorithm partial products are generated according to the following table Row xi 1 xi xi 1 Partial Product 1 0 0 0 0 2 0 0 1 Y 3 0 1 0 Y 4 0 1 1 2Y 5 1 0 0 6 1 0 1 Y 7 1 1 0 Y 8 1 1 1 The partial products for rows 5 and 8 are 2Y and Y 2Y and 2Y 2Y and 0 0 and Y ,Booth Recoding,15 When multiplicand Y is multiplied by multiplier X x_ n 1 x_ n 2 dots x_0 using bit pair recoding in Booth s algorithm partial products are generated according to the following table Row xi 1 xi xi 1 Partial Product 1 0 0 0 0 2 0 0 1 Y 3 0 1 0 Y 4 0 1 1 2Y 5 1 0 0 6 1 0 1 Y 7 1 1 0 Y 8 1 1 1 The partial products for rows 5 and 8 are 2Y and Y 2Y and 2Y 2Y and 0 0 and Y ,Booth Recoding,15 When multiplicand Y is multiplied by multiplier X x_ n 1 x_ n 2 dots x_0 using bit pair recoding in Booth s algorithm partial products are generated according to the following table Row xi 1 xi xi 1 Partial Product 1 0 0 0 0 2 0 0 1 Y 3 0 1 0 Y 4 0 1 1 2Y 5 1 0 0 6 1 0 1 Y 7 1 1 0 Y 8 1 1 1 The partial products for rows 5 and 8 are 2Y and Y 2Y and 2Y 2Y and 0 0 and Y ,Booth Recoding,15 When multiplicand Y is multiplied by multiplier X x_ n 1 x_ n 2 dots x_0 using bit pair recoding in Booth s algorithm partial products are generated according to the following table Row xi 1 xi xi 1 Partial Product 1 0 0 0 0 2 0 0 1 Y 3 0 1 0 Y 4 0 1 1 2Y 5 1 0 0 6 1 0 1 Y 7 1 1 0 Y 8 1 1 1 The partial products for rows 5 and 8 are 2Y and Y 2Y and 2Y 2Y and 0 0 and Y ,Booth Recoding,15 When multiplicand Y is multiplied by multiplier X x_ n 1 x_ n 2 dots x_0 using bit pair recoding in Booth s algorithm partial products are generated according to the following table Row xi 1 xi xi 1 Partial Product 1 0 0 0 0 2 0 0 1 Y 3 0 1 0 Y 4 0 1 1 2Y 5 1 0 0 6 1 0 1 Y 7 1 1 0 Y 8 1 1 1 The partial products for rows 5 and 8 are 2Y and Y 2Y and 2Y 2Y and 0 0 and Y ,Booth Recoding,15 When multiplicand Y is multiplied by multiplier X x_ n 1 x_ n 2 dots x_0 using bit pair recoding in Booth s algorithm partial products are generated according to the following table Row xi 1 xi xi 1 Partial Product 1 0 0 0 0 2 0 0 1 Y 3 0 1 0 Y 4 0 1 1 2Y 5 1 0 0 6 1 0 1 Y 7 1 1 0 Y 8 1 1 1 The partial products for rows 5 and 8 are 2Y and Y 2Y and 2Y 2Y and 0 0 and Y ,Booth Recoding,15 When multiplicand Y is multiplied by multiplier X x_ n 1 x_ n 2 dots x_0 using bit pair recoding in Booth s algorithm partial products are generated according to the following table Row xi 1 xi xi 1 Partial Product 1 0 0 0 0 2 0 0 1 Y 3 0 1 0 Y 4 0 1 1 2Y 5 1 0 0 6 1 0 1 Y 7 1 1 0 Y 8 1 1 1 The partial products for rows 5 and 8 are 2Y and Y 2Y and 2Y 2Y and 0 0 and Y ,Booth Recoding,15 When multiplicand Y is multiplied by multiplier X x_ n 1 x_ n 2 dots x_0 using bit pair recoding in Booth s algorithm partial products are generated according to the following table Row xi 1 xi xi 1 Partial Product 1 0 0 0 0 2 0 0 1 Y 3 0 1 0 Y 4 0 1 1 2Y 5 1 0 0 6 1 0 1 Y 7 1 1 0 Y 8 1 1 1 The partial products for rows 5 and 8 are 2Y and Y 2Y and 2Y 2Y and 0 0 and Y ,Booth Recoding,15 When multiplicand Y is multiplied by multiplier X x_ n 1 x_ n 2 dots x_0 using bit pair recoding in Booth s algorithm partial products are generated according to the following table Row xi 1 xi xi 1 Partial Product 1 0 0 0 0 2 0 0 1 Y 3 0 1 0 Y 4 0 1 1 2Y 5 1 0 0 6 1 0 1 Y 7 1 1 0 Y 8 1 1 1 The partial products for rows 5 and 8 are 2Y and Y 2Y and 2Y 2Y and 0 0 and Y ,Booth Recoding,15 When multiplicand Y is multiplied by multiplier X x_ n 1 x_ n 2 dots x_0 using bit pair recoding in Booth s algorithm partial products are generated according to the following table Row xi 1 xi xi 1 Partial Product 1 0 0 0 0 2 0 0 1 Y 3 0 1 0 Y 4 0 1 1 2Y 5 1 0 0 6 1 0 1 Y 7 1 1 0 Y 8 1 1 1 The partial products for rows 5 and 8 are 2Y and Y 2Y and 2Y 2Y and 0 0 and Y ,Booth Recoding,15 When multiplicand Y is multiplied by multiplier X x_ n 1 x_ n 2 dots x_0 using bit pair recoding in Booth s algorithm partial products are generated according to the following table Row xi 1 xi xi 1 Partial Product 1 0 0 0 0 2 0 0 1 Y 3 0 1 0 Y 4 0 1 1 2Y 5 1 0 0 6 1 0 1 Y 7 1 1 0 Y 8 1 1 1 The partial products for rows 5 and 8 are 2Y and Y 2Y and 2Y 2Y and 0 0 and Y ,Booth Recoding,15 When multiplicand Y is multiplied by multiplier X x_ n 1 x_ n 2 dots x_0 using bit pair recoding in Booth s algorithm partial products are generated according to the following table Row xi 1 xi xi 1 Partial Product 1 0 0 0 0 2 0 0 1 Y 3 0 1 0 Y 4 0 1 1 2Y 5 1 0 0 6 1 0 1 Y 7 1 1 0 Y 8 1 1 1 The partial products for rows 5 and 8 are 2Y and Y 2Y and 2Y 2Y and 0 0 and Y ,Booth Recoding,15 When multiplicand Y is multiplied by multiplier X x_ n 1 x_ n 2 dots x_0 using bit pair recoding in Booth s algorithm partial products are generated according to the following table Row xi 1 xi xi 1 Partial Product 1 0 0 0 0 2 0 0 1 Y 3 0 1 0 Y 4 0 1 1 2Y 5 1 0 0 6 1 0 1 Y 7 1 1 0 Y 8 1 1 1 The partial products for rows 5 and 8 are 2Y and Y 2Y and 2Y 2Y and 0 0 and Y ,Booth Recoding,15 Booth s coding in 8 bits for the decimal number 57 is 0 100 1000 0 100 100 1 0 1 100 10 1 00 10 100 1 ,Booths Algorithm,16 Booth u2019s algorithm for integer multiplication gives worst performance when the multiplier pattern is 101010 u2026 1010 100000 u2026 0001 111111 u2026 1111 011111 u2026 1110 ,Booths Algorithm,16 Booth u2019s algorithm for integer multiplication gives worst performance when the multiplier pattern is 101010 u2026 1010 100000 u2026 0001 111111 u2026 1111 011111 u2026 1110 ,Booths Algorithm,16 Booth s coding in 8 bits for the decimal number 57 is 0 100 1000 0 100 100 1 0 1 100 10 1 00 10 100 1 ,Booths Algorithm,16 Using Booth s Algorithm for multiplication the multiplier 57 will be recoded as 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 ,Booths Algorithm,16 The two numbers given below are multiplied using the Booth s algorithm Multiplicand 0101 1010 1110 1110 Multiplier 0111 0111 1011 1101 How many additions Subtractions are required for the multiplication of the above two numbers 6 8 10 12 ,Booths Algorithm,16 Using Booth s Algorithm for multiplication the multiplier 57 will be recoded as 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 ,Booths Algorithm,16 Booth u2019s algorithm for integer multiplication gives worst performance when the multiplier pattern is 101010 u2026 1010 100000 u2026 0001 111111 u2026 1111 011111 u2026 1110 ,Booths Algorithm,16 Booth s coding in 8 bits for the decimal number 57 is 0 100 1000 0 100 100 1 0 1 100 10 1 00 10 100 1 ,Booths Algorithm,16 Booth u2019s algorithm for integer multiplication gives worst performance when the multiplier pattern is 101010 u2026 1010 100000 u2026 0001 111111 u2026 1111 011111 u2026 1110 ,Booths Algorithm,16 Booth s coding in 8 bits for the decimal number 57 is 0 100 1000 0 100 100 1 0 1 100 10 1 00 10 100 1 ,Booths Algorithm,16 A prime attribute of a relation scheme R is an attribute that appears in all candidate keys of R in some candidate key of R in a foreign key of R only in the primary key of R ,Candidate Keys,17 An instance of a relational scheme R A B C has distinct values for attribute A Can you conclude that A is a candidate key for R ,Candidate Keys,17 An instance of a relational scheme R A B C has distinct values for attribute A Can you conclude that A is a candidate key for R ,Candidate Keys,17 An instance of a relational scheme R A B C has distinct values for attribute A Can you conclude that A is a candidate key for R ,Candidate Keys,17 The maximum number of superkeys for the relation schema R E F G H with E as the key is _____ ,Candidate Keys,17 The maximum number of superkeys for the relation schema R E F G H with E as the key is _____ ,Candidate Keys,17 Consider a relational table with a single record for each registered student with the following attributes ext Registration_Num Unique registration number for each registered student ext UID Unique identity number unique at the national level for each citizen ext BankAccount_Num Unique account number at the bank A student can have multiple accounts or joint accounts This attribute stores the primary account number ext Name Name of the student ext Hostel_Room Room number of the hostel Which of the following options is INCORRECT A ext BankAccount_Num is a candidate key B ext Registration_Num can be a primary key C ext UID is a candidate key if all students are from the same country D If S is a super key such that S cap ext UID is ext NULL then S cup ext UID is also a superkey,Candidate Keys,17 An instance of a relational scheme R A B C has distinct values for attribute A Can you conclude that A is a candidate key for R ,Candidate Keys,17 A prime attribute of a relation scheme R is an attribute that appears in all candidate keys of R in some candidate key of R in a foreign key of R only in the primary key of R ,Candidate Keys,17 Consider a relational table with a single record for each registered student with the following attributes ext Registration_Num Unique registration number for each registered student ext UID Unique identity number unique at the national level for each citizen ext BankAccount_Num Unique account number at the bank A student can have multiple accounts or joint accounts This attribute stores the primary account number ext Name Name of the student ext Hostel_Room Room number of the hostel Which of the following options is INCORRECT A ext BankAccount_Num is a candidate key B ext Registration_Num can be a primary key C ext UID is a candidate key if all students are from the same country D If S is a super key such that S cap ext UID is ext NULL then S cup ext UID is also a superkey,Candidate Keys,17 A Boolean expression is an expression made out of propositional letters such as p q r and operators wedge vee and eg e g p wedge eg q vee eg r An expression is said to be in sum of product form also called disjunctive normal form if all eg occur just before letters and no vee occurs in scope of wedge e g p wedge eg q vee eg p wedge q The expression is said to be in product of sum form also called conjunctive normal form if all negations occur just before letters and no wedge occurs in the scope of vee e g p vee eg q wedge eg p vee q Which of the following is not correct Every Boolean expression is equivalent to an expression is sum of product form Every Boolean expression is equivalent to an expression in product of sum form Every Boolean expression is equivalent to an expression without vee operator Every Boolean expression is equivalent to an expression without wedge operator Every Boolean expression is equivalent to an expression without eg operator ,Canonical Normal Form,18 Given f_1 f_3 and f in canonical sum of products form in decimal for the circuit f_1 Sigma m 4 5 6 7 8 f_3 Sigma m 1 6 15 f Sigma m 1 6 8 15 hen f_2 is Sigma m 4 6 Sigma m 4 8 Sigma m 6 8 Sigma m 4 6 8 ,Canonical Normal Form,18 The total number of prime implicants of the function f w x y z sum 0 2 4 5 6 10 is __________,Canonical Normal Form,18 The minterm expansion of f P Q R PQ Q bar R P bar R is m_2 m_4 m_6 m_7 m_0 m_1 m_3 m_5 m_0 m_1 m_6 m_7 m_2 m_3 m_4 m_5 ,Canonical Normal Form,18 A Boolean expression is an expression made out of propositional letters such as p q r and operators wedge vee and eg e g p wedge eg q vee eg r An expression is said to be in sum of product form also called disjunctive normal form if all eg occur just before letters and no vee occurs in scope of wedge e g p wedge eg q vee eg p wedge q The expression is said to be in product of sum form also called conjunctive normal form if all negations occur just before letters and no wedge occurs in the scope of vee e g p vee eg q wedge eg p vee q Which of the following is not correct Every Boolean expression is equivalent to an expression is sum of product form Every Boolean expression is equivalent to an expression in product of sum form Every Boolean expression is equivalent to an expression without vee operator Every Boolean expression is equivalent to an expression without wedge operator Every Boolean expression is equivalent to an expression without eg operator ,Canonical Normal Form,18 The total number of prime implicants of the function f w x y z sum 0 2 4 5 6 10 is __________,Canonical Normal Form,18 The total number of prime implicants of the function f w x y z sum 0 2 4 5 6 10 is __________,Canonical Normal Form,18 Given the function F P QR where F is a function in three Boolean variables P Q and R and P P consider the following statements S1 F sum 4 5 6 S2 F sum 0 1 2 3 7 S3 F Pi 4 5 6 S4 F Pi 0 1 2 3 7 Which of the following is true S1 False S2 True S3 True S4 False S1 True S2 False S3 False S4 True S1 False S2 False S3 True S4 True S1 True S2 True S3 False S4 False ,Canonical Normal Form,18 Given two three bit numbers a_ 2 a_ 1 a_ 0 and b_ 2 b_ 1 b_ 0 and c the carry in the function that represents the carry generate function when these two numbers are added is a_ 2 b_ 2 a_ 2 a_ 1 b_ 1 a_ 2 a_ 1 a_ 0 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 1 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 b_ 0 a_ 0 b_ 2 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 b_ 1 b_ 0 a_ 2 a_ 1 b_ 1 b_ 0 a_ 1 a_ 0 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 a_ 1 a_ 0 b_ 2 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 oplus b_ 2 a_ 1 b_ 1 a_ 1 oplus b_ 1 a_ 0 b_ 0 a_ 2 b_ 2 overline a_ 2 a_ 1 b_ 1 overline a_ 2 a_ 1 a_ 0 b_ 0 overline a_ 2 a_ 0 overline b_ 1 b_ 0 a_ 1 overline b_ 2 b_ 1 overline a_ 1 a_ 0 overline b_ 2 b_ 0 a_ 0 overline b_ 2 b_ 1 b_ 0 ,Carry Generator,19 In a look ahead carry generator the carry generate function G_i and the carry propagate function P_i for inputs A_i and B_i are given by P_i A_i oplus B_i ext and G_i A_iB_i The expressions for the sum bit S_i and the carry bit C_ i 1 of the look ahead carry adder are given by S_i P_i oplus C_i ext and C_ i 1 G_i P_iC_i ext where C_0 ext is the input carry Consider a two level logic implementation of the look ahead carry generator Assume that all P_i and G_i are available for the carry generator circuit and that the AND and OR gates can have any number of inputs The number of AND gates and OR gates needed to implement the look ahead carry generator for a 4 bit adder with S_3 S_2 S_1 S_0 and C_4 as its outputs are respectively 6 3 10 4 6 4 10 5 ,Carry Generator,19 Given two three bit numbers a_ 2 a_ 1 a_ 0 and b_ 2 b_ 1 b_ 0 and c the carry in the function that represents the carry generate function when these two numbers are added is a_ 2 b_ 2 a_ 2 a_ 1 b_ 1 a_ 2 a_ 1 a_ 0 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 1 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 b_ 0 a_ 0 b_ 2 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 b_ 1 b_ 0 a_ 2 a_ 1 b_ 1 b_ 0 a_ 1 a_ 0 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 a_ 1 a_ 0 b_ 2 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 oplus b_ 2 a_ 1 b_ 1 a_ 1 oplus b_ 1 a_ 0 b_ 0 a_ 2 b_ 2 overline a_ 2 a_ 1 b_ 1 overline a_ 2 a_ 1 a_ 0 b_ 0 overline a_ 2 a_ 0 overline b_ 1 b_ 0 a_ 1 overline b_ 2 b_ 1 overline a_ 1 a_ 0 overline b_ 2 b_ 0 a_ 0 overline b_ 2 b_ 1 b_ 0 ,Carry Generator,19 In a look ahead carry generator the carry generate function G_i and the carry propagate function P_i for inputs A_i and B_i are given by P_i A_i oplus B_i ext and G_i A_iB_i The expressions for the sum bit S_i and the carry bit C_ i 1 of the look ahead carry adder are given by S_i P_i oplus C_i ext and C_ i 1 G_i P_iC_i ext where C_0 ext is the input carry Consider a two level logic implementation of the look ahead carry generator Assume that all P_i and G_i are available for the carry generator circuit and that the AND and OR gates can have any number of inputs The number of AND gates and OR gates needed to implement the look ahead carry generator for a 4 bit adder with S_3 S_2 S_1 S_0 and C_4 as its outputs are respectively 6 3 10 4 6 4 10 5 ,Carry Generator,19 Given two three bit numbers a_ 2 a_ 1 a_ 0 and b_ 2 b_ 1 b_ 0 and c the carry in the function that represents the carry generate function when these two numbers are added is a_ 2 b_ 2 a_ 2 a_ 1 b_ 1 a_ 2 a_ 1 a_ 0 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 1 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 b_ 0 a_ 0 b_ 2 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 b_ 1 b_ 0 a_ 2 a_ 1 b_ 1 b_ 0 a_ 1 a_ 0 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 a_ 1 a_ 0 b_ 2 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 oplus b_ 2 a_ 1 b_ 1 a_ 1 oplus b_ 1 a_ 0 b_ 0 a_ 2 b_ 2 overline a_ 2 a_ 1 b_ 1 overline a_ 2 a_ 1 a_ 0 b_ 0 overline a_ 2 a_ 0 overline b_ 1 b_ 0 a_ 1 overline b_ 2 b_ 1 overline a_ 1 a_ 0 overline b_ 2 b_ 0 a_ 0 overline b_ 2 b_ 1 b_ 0 ,Carry Generator,19 In a look ahead carry generator the carry generate function G_i and the carry propagate function P_i for inputs A_i and B_i are given by P_i A_i oplus B_i ext and G_i A_iB_i The expressions for the sum bit S_i and the carry bit C_ i 1 of the look ahead carry adder are given by S_i P_i oplus C_i ext and C_ i 1 G_i P_iC_i ext where C_0 ext is the input carry Consider a two level logic implementation of the look ahead carry generator Assume that all P_i and G_i are available for the carry generator circuit and that the AND and OR gates can have any number of inputs The number of AND gates and OR gates needed to implement the look ahead carry generator for a 4 bit adder with S_3 S_2 S_1 S_0 and C_4 as its outputs are respectively 6 3 10 4 6 4 10 5 ,Carry Generator,19 Given two three bit numbers a_ 2 a_ 1 a_ 0 and b_ 2 b_ 1 b_ 0 and c the carry in the function that represents the carry generate function when these two numbers are added is a_ 2 b_ 2 a_ 2 a_ 1 b_ 1 a_ 2 a_ 1 a_ 0 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 1 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 b_ 0 a_ 0 b_ 2 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 b_ 1 b_ 0 a_ 2 a_ 1 b_ 1 b_ 0 a_ 1 a_ 0 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 a_ 1 a_ 0 b_ 2 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 oplus b_ 2 a_ 1 b_ 1 a_ 1 oplus b_ 1 a_ 0 b_ 0 a_ 2 b_ 2 overline a_ 2 a_ 1 b_ 1 overline a_ 2 a_ 1 a_ 0 b_ 0 overline a_ 2 a_ 0 overline b_ 1 b_ 0 a_ 1 overline b_ 2 b_ 1 overline a_ 1 a_ 0 overline b_ 2 b_ 0 a_ 0 overline b_ 2 b_ 1 b_ 0 ,Carry Generator,19 Given two three bit numbers a_ 2 a_ 1 a_ 0 and b_ 2 b_ 1 b_ 0 and c the carry in the function that represents the carry generate function when these two numbers are added is a_ 2 b_ 2 a_ 2 a_ 1 b_ 1 a_ 2 a_ 1 a_ 0 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 1 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 b_ 0 a_ 0 b_ 2 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 b_ 1 b_ 0 a_ 2 a_ 1 b_ 1 b_ 0 a_ 1 a_ 0 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 a_ 1 a_ 0 b_ 2 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 oplus b_ 2 a_ 1 b_ 1 a_ 1 oplus b_ 1 a_ 0 b_ 0 a_ 2 b_ 2 overline a_ 2 a_ 1 b_ 1 overline a_ 2 a_ 1 a_ 0 b_ 0 overline a_ 2 a_ 0 overline b_ 1 b_ 0 a_ 1 overline b_ 2 b_ 1 overline a_ 1 a_ 0 overline b_ 2 b_ 0 a_ 0 overline b_ 2 b_ 1 b_ 0 ,Carry Generator,19 In a look ahead carry generator the carry generate function G_i and the carry propagate function P_i for inputs A_i and B_i are given by P_i A_i oplus B_i ext and G_i A_iB_i The expressions for the sum bit S_i and the carry bit C_ i 1 of the look ahead carry adder are given by S_i P_i oplus C_i ext and C_ i 1 G_i P_iC_i ext where C_0 ext is the input carry Consider a two level logic implementation of the look ahead carry generator Assume that all P_i and G_i are available for the carry generator circuit and that the AND and OR gates can have any number of inputs The number of AND gates and OR gates needed to implement the look ahead carry generator for a 4 bit adder with S_3 S_2 S_1 S_0 and C_4 as its outputs are respectively 6 3 10 4 6 4 10 5 ,Carry Generator,19 Given two three bit numbers a_ 2 a_ 1 a_ 0 and b_ 2 b_ 1 b_ 0 and c the carry in the function that represents the carry generate function when these two numbers are added is a_ 2 b_ 2 a_ 2 a_ 1 b_ 1 a_ 2 a_ 1 a_ 0 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 1 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 b_ 0 a_ 0 b_ 2 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 b_ 1 b_ 0 a_ 2 a_ 1 b_ 1 b_ 0 a_ 1 a_ 0 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 a_ 1 a_ 0 b_ 2 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 oplus b_ 2 a_ 1 b_ 1 a_ 1 oplus b_ 1 a_ 0 b_ 0 a_ 2 b_ 2 overline a_ 2 a_ 1 b_ 1 overline a_ 2 a_ 1 a_ 0 b_ 0 overline a_ 2 a_ 0 overline b_ 1 b_ 0 a_ 1 overline b_ 2 b_ 1 overline a_ 1 a_ 0 overline b_ 2 b_ 0 a_ 0 overline b_ 2 b_ 1 b_ 0 ,Carry Generator,19 In a look ahead carry generator the carry generate function G_i and the carry propagate function P_i for inputs A_i and B_i are given by P_i A_i oplus B_i ext and G_i A_iB_i The expressions for the sum bit S_i and the carry bit C_ i 1 of the look ahead carry adder are given by S_i P_i oplus C_i ext and C_ i 1 G_i P_iC_i ext where C_0 ext is the input carry Consider a two level logic implementation of the look ahead carry generator Assume that all P_i and G_i are available for the carry generator circuit and that the AND and OR gates can have any number of inputs The number of AND gates and OR gates needed to implement the look ahead carry generator for a 4 bit adder with S_3 S_2 S_1 S_0 and C_4 as its outputs are respectively 6 3 10 4 6 4 10 5 ,Carry Generator,19 Given two three bit numbers a_ 2 a_ 1 a_ 0 and b_ 2 b_ 1 b_ 0 and c the carry in the function that represents the carry generate function when these two numbers are added is a_ 2 b_ 2 a_ 2 a_ 1 b_ 1 a_ 2 a_ 1 a_ 0 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 1 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 b_ 0 a_ 0 b_ 2 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 b_ 1 b_ 0 a_ 2 a_ 1 b_ 1 b_ 0 a_ 1 a_ 0 b_ 2 b_ 1 a_ 1 a_ 0 b_ 2 a_ 1 a_ 0 b_ 2 b_ 0 a_ 2 a_ 0 b_ 1 b_ 0 a_ 2 b_ 2 a_ 2 oplus b_ 2 a_ 1 b_ 1 a_ 1 oplus b_ 1 a_ 0 b_ 0 a_ 2 b_ 2 overline a_ 2 a_ 1 b_ 1 overline a_ 2 a_ 1 a_ 0 b_ 0 overline a_ 2 a_ 0 overline b_ 1 b_ 0 a_ 1 overline b_ 2 b_ 1 overline a_ 1 a_ 0 overline b_ 2 b_ 0 a_ 0 overline b_ 2 b_ 1 b_ 0 ,Carry Generator,19 In a look ahead carry generator the carry generate function G_i and the carry propagate function P_i for inputs A_i and B_i are given by P_i A_i oplus B_i ext and G_i A_iB_i The expressions for the sum bit S_i and the carry bit C_ i 1 of the look ahead carry adder are given by S_i P_i oplus C_i ext and C_ i 1 G_i P_iC_i ext where C_0 ext is the input carry Consider a two level logic implementation of the look ahead carry generator Assume that all P_i and G_i are available for the carry generator circuit and that the AND and OR gates can have any number of inputs The number of AND gates and OR gates needed to implement the look ahead carry generator for a 4 bit adder with S_3 S_2 S_1 S_0 and C_4 as its outputs are respectively 6 3 10 4 6 4 10 5 ,Carry Generator,19 At what time between 6 a m and 7 a m will the minute hand and hour hand of a clock make an angle closest to 60 u00b0 6 22 a m 6 27 a m 6 38 a m 6 45 a m ,Clock Time,21 At what time between 6 a m and 7 a m will the minute hand and hour hand of a clock make an angle closest to 60 u00b0 6 22 a m 6 27 a m 6 38 a m 6 45 a m ,Clock Time,21 At what time between 6 a m and 7 a m will the minute hand and hour hand of a clock make an angle closest to 60 u00b0 6 22 a m 6 27 a m 6 38 a m 6 45 a m ,Clock Time,21 At what time between 6 a m and 7 a m will the minute hand and hour hand of a clock make an angle closest to 60 u00b0 6 22 a m 6 27 a m 6 38 a m 6 45 a m ,Clock Time,21 At what time between 6 a m and 7 a m will the minute hand and hour hand of a clock make an angle closest to 60 u00b0 6 22 a m 6 27 a m 6 38 a m 6 45 a m ,Clock Time,21 At what time between 6 a m and 7 a m will the minute hand and hour hand of a clock make an angle closest to 60 u00b0 6 22 a m 6 27 a m 6 38 a m 6 45 a m ,Clock Time,21 At what time between 6 a m and 7 a m will the minute hand and hour hand of a clock make an angle closest to 60 u00b0 6 22 a m 6 27 a m 6 38 a m 6 45 a m ,Clock Time,21 At what time between 6 a m and 7 a m will the minute hand and hour hand of a clock make an angle closest to 60 u00b0 6 22 a m 6 27 a m 6 38 a m 6 45 a m ,Clock Time,21 At what time between 6 a m and 7 a m will the minute hand and hour hand of a clock make an angle closest to 60 u00b0 6 22 a m 6 27 a m 6 38 a m 6 45 a m ,Clock Time,21 At what time between 6 a m and 7 a m will the minute hand and hour hand of a clock make an angle closest to 60 u00b0 6 22 a m 6 27 a m 6 38 a m 6 45 a m ,Clock Time,21 At what time between 6 a m and 7 a m will the minute hand and hour hand of a clock make an angle closest to 60 u00b0 6 22 a m 6 27 a m 6 38 a m 6 45 a m ,Clock Time,21 At what time between 6 a m and 7 a m will the minute hand and hour hand of a clock make an angle closest to 60 u00b0 6 22 a m 6 27 a m 6 38 a m 6 45 a m ,Clock Time,21 At what time between 6 a m and 7 a m will the minute hand and hour hand of a clock make an angle closest to 60 u00b0 6 22 a m 6 27 a m 6 38 a m 6 45 a m ,Clock Time,21 At what time between 6 a m and 7 a m will the minute hand and hour hand of a clock make an angle closest to 60 u00b0 6 22 a m 6 27 a m 6 38 a m 6 45 a m ,Clock Time,21 Consider the following types of languages L_ 1 Regular L_ 2 Context free L_ 3 Recursive L_ 4 Recursively enumerable Which of the following is are TRUE bar L_ 3 cup L_ 4 is recursively enumerable bar L_ 2 cup L_ 3 is recursive L _ 1 cap L_ 2 is context free L_ 1 cup bar L_ 2 is context free I only I and III only I and IV only I II and III only ,Closure Property,22 Consider the following types of languages L_ 1 Regular L_ 2 Context free L_ 3 Recursive L_ 4 Recursively enumerable Which of the following is are TRUE bar L_ 3 cup L_ 4 is recursively enumerable bar L_ 2 cup L_ 3 is recursive L _ 1 cap L_ 2 is context free L_ 1 cup bar L_ 2 is context free I only I and III only I and IV only I II and III only ,Closure Property,22 Consider the following types of languages L_ 1 Regular L_ 2 Context free L_ 3 Recursive L_ 4 Recursively enumerable Which of the following is are TRUE bar L_ 3 cup L_ 4 is recursively enumerable bar L_ 2 cup L_ 3 is recursive L _ 1 cap L_ 2 is context free L_ 1 cup bar L_ 2 is context free I only I and III only I and IV only I II and III only ,Closure Property,22 Context free languages and regular languages are both closed under the operation s of Union Intersection Concatenation Complementation ,Closure Property,22 Let L_1 L_2 be any two context free languages and R be any regular language Then which of the following is are CORRECT L_1 cup L_2 is context free overline L_1 is context free L_1 R is context free L_1 cap L_2 is context free I II and IV only I and III only II and IV only I only ,Closure Property,22 Let L_1 L_2 be any two context free languages and R be any regular language Then which of the following is are CORRECT L_1 cup L_2 is context free overline L_1 is context free L_1 R is context free L_1 cap L_2 is context free I II and IV only I and III only II and IV only I only ,Closure Property,22 Let L_1 L_2 be any two context free languages and R be any regular language Then which of the following is are CORRECT L_1 cup L_2 is context free overline L_1 is context free L_1 R is context free L_1 cap L_2 is context free I II and IV only I and III only II and IV only I only ,Closure Property,22 Let L_1 L_2 be any two context free languages and R be any regular language Then which of the following is are CORRECT L_1 cup L_2 is context free overline L_1 is context free L_1 R is context free L_1 cap L_2 is context free I II and IV only I and III only II and IV only I only ,Closure Property,22 Context free languages and regular languages are both closed under the operation s of Union Intersection Concatenation Complementation ,Closure Property,22 Which of the following statements is FALSE The intersection of a context free language with a regular language is context free The intersection of two regular languages is regular The intersection of two context free languages is context free The intersection of a context free language and the complement of a regular language is context free The intersection of a regular language and the complement of a regular language is regular ,Closure Property,22 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is an example of a spooled device The terminal used to input data for a program being executed The secondary memory device in a virtual memory system A line printer used to print the output of a number of jobs None of the above ,Computer Peripherals,23 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is an example of a spooled device The terminal used to input data for a program being executed The secondary memory device in a virtual memory system A line printer used to print the output of a number of jobs None of the above ,Computer Peripherals,23 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is an example of a spooled device The terminal used to input data for a program being executed The secondary memory device in a virtual memory system A line printer used to print the output of a number of jobs None of the above ,Computer Peripherals,23 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is an example of a spooled device The terminal used to input data for a program being executed The secondary memory device in a virtual memory system A line printer used to print the output of a number of jobs None of the above ,Computer Peripherals,23 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is an example of a spooled device The terminal used to input data for a program being executed The secondary memory device in a virtual memory system A line printer used to print the output of a number of jobs None of the above ,Computer Peripherals,23 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is an example of a spooled device The terminal used to input data for a program being executed The secondary memory device in a virtual memory system A line printer used to print the output of a number of jobs None of the above ,Computer Peripherals,23 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is an example of a spooled device The terminal used to input data for a program being executed The secondary memory device in a virtual memory system A line printer used to print the output of a number of jobs None of the above ,Computer Peripherals,23 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is an example of a spooled device The terminal used to input data for a program being executed The secondary memory device in a virtual memory system A line printer used to print the output of a number of jobs None of the above ,Computer Peripherals,23 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is an example of a spooled device The terminal used to input data for a program being executed The secondary memory device in a virtual memory system A line printer used to print the output of a number of jobs None of the above ,Computer Peripherals,23 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is an example of a spooled device The terminal used to input data for a program being executed The secondary memory device in a virtual memory system A line printer used to print the output of a number of jobs None of the above ,Computer Peripherals,23 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is an example of a spooled device The terminal used to input data for a program being executed The secondary memory device in a virtual memory system A line printer used to print the output of a number of jobs None of the above ,Computer Peripherals,23 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is an example of a spooled device The terminal used to input data for a program being executed The secondary memory device in a virtual memory system A line printer used to print the output of a number of jobs None of the above ,Computer Peripherals,23 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is an example of a spooled device The terminal used to input data for a program being executed The secondary memory device in a virtual memory system A line printer used to print the output of a number of jobs None of the above ,Computer Peripherals,23 Choose the correct alternatives more than one may be correct and write the corresponding letters only Which of the following is an example of a spooled device The terminal used to input data for a program being executed The secondary memory device in a virtual memory system A line printer used to print the output of a number of jobs None of the above ,Computer Peripherals,23 Consider the following functions f and g f x x 50 y y 50 g a a x a a y Suppose we start with initial values of 100 for x 200 for y and 0 for a and then execute f and g in parallel u2014that is at each step we either execute one statement from f or one statement from g Which of the following is not a possible final value of a 300 250 350 200 ,Concurrency,24 The following two functions P1 and P2 that share a variable B with an initial value of 2 execute concurrently P1 C B 1 B 2 C P2 D 2 B B D 1 The number of distinct values that B can possibly take after the execution is______________________ ,Concurrency,24 Consider the following database schedule with two transactions T_ 1 and T_ 2 S r_ 2 left X right r_ 1 left X right r_ 2 left Y right w_ 1 left X right r_ 1 left Y right w_ 2 left X right a_ 1 a_ 2 Where r_ i Z denotes a read operation by transaction T_ i on a variable Z w_ i Z denotes a write operation by T_ i on a variable Z and a_ i denotes an abort by transaction T_ i Which one of the following statements about the above schedule is TRUE S is non recoverable S is recoverable but has a cascading abort S does not have a cascading abort S is strict ,Concurrency,24 The following two functions P1 and P2 that share a variable B with an initial value of 2 execute concurrently P1 C B 1 B 2 C P2 D 2 B B D 1 The number of distinct values that B can possibly take after the execution is______________________ ,Concurrency,24 Consider the following database schedule with two transactions T_ 1 and T_ 2 S r_ 2 left X right r_ 1 left X right r_ 2 left Y right w_ 1 left X right r_ 1 left Y right w_ 2 left X right a_ 1 a_ 2 Where r_ i Z denotes a read operation by transaction T_ i on a variable Z w_ i Z denotes a write operation by T_ i on a variable Z and a_ i denotes an abort by transaction T_ i Which one of the following statements about the above schedule is TRUE S is non recoverable S is recoverable but has a cascading abort S does not have a cascading abort S is strict ,Concurrency,24 Consider the following functions f and g f x x 50 y y 50 g a a x a a y Suppose we start with initial values of 100 for x 200 for y and 0 for a and then execute f and g in parallel u2014that is at each step we either execute one statement from f or one statement from g Which of the following is not a possible final value of a 300 250 350 200 ,Concurrency,24 The following two functions P1 and P2 that share a variable B with an initial value of 2 execute concurrently P1 C B 1 B 2 C P2 D 2 B B D 1 The number of distinct values that B can possibly take after the execution is______________________ ,Concurrency,24 Consider the concurrent program x 1 cobegin x x x 1 x x 2 coend Reading and writing of a variable is atomic but evaluation of an expression is not atomic The set of possible values of variable x at the end of execution of the program is left 3 right left 7 right left 3 5 7 right left 3 7 right left 3 5 right ,Concurrency,24 Consider the concurrent program x 1 cobegin x x x 1 x x 2 coend Reading and writing of a variable is atomic but evaluation of an expression is not atomic The set of possible values of variable x at the end of execution of the program is left 3 right left 7 right left 3 5 7 right left 3 7 right left 3 5 right ,Concurrency,24 Consider the following database schedule with two transactions T_ 1 and T_ 2 S r_ 2 left X right r_ 1 left X right r_ 2 left Y right w_ 1 left X right r_ 1 left Y right w_ 2 left X right a_ 1 a_ 2 Where r_ i Z denotes a read operation by transaction T_ i on a variable Z w_ i Z denotes a write operation by T_ i on a variable Z and a_ i denotes an abort by transaction T_ i Which one of the following statements about the above schedule is TRUE S is non recoverable S is recoverable but has a cascading abort S does not have a cascading abort S is strict ,Concurrency,24 The following two functions P1 and P2 that share a variable B with an initial value of 2 execute concurrently P1 C B 1 B 2 C P2 D 2 B B D 1 The number of distinct values that B can possibly take after the execution is______________________ ,Concurrency,24 Amar and Akbar both tell the truth with probability dfrac 3 4 and lie with probability dfrac 1 4 Amar watches a test match and talks to Akbar about the outcome Akbar in turn tells Anthony Amar told me that India won What probability should Anthony assign to India s win left dfrac 9 16 right left dfrac 6 16 right left dfrac 7 16 right left dfrac 10 16 right None of the above ,Conditional Probability,25 Amar and Akbar both tell the truth with probability dfrac 3 4 and lie with probability dfrac 1 4 Amar watches a test match and talks to Akbar about the outcome Akbar in turn tells Anthony Amar told me that India won What probability should Anthony assign to India s win left dfrac 9 16 right left dfrac 6 16 right left dfrac 7 16 right left dfrac 10 16 right None of the above ,Conditional Probability,25 Suppose that a shop has an equal number of LED bulbs of two different types The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0 7 and given that it is of Type 2 is 0 4 The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________ ,Conditional Probability,25 Amar and Akbar both tell the truth with probability dfrac 3 4 and lie with probability dfrac 1 4 Amar watches a test match and talks to Akbar about the outcome Akbar in turn tells Anthony Amar told me that India won What probability should Anthony assign to India s win left dfrac 9 16 right left dfrac 6 16 right left dfrac 7 16 right left dfrac 10 16 right None of the above ,Conditional Probability,25 P and Q are considering to apply for a job The probability that P applies for the job is dfrac 1 4 the probability that P applies for the job given that Q applies for the job is dfrac 1 2 and the probability that Q applies for the job given that P applies for the job is dfrac 1 3 Then the probability that P does not apply for the job given that Q does not apply for this job is left dfrac 4 5 right left dfrac 5 6 right left dfrac 7 8 right left dfrac 11 12 right ,Conditional Probability,25 Karan tells truth with probability dfrac 1 3 and lies with probability dfrac 2 3 Independently Arjun tells truth with probability dfrac 3 4 and lies with probability dfrac 1 4 Both watch a cricket match Arjun tells you that India won Karan tells you that India lost What probability will you assign to India s win left dfrac 1 2 right left dfrac 2 3 right left dfrac 3 4 right left dfrac 5 6 right left dfrac 6 7 right ,Conditional Probability,25 Karan tells truth with probability dfrac 1 3 and lies with probability dfrac 2 3 Independently Arjun tells truth with probability dfrac 3 4 and lies with probability dfrac 1 4 Both watch a cricket match Arjun tells you that India won Karan tells you that India lost What probability will you assign to India s win left dfrac 1 2 right left dfrac 2 3 right left dfrac 3 4 right left dfrac 5 6 right left dfrac 6 7 right ,Conditional Probability,25 Suppose that a shop has an equal number of LED bulbs of two different types The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0 7 and given that it is of Type 2 is 0 4 The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________ ,Conditional Probability,25 Let A and B be any two arbitrary events then which one of the following is true P A cap B P A P B P A cup B P A P B P A mid B P A cap B P B P A cup B leq P A P B ,Conditional Probability,25 P and Q are considering to apply for a job The probability that P applies for the job is dfrac 1 4 the probability that P applies for the job given that Q applies for the job is dfrac 1 2 and the probability that Q applies for the job given that P applies for the job is dfrac 1 3 Then the probability that P does not apply for the job given that Q does not apply for this job is left dfrac 4 5 right left dfrac 5 6 right left dfrac 7 8 right left dfrac 11 12 right ,Conditional Probability,25 Two transactions T_1 and T_2 are given as T_1 r_1 X w_1 X r_1 Y w_1 Y T_2 r_2 Y w_2 Y r_2 Z w_2 Z where r_i V denotes a extit read operation by transaction T_i on a variable V and w_i V denotes a extit write operation by transaction T_i on a variable V The total number of conflict serializable schedules that can be formed by T_1 and T_2 is ______,Conflict Serializable,26 Two transactions T_1 and T_2 are given as T_1 r_1 X w_1 X r_1 Y w_1 Y T_2 r_2 Y w_2 Y r_2 Z w_2 Z where r_i V denotes a extit read operation by transaction T_i on a variable V and w_i V denotes a extit write operation by transaction T_i on a variable V The total number of conflict serializable schedules that can be formed by T_1 and T_2 is ______,Conflict Serializable,26 Two transactions T_1 and T_2 are given as T_1 r_1 X w_1 X r_1 Y w_1 Y T_2 r_2 Y w_2 Y r_2 Z w_2 Z where r_i V denotes a extit read operation by transaction T_i on a variable V and w_i V denotes a extit write operation by transaction T_i on a variable V The total number of conflict serializable schedules that can be formed by T_1 and T_2 is ______,Conflict Serializable,26 Two transactions T_1 and T_2 are given as T_1 r_1 X w_1 X r_1 Y w_1 Y T_2 r_2 Y w_2 Y r_2 Z w_2 Z where r_i V denotes a extit read operation by transaction T_i on a variable V and w_i V denotes a extit write operation by transaction T_i on a variable V The total number of conflict serializable schedules that can be formed by T_1 and T_2 is ______,Conflict Serializable,26 Two transactions T_1 and T_2 are given as T_1 r_1 X w_1 X r_1 Y w_1 Y T_2 r_2 Y w_2 Y r_2 Z w_2 Z where r_i V denotes a extit read operation by transaction T_i on a variable V and w_i V denotes a extit write operation by transaction T_i on a variable V The total number of conflict serializable schedules that can be formed by T_1 and T_2 is ______,Conflict Serializable,26 Two transactions T_1 and T_2 are given as T_1 r_1 X w_1 X r_1 Y w_1 Y T_2 r_2 Y w_2 Y r_2 Z w_2 Z where r_i V denotes a extit read operation by transaction T_i on a variable V and w_i V denotes a extit write operation by transaction T_i on a variable V The total number of conflict serializable schedules that can be formed by T_1 and T_2 is ______,Conflict Serializable,26 Two transactions T_1 and T_2 are given as T_1 r_1 X w_1 X r_1 Y w_1 Y T_2 r_2 Y w_2 Y r_2 Z w_2 Z where r_i V denotes a extit read operation by transaction T_i on a variable V and w_i V denotes a extit write operation by transaction T_i on a variable V The total number of conflict serializable schedules that can be formed by T_1 and T_2 is ______,Conflict Serializable,26 Two transactions T_1 and T_2 are given as T_1 r_1 X w_1 X r_1 Y w_1 Y T_2 r_2 Y w_2 Y r_2 Z w_2 Z where r_i V denotes a extit read operation by transaction T_i on a variable V and w_i V denotes a extit write operation by transaction T_i on a variable V The total number of conflict serializable schedules that can be formed by T_1 and T_2 is ______,Conflict Serializable,26 Two transactions T_1 and T_2 are given as T_1 r_1 X w_1 X r_1 Y w_1 Y T_2 r_2 Y w_2 Y r_2 Z w_2 Z where r_i V denotes a extit read operation by transaction T_i on a variable V and w_i V denotes a extit write operation by transaction T_i on a variable V The total number of conflict serializable schedules that can be formed by T_1 and T_2 is ______,Conflict Serializable,26 Two transactions T_1 and T_2 are given as T_1 r_1 X w_1 X r_1 Y w_1 Y T_2 r_2 Y w_2 Y r_2 Z w_2 Z where r_i V denotes a extit read operation by transaction T_i on a variable V and w_i V denotes a extit write operation by transaction T_i on a variable V The total number of conflict serializable schedules that can be formed by T_1 and T_2 is ______,Conflict Serializable,26 Two transactions T_1 and T_2 are given as T_1 r_1 X w_1 X r_1 Y w_1 Y T_2 r_2 Y w_2 Y r_2 Z w_2 Z where r_i V denotes a extit read operation by transaction T_i on a variable V and w_i V denotes a extit write operation by transaction T_i on a variable V The total number of conflict serializable schedules that can be formed by T_1 and T_2 is ______,Conflict Serializable,26 Two transactions T_1 and T_2 are given as T_1 r_1 X w_1 X r_1 Y w_1 Y T_2 r_2 Y w_2 Y r_2 Z w_2 Z where r_i V denotes a extit read operation by transaction T_i on a variable V and w_i V denotes a extit write operation by transaction T_i on a variable V The total number of conflict serializable schedules that can be formed by T_1 and T_2 is ______,Conflict Serializable,26 Two transactions T_1 and T_2 are given as T_1 r_1 X w_1 X r_1 Y w_1 Y T_2 r_2 Y w_2 Y r_2 Z w_2 Z where r_i V denotes a extit read operation by transaction T_i on a variable V and w_i V denotes a extit write operation by transaction T_i on a variable V The total number of conflict serializable schedules that can be formed by T_1 and T_2 is ______,Conflict Serializable,26 Two transactions T_1 and T_2 are given as T_1 r_1 X w_1 X r_1 Y w_1 Y T_2 r_2 Y w_2 Y r_2 Z w_2 Z where r_i V denotes a extit read operation by transaction T_i on a variable V and w_i V denotes a extit write operation by transaction T_i on a variable V The total number of conflict serializable schedules that can be formed by T_1 and T_2 is ______,Conflict Serializable,26 If L_1 and L_2 are context free languages and R a regular set one of the languages below is not necessarily a context free language Which one L_1 L_2 L_1 cap L_2 L_1 cap R L_1 cup L_2 ,Context Free Language,27 02 Choose the correct alternatives more than one may be correct and write the corresponding letters only xix Context free languages are closed under union closed under complementation closed under intersection closed under Kleene closure ,Context Free Language,27 Which of the following actions is are typically not performed by the operating system when switching context from process A to process B Saving current register values and restoring saved register values for process B Changing address translation tables Swapping out the memory image of process A to the disk Invalidating the translation look aside buffer ,Context Switch,28 Which of the following actions is are typically not performed by the operating system when switching context from process A to process B Saving current register values and restoring saved register values for process B Changing address translation tables Swapping out the memory image of process A to the disk Invalidating the translation look aside buffer ,Context Switch,28 Let the time taken to switch from user mode to kernel mode of execution be T1 while time taken to switch between two user processes be T2 Which of the following is correct T1 gt T2 T1 T2 T1 lt T2 Nothing can be said about the relation between T1 and T2 ,Context Switch,28 Let the time taken to switch from user mode to kernel mode of execution be T1 while time taken to switch between two user processes be T2 Which of the following is correct T1 gt T2 T1 T2 T1 lt T2 Nothing can be said about the relation between T1 and T2 ,Context Switch,28 Which of the following actions is are typically not performed by the operating system when switching context from process A to process B Saving current register values and restoring saved register values for process B Changing address translation tables Swapping out the memory image of process A to the disk Invalidating the translation look aside buffer ,Context Switch,28 Which of the following actions is are typically not performed by the operating system when switching context from process A to process B Saving current register values and restoring saved register values for process B Changing address translation tables Swapping out the memory image of process A to the disk Invalidating the translation look aside buffer ,Context Switch,28 Let the time taken to switch from user mode to kernel mode of execution be T1 while time taken to switch between two user processes be T2 Which of the following is correct T1 gt T2 T1 T2 T1 lt T2 Nothing can be said about the relation between T1 and T2 ,Context Switch,28 Let the time taken to switch from user mode to kernel mode of execution be T1 while time taken to switch between two user processes be T2 Which of the following is correct T1 gt T2 T1 T2 T1 lt T2 Nothing can be said about the relation between T1 and T2 ,Context Switch,28 Which of the following actions is are typically not performed by the operating system when switching context from process A to process B Saving current register values and restoring saved register values for process B Changing address translation tables Swapping out the memory image of process A to the disk Invalidating the translation look aside buffer ,Context Switch,28 Which of the following actions is are typically not performed by the operating system when switching context from process A to process B Saving current register values and restoring saved register values for process B Changing address translation tables Swapping out the memory image of process A to the disk Invalidating the translation look aside buffer ,Context Switch,28 Which of the following actions is are typically not performed by the operating system when switching context from process A to process B Saving current register values and restoring saved register values for process B Changing address translation tables Swapping out the memory image of process A to the disk Invalidating the translation look aside buffer ,Context Switch,28 Which of the following actions is are typically not performed by the operating system when switching context from process A to process B Saving current register values and restoring saved register values for process B Changing address translation tables Swapping out the memory image of process A to the disk Invalidating the translation look aside buffer ,Context Switch,28 Which of the following actions is are typically not performed by the operating system when switching context from process A to process B Saving current register values and restoring saved register values for process B Changing address translation tables Swapping out the memory image of process A to the disk Invalidating the translation look aside buffer ,Context Switch,28 The function y 2 3x u200b a is continuous u2200 x u2208 R and differentiable u2200 x u2208 R b is continuous u2200 x u2208 R and differentiable u2200 x u2208 R except at x frac 3 2 c is continuous u2200 x u2208 R and differentiable u2200 x u2208 R except at x frac 2 3 d is continuous u2200 x u2208 R except x 3 and differentiable u2200 x u2208 R,Continuity,29 Let f x x left frac 1 3 right and A denote the area of region bounded by f x and the X axis when x varies from 1 to 1 Which of the following statements is are TRUE f is continuous in 1 1 f is not bounded in 1 1 A is nonzero and finite II only III only II and III only I II and III ,Continuity,29 Let f x x left frac 1 3 right and A denote the area of region bounded by f x and the X axis when x varies from 1 to 1 Which of the following statements is are TRUE f is continuous in 1 1 f is not bounded in 1 1 A is nonzero and finite II only III only II and III only I II and III ,Continuity,29 A function f x is continuous in the interval 0 2 It is known that f 0 f 2 1 and f 1 1 Which one of the following statements must be true There exists a y in the interval 0 1 such that f y f y 1 For every y in the interval 0 1 f y f 2 y The maximum value of the function in the interval 0 2 is 1 There exists a y in the interval 0 1 such that f y f 2 y ,Continuity,29 Let f x x left frac 1 3 right and A denote the area of region bounded by f x and the X axis when x varies from 1 to 1 Which of the following statements is are TRUE f is continuous in 1 1 f is not bounded in 1 1 A is nonzero and finite II only III only II and III only I II and III ,Continuity,29 A function f x is continuous in the interval 0 2 It is known that f 0 f 2 1 and f 1 1 Which one of the following statements must be true There exists a y in the interval 0 1 such that f y f y 1 For every y in the interval 0 1 f y f 2 y The maximum value of the function in the interval 0 2 is 1 There exists a y in the interval 0 1 such that f y f 2 y ,Continuity,29 A function f x is continuous in the interval 0 2 It is known that f 0 f 2 1 and f 1 1 Which one of the following statements must be true There exists a y in the interval 0 1 such that f y f y 1 For every y in the interval 0 1 f y f 2 y The maximum value of the function in the interval 0 2 is 1 There exists a y in the interval 0 1 such that f y f 2 y ,Continuity,29 Let f x x left frac 1 3 right and A denote the area of region bounded by f x and the X axis when x varies from 1 to 1 Which of the following statements is are TRUE f is continuous in 1 1 f is not bounded in 1 1 A is nonzero and finite II only III only II and III only I II and III ,Continuity,29 The function y 2 3x u200b a is continuous u2200 x u2208 R and differentiable u2200 x u2208 R b is continuous u2200 x u2208 R and differentiable u2200 x u2208 R except at x frac 3 2 c is continuous u2200 x u2208 R and differentiable u2200 x u2208 R except at x frac 2 3 d is continuous u2200 x u2208 R except x 3 and differentiable u2200 x u2208 R,Continuity,29 The function y 2 3x u200b a is continuous u2200 x u2208 R and differentiable u2200 x u2208 R b is continuous u2200 x u2208 R and differentiable u2200 x u2208 R except at x frac 3 2 c is continuous u2200 x u2208 R and differentiable u2200 x u2208 R except at x frac 2 3 d is continuous u2200 x u2208 R except x 3 and differentiable u2200 x u2208 R,Continuity,29 A function f x is continuous in the interval 0 2 It is known that f 0 f 2 1 and f 1 1 Which one of the following statements must be true There exists a y in the interval 0 1 such that f y f y 1 For every y in the interval 0 1 f y f 2 y The maximum value of the function in the interval 0 2 is 1 There exists a y in the interval 0 1 such that f y f 2 y ,Continuity,29 A function f x is continuous in the interval 0 2 It is known that f 0 f 2 1 and f 1 1 Which one of the following statements must be true There exists a y in the interval 0 1 such that f y f y 1 For every y in the interval 0 1 f y f 2 y The maximum value of the function in the interval 0 2 is 1 There exists a y in the interval 0 1 such that f y f 2 y ,Continuity,29 The cost function for a product in a firm is given by 5q 2 where q is the amount of production The firm can sell the product at a market price of u20b9 50 per unit The number of units to be produced by the firm such that the profit is maximized is A 5 B 10 C 15 D 25,Cost Market Price,30 The cost function for a product in a firm is given by 5q 2 where q is the amount of production The firm can sell the product at a market price of u20b9 50 per unit The number of units to be produced by the firm such that the profit is maximized is A 5 B 10 C 15 D 25,Cost Market Price,30 The cost function for a product in a firm is given by 5q 2 where q is the amount of production The firm can sell the product at a market price of u20b9 50 per unit The number of units to be produced by the firm such that the profit is maximized is A 5 B 10 C 15 D 25,Cost Market Price,30 The cost function for a product in a firm is given by 5q 2 where q is the amount of production The firm can sell the product at a market price of u20b9 50 per unit The number of units to be produced by the firm such that the profit is maximized is A 5 B 10 C 15 D 25,Cost Market Price,30 The cost function for a product in a firm is given by 5q 2 where q is the amount of production The firm can sell the product at a market price of u20b9 50 per unit The number of units to be produced by the firm such that the profit is maximized is A 5 B 10 C 15 D 25,Cost Market Price,30 The cost function for a product in a firm is given by 5q 2 where q is the amount of production The firm can sell the product at a market price of u20b9 50 per unit The number of units to be produced by the firm such that the profit is maximized is A 5 B 10 C 15 D 25,Cost Market Price,30 The cost function for a product in a firm is given by 5q 2 where q is the amount of production The firm can sell the product at a market price of u20b9 50 per unit The number of units to be produced by the firm such that the profit is maximized is A 5 B 10 C 15 D 25,Cost Market Price,30 The cost function for a product in a firm is given by 5q 2 where q is the amount of production The firm can sell the product at a market price of u20b9 50 per unit The number of units to be produced by the firm such that the profit is maximized is A 5 B 10 C 15 D 25,Cost Market Price,30 The cost function for a product in a firm is given by 5q 2 where q is the amount of production The firm can sell the product at a market price of u20b9 50 per unit The number of units to be produced by the firm such that the profit is maximized is A 5 B 10 C 15 D 25,Cost Market Price,30 The cost function for a product in a firm is given by 5q 2 where q is the amount of production The firm can sell the product at a market price of u20b9 50 per unit The number of units to be produced by the firm such that the profit is maximized is A 5 B 10 C 15 D 25,Cost Market Price,30 The cost function for a product in a firm is given by 5q 2 where q is the amount of production The firm can sell the product at a market price of u20b9 50 per unit The number of units to be produced by the firm such that the profit is maximized is A 5 B 10 C 15 D 25,Cost Market Price,30 The cost function for a product in a firm is given by 5q 2 where q is the amount of production The firm can sell the product at a market price of u20b9 50 per unit The number of units to be produced by the firm such that the profit is maximized is A 5 B 10 C 15 D 25,Cost Market Price,30 The cost function for a product in a firm is given by 5q 2 where q is the amount of production The firm can sell the product at a market price of u20b9 50 per unit The number of units to be produced by the firm such that the profit is maximized is A 5 B 10 C 15 D 25,Cost Market Price,30 The cost function for a product in a firm is given by 5q 2 where q is the amount of production The firm can sell the product at a market price of u20b9 50 per unit The number of units to be produced by the firm such that the profit is maximized is A 5 B 10 C 15 D 25,Cost Market Price,30 Given Sigma a b which one of the following sets is not countable a Set of all strings over Sigma b Set of all languages over Sigma c Set of all regular languages over Sigma d Set of all languages over Sigma accepted by Turing machines,Countable Set,31 Given Sigma a b which one of the following sets is not countable a Set of all strings over Sigma b Set of all languages over Sigma c Set of all regular languages over Sigma d Set of all languages over Sigma accepted by Turing machines,Countable Set,31 Given Sigma a b which one of the following sets is not countable a Set of all strings over Sigma b Set of all languages over Sigma c Set of all regular languages over Sigma d Set of all languages over Sigma accepted by Turing machines,Countable Set,31 Given Sigma a b which one of the following sets is not countable a Set of all strings over Sigma b Set of all languages over Sigma c Set of all regular languages over Sigma d Set of all languages over Sigma accepted by Turing machines,Countable Set,31 Given Sigma a b which one of the following sets is not countable a Set of all strings over Sigma b Set of all languages over Sigma c Set of all regular languages over Sigma d Set of all languages over Sigma accepted by Turing machines,Countable Set,31 Given Sigma a b which one of the following sets is not countable a Set of all strings over Sigma b Set of all languages over Sigma c Set of all regular languages over Sigma d Set of all languages over Sigma accepted by Turing machines,Countable Set,31 Given Sigma a b which one of the following sets is not countable a Set of all strings over Sigma b Set of all languages over Sigma c Set of all regular languages over Sigma d Set of all languages over Sigma accepted by Turing machines,Countable Set,31 Given Sigma a b which one of the following sets is not countable a Set of all strings over Sigma b Set of all languages over Sigma c Set of all regular languages over Sigma d Set of all languages over Sigma accepted by Turing machines,Countable Set,31 Given Sigma a b which one of the following sets is not countable a Set of all strings over Sigma b Set of all languages over Sigma c Set of all regular languages over Sigma d Set of all languages over Sigma accepted by Turing machines,Countable Set,31 Given Sigma a b which one of the following sets is not countable a Set of all strings over Sigma b Set of all languages over Sigma c Set of all regular languages over Sigma d Set of all languages over Sigma accepted by Turing machines,Countable Set,31 Given Sigma a b which one of the following sets is not countable a Set of all strings over Sigma b Set of all languages over Sigma c Set of all regular languages over Sigma d Set of all languages over Sigma accepted by Turing machines,Countable Set,31 Given Sigma a b which one of the following sets is not countable a Set of all strings over Sigma b Set of all languages over Sigma c Set of all regular languages over Sigma d Set of all languages over Sigma accepted by Turing machines,Countable Set,31 Given Sigma a b which one of the following sets is not countable a Set of all strings over Sigma b Set of all languages over Sigma c Set of all regular languages over Sigma d Set of all languages over Sigma accepted by Turing machines,Countable Set,31 Given Sigma a b which one of the following sets is not countable a Set of all strings over Sigma b Set of all languages over Sigma c Set of all regular languages over Sigma d Set of all languages over Sigma accepted by Turing machines,Countable Set,31 The number of distinct simple graphs with up to three nodes is 15 10 7 9 ,Counting,32 Let G be a complete undirected graph on 6 vertices If vertices of G are labeled then the number of distinct cycles of length 4 in G is equal to 15 30 90 360 ,Counting,32 The number of distinct simple graphs with up to three nodes is 15 10 7 9 ,Counting,32 How many distinct binary search trees can be created out of 4 distinct keys 5 14 24 42 ,Counting,32 Let G be a complete undirected graph on 6 vertices If vertices of G are labeled then the number of distinct cycles of length 4 in G is equal to 15 30 90 360 ,Counting,32 The number of distinct simple graphs with up to three nodes is 15 10 7 9 ,Counting,32 What is the minimum number of ordered pairs of non negative numbers that should be chosen to ensure that there are two pairs a b and c d in the chosen set such that a equiv c mod 3 and b equiv d mod 5 4 6 16 24 ,Counting,32 What is the minimum number of ordered pairs of non negative numbers that should be chosen to ensure that there are two pairs a b and c d in the chosen set such that a equiv c mod 3 and b equiv d mod 5 4 6 16 24 ,Counting,32 A critical region is One which is enclosed by a pair of P and V operations on semaphores A program segment that has not been proved bug free A program segment that often causes unexpected system crashes A program segment where shared resources are accessed ,Critical Section,33 A critical region is One which is enclosed by a pair of P and V operations on semaphores A program segment that has not been proved bug free A program segment that often causes unexpected system crashes A program segment where shared resources are accessed ,Critical Section,33 A critical region is One which is enclosed by a pair of P and V operations on semaphores A program segment that has not been proved bug free A program segment that often causes unexpected system crashes A program segment where shared resources are accessed ,Critical Section,33 A critical region is One which is enclosed by a pair of P and V operations on semaphores A program segment that has not been proved bug free A program segment that often causes unexpected system crashes A program segment where shared resources are accessed ,Critical Section,33 A critical region is One which is enclosed by a pair of P and V operations on semaphores A program segment that has not been proved bug free A program segment that often causes unexpected system crashes A program segment where shared resources are accessed ,Critical Section,33 A critical region is One which is enclosed by a pair of P and V operations on semaphores A program segment that has not been proved bug free A program segment that often causes unexpected system crashes A program segment where shared resources are accessed ,Critical Section,33 A critical region is One which is enclosed by a pair of P and V operations on semaphores A program segment that has not been proved bug free A program segment that often causes unexpected system crashes A program segment where shared resources are accessed ,Critical Section,33 A critical region is One which is enclosed by a pair of P and V operations on semaphores A program segment that has not been proved bug free A program segment that often causes unexpected system crashes A program segment where shared resources are accessed ,Critical Section,33 A critical region is One which is enclosed by a pair of P and V operations on semaphores A program segment that has not been proved bug free A program segment that often causes unexpected system crashes A program segment where shared resources are accessed ,Critical Section,33 A critical region is One which is enclosed by a pair of P and V operations on semaphores A program segment that has not been proved bug free A program segment that often causes unexpected system crashes A program segment where shared resources are accessed ,Critical Section,33 A critical region is One which is enclosed by a pair of P and V operations on semaphores A program segment that has not been proved bug free A program segment that often causes unexpected system crashes A program segment where shared resources are accessed ,Critical Section,33 A critical region is One which is enclosed by a pair of P and V operations on semaphores A program segment that has not been proved bug free A program segment that often causes unexpected system crashes A program segment where shared resources are accessed ,Critical Section,33 A critical region is One which is enclosed by a pair of P and V operations on semaphores A program segment that has not been proved bug free A program segment that often causes unexpected system crashes A program segment where shared resources are accessed ,Critical Section,33 A critical region is One which is enclosed by a pair of P and V operations on semaphores A program segment that has not been proved bug free A program segment that often causes unexpected system crashes A program segment where shared resources are accessed ,Critical Section,33 State True or False with reason Logical data independence is easier to achieve than physical data independence,Data Independence,34 State True or False with reason Logical data independence is easier to achieve than physical data independence,Data Independence,34 State True or False with reason Logical data independence is easier to achieve than physical data independence,Data Independence,34 State True or False with reason Logical data independence is easier to achieve than physical data independence,Data Independence,34 State True or False with reason Logical data independence is easier to achieve than physical data independence,Data Independence,34 State True or False with reason Logical data independence is easier to achieve than physical data independence,Data Independence,34 State True or False with reason Logical data independence is easier to achieve than physical data independence,Data Independence,34 State True or False with reason Logical data independence is easier to achieve than physical data independence,Data Independence,34 State True or False with reason Logical data independence is easier to achieve than physical data independence,Data Independence,34 State True or False with reason Logical data independence is easier to achieve than physical data independence,Data Independence,34 State True or False with reason Logical data independence is easier to achieve than physical data independence,Data Independence,34 State True or False with reason Logical data independence is easier to achieve than physical data independence,Data Independence,34 State True or False with reason Logical data independence is easier to achieve than physical data independence,Data Independence,34 State True or False with reason Logical data independence is easier to achieve than physical data independence,Data Independence,34 An air pressure contour line joins locations in a region having the same atmospheric pressure The following is an air pressure contour plot of a geographical religion Contour lines are shown at 0 05 bar intervals in this plot If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region which of the following regions is most likely to have a thunderstorm P Q R S ,Data Interpretation,35 A contour line joins locations having the same height above the mean sea level The following is a contour plot of a geographical region Contour lines are shown at 25 m intervals in this plot If in a flood the water level rises to 525 m which of the villages P Q R S T get submerged P Q P Q T R S T Q R S ,Data Interpretation,35 The ratio of male to female students in a college for five years is plotted in the following line graph If the number of female students doubled in 2009 by what percent did the number of male students increase in 2009 ,Data Interpretation,35 The ratio of male to female students in a college for five years is plotted in the following line graph If the number of female students doubled in 2009 by what percent did the number of male students increase in 2009 ,Data Interpretation,35 The table below has question wise data on the performance of students in an examination The marks for each question are also listed There is no negative or partial marking in the examination Q No Marks Answered Correctly Answered Wrongly Not Attempted 1 2 21 17 6 2 3 15 27 2 3 2 23 18 3 What is the average of the marks obtained by the class in the examination 1 34 1 74 3 02 3 91 ,Data Interpretation,35 The exports and imports in crores of Rs of a country from the year 2000 to 2007 are given in the following bar chart In which year is the combined percentage increase in imports and exports the highest ,Data Interpretation,35 An ER model of a database consists of entity types A and B These are connected by a relationship R which does not have its own attribute Under which one of the following conditions can the relational table for R be merged with that of A Relationship R is one to many and the participation of A in R is total Relationship R is one to many and the participation of A in R is partial Relationship R is many to one and the participation of A in R is total Relationship R is many to one and the participation of A in R is partial ,Database,36 An ER model of a database consists of entity types A and B These are connected by a relationship R which does not have its own attribute Under which one of the following conditions can the relational table for R be merged with that of A Relationship R is one to many and the participation of A in R is total Relationship R is one to many and the participation of A in R is partial Relationship R is many to one and the participation of A in R is total Relationship R is many to one and the participation of A in R is partial ,Database,36 An ER model of a database consists of entity types A and B These are connected by a relationship R which does not have its own attribute Under which one of the following conditions can the relational table for R be merged with that of A Relationship R is one to many and the participation of A in R is total Relationship R is one to many and the participation of A in R is partial Relationship R is many to one and the participation of A in R is total Relationship R is many to one and the participation of A in R is partial ,Database,36 An ER model of a database consists of entity types A and B These are connected by a relationship R which does not have its own attribute Under which one of the following conditions can the relational table for R be merged with that of A Relationship R is one to many and the participation of A in R is total Relationship R is one to many and the participation of A in R is partial Relationship R is many to one and the participation of A in R is total Relationship R is many to one and the participation of A in R is partial ,Database,36 An ER model of a database consists of entity types A and B These are connected by a relationship R which does not have its own attribute Under which one of the following conditions can the relational table for R be merged with that of A Relationship R is one to many and the participation of A in R is total Relationship R is one to many and the participation of A in R is partial Relationship R is many to one and the participation of A in R is total Relationship R is many to one and the participation of A in R is partial ,Database,36 An ER model of a database consists of entity types A and B These are connected by a relationship R which does not have its own attribute Under which one of the following conditions can the relational table for R be merged with that of A Relationship R is one to many and the participation of A in R is total Relationship R is one to many and the participation of A in R is partial Relationship R is many to one and the participation of A in R is total Relationship R is many to one and the participation of A in R is partial ,Database,36 An ER model of a database consists of entity types A and B These are connected by a relationship R which does not have its own attribute Under which one of the following conditions can the relational table for R be merged with that of A Relationship R is one to many and the participation of A in R is total Relationship R is one to many and the participation of A in R is partial Relationship R is many to one and the participation of A in R is total Relationship R is many to one and the participation of A in R is partial ,Database,36 An ER model of a database consists of entity types A and B These are connected by a relationship R which does not have its own attribute Under which one of the following conditions can the relational table for R be merged with that of A Relationship R is one to many and the participation of A in R is total Relationship R is one to many and the participation of A in R is partial Relationship R is many to one and the participation of A in R is total Relationship R is many to one and the participation of A in R is partial ,Database,36 An ER model of a database consists of entity types A and B These are connected by a relationship R which does not have its own attribute Under which one of the following conditions can the relational table for R be merged with that of A Relationship R is one to many and the participation of A in R is total Relationship R is one to many and the participation of A in R is partial Relationship R is many to one and the participation of A in R is total Relationship R is many to one and the participation of A in R is partial ,Database,36 An ER model of a database consists of entity types A and B These are connected by a relationship R which does not have its own attribute Under which one of the following conditions can the relational table for R be merged with that of A Relationship R is one to many and the participation of A in R is total Relationship R is one to many and the participation of A in R is partial Relationship R is many to one and the participation of A in R is total Relationship R is many to one and the participation of A in R is partial ,Database,36 An ER model of a database consists of entity types A and B These are connected by a relationship R which does not have its own attribute Under which one of the following conditions can the relational table for R be merged with that of A Relationship R is one to many and the participation of A in R is total Relationship R is one to many and the participation of A in R is partial Relationship R is many to one and the participation of A in R is total Relationship R is many to one and the participation of A in R is partial ,Database,36 An ER model of a database consists of entity types A and B These are connected by a relationship R which does not have its own attribute Under which one of the following conditions can the relational table for R be merged with that of A Relationship R is one to many and the participation of A in R is total Relationship R is one to many and the participation of A in R is partial Relationship R is many to one and the participation of A in R is total Relationship R is many to one and the participation of A in R is partial ,Database,36 An ER model of a database consists of entity types A and B These are connected by a relationship R which does not have its own attribute Under which one of the following conditions can the relational table for R be merged with that of A Relationship R is one to many and the participation of A in R is total Relationship R is one to many and the participation of A in R is partial Relationship R is many to one and the participation of A in R is total Relationship R is many to one and the participation of A in R is partial ,Database,36 An ER model of a database consists of entity types A and B These are connected by a relationship R which does not have its own attribute Under which one of the following conditions can the relational table for R be merged with that of A Relationship R is one to many and the participation of A in R is total Relationship R is one to many and the participation of A in R is partial Relationship R is many to one and the participation of A in R is total Relationship R is many to one and the participation of A in R is partial ,Database,36 Let L be a language over Sigma i e L subseteq Sigma Suppose L satisfies the two conditions given below L is in NP and For every n there is exactly one string of length n that belongs to L Let L c be the complement of L over Sigma Show that L c is also in NP ,Decidability,38 Answer the following questions Which of the following problems are undecidable Membership problem in context free languages Whether a given context free language is regular Whether a finite state automation halts on all inputs Membership problem for type 0 languages ,Decidability,38 Choose the correct alternatives More than one may be correct It is undecidable whether An arbitrary Turing machine halts after 100 steps A Turing machine prints a specific letter A Turing machine computes the products of two numbers None of the above ,Decidability,38 Which one of the following is not decidable Given a Turing machine M a string s and an integer k M accepts s within k steps Equivalence of two given Turing machines Language accepted by a given finite state machine is not empty Language generated by a context free grammar is non empty ,Decidability,38 Answer the following questions Which of the following problems are undecidable Membership problem in context free languages Whether a given context free language is regular Whether a finite state automation halts on all inputs Membership problem for type 0 languages ,Decidability,38 Let L be a language over Sigma i e L subseteq Sigma Suppose L satisfies the two conditions given below L is in NP and For every n there is exactly one string of length n that belongs to L Let L c be the complement of L over Sigma Show that L c is also in NP ,Decidability,38 Let L be a language over Sigma i e L subseteq Sigma Suppose L satisfies the two conditions given below L is in NP and For every n there is exactly one string of length n that belongs to L Let L c be the complement of L over Sigma Show that L c is also in NP ,Decidability,38 How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 ,Decoder,39 How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 ,Decoder,39 How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 ,Decoder,39 How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 ,Decoder,39 How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 ,Decoder,39 How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 ,Decoder,39 How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 ,Decoder,39 How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 ,Decoder,39 How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 ,Decoder,39 How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 ,Decoder,39 How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 ,Decoder,39 How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 ,Decoder,39 How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 ,Decoder,39 How many 3 to 8 line decoders with an enable input are needed to construct a 6 to 64 line decoder without using any other logic gates 7 8 9 10 ,Decoder,39 The 2 n vertices of a graph G corresponds to all subsets of a set of size n for n geq 6 Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements The number of vertices of degree zero in G is 1 n n 1 2 n ,Degree Of Graph,40 Show that all vertices in an undirected finite graph cannot have distinct degrees if the graph has at least two vertices ,Degree Of Graph,40 The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order Which of the following sequences can not be the degree sequence of any graph 7 6 5 4 4 3 2 1 6 6 6 6 3 3 2 2 7 6 6 4 4 3 2 2 8 7 7 6 4 2 1 1 I and II III and IV IV only II and IV ,Degree Of Graph,40 The 2 n vertices of a graph G corresponds to all subsets of a set of size n for n geq 6 Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements The maximum degree of a vertex in G is binom frac n 2 2 2 frac n 2 2 n 2 2 n 3 imes 3 2 n 1 ,Degree Of Graph,40 The determinant of the matrix given below is begin bmatrix 0 amp 1 amp 0 amp 2 1 amp 1 amp 1 amp 3 0 amp 0 amp 0 amp 1 1 amp 2 amp 0 amp 1 end bmatrix 1 0 1 2 ,Determinant,41 If the matrix A is such that A begin bmatrix 2 u22124 7 end bmatrix begin bmatrix 1 amp 9 amp 5 end bmatrix then the determinant of A is equal to ______ ,Determinant,41 The determinant of the matrix given below is begin bmatrix 0 amp 1 amp 0 amp 2 1 amp 1 amp 1 amp 3 0 amp 0 amp 0 amp 1 1 amp 2 amp 0 amp 1 end bmatrix 1 0 1 2 ,Determinant,41 The determinant of the matrix begin bmatrix 6 amp 8 amp 1 amp 1 0 amp 2 amp 4 amp 6 0 amp 0 amp 4 amp 8 0 amp 0 amp 0 amp 1 end bmatrix 11 48 0 24 ,Determinant,41 The determinant of the matrix given below is begin bmatrix 0 amp 1 amp 0 amp 2 1 amp 1 amp 1 amp 3 0 amp 0 amp 0 amp 1 1 amp 2 amp 0 amp 1 end bmatrix 1 0 1 2 ,Determinant,41 If the matrix A is such that A begin bmatrix 2 u22124 7 end bmatrix begin bmatrix 1 amp 9 amp 5 end bmatrix then the determinant of A is equal to ______ ,Determinant,41 If the matrix A is such that A begin bmatrix 2 u22124 7 end bmatrix begin bmatrix 1 amp 9 amp 5 end bmatrix then the determinant of A is equal to ______ ,Determinant,41 The determinant of the matrix begin bmatrix 2 amp 0 amp 0 amp 0 8 amp 1 amp 7 amp 2 2 amp 0 amp 2 amp 0 9 amp 0 amp 6 amp 1 end bmatrix 4 0 15 20 ,Determinant,41 The determinant of the matrix begin bmatrix 6 amp 8 amp 1 amp 1 0 amp 2 amp 4 amp 6 0 amp 0 amp 4 amp 8 0 amp 0 amp 0 amp 1 end bmatrix 11 48 0 24 ,Determinant,41 The determinant of the matrix given below is begin bmatrix 0 amp 1 amp 0 amp 2 1 amp 1 amp 1 amp 3 0 amp 0 amp 0 amp 1 1 amp 2 amp 0 amp 1 end bmatrix 1 0 1 2 ,Determinant,41 The determinant of the matrix begin bmatrix 6 amp 8 amp 1 amp 1 0 amp 2 amp 4 amp 6 0 amp 0 amp 4 amp 8 0 amp 0 amp 0 amp 1 end bmatrix 11 48 0 24 ,Determinant,41 Let the function f heta begin vmatrix sin heta amp cos heta amp an heta sin frac pi 6 amp cos frac pi 6 amp an frac pi 6 amp sin frac pi 3 amp cos frac pi 3 amp an frac pi 3 end vmatrix where heta in left frac pi 6 frac pi 3 right and f heta denote the derivative of f with respect to heta Which of the following statements is are TRUE There exists heta in frac pi 6 frac pi 3 such that f heta 0 There exists heta in frac pi 6 frac pi 3 such that f heta eq 0 I only II only Both I and II Neither I Nor II ,Differentiability,42 Let f be a function defined by f x begin cases x 2 amp ext for x leq 1 ax 2 bx c amp ext for 1 lt x leq 2 x d amp ext for x gt 2 end cases Find the values for the constants a b c and d so that f is continuous and differentiable everywhere on the real line ,Differentiability,42 Let the function f heta begin vmatrix sin heta amp cos heta amp an heta sin frac pi 6 amp cos frac pi 6 amp an frac pi 6 amp sin frac pi 3 amp cos frac pi 3 amp an frac pi 3 end vmatrix where heta in left frac pi 6 frac pi 3 right and f heta denote the derivative of f with respect to heta Which of the following statements is are TRUE There exists heta in frac pi 6 frac pi 3 such that f heta 0 There exists heta in frac pi 6 frac pi 3 such that f heta eq 0 I only II only Both I and II Neither I Nor II ,Differentiability,42 Let f be a function defined by f x begin cases x 2 amp ext for x leq 1 ax 2 bx c amp ext for 1 lt x leq 2 x d amp ext for x gt 2 end cases Find the values for the constants a b c and d so that f is continuous and differentiable everywhere on the real line ,Differentiability,42 If f x R sin frac pi x 2 S f u2019 frac 1 2 sqrt 2 and int_0 1 f x dx frac 2R pi then the constants R and S are frac 2 pi and frac 16 pi frac 2 pi and 0 frac 4 pi and 0 frac 4 pi and frac 16 pi ,Differentiability,42 Let f be a function defined by f x begin cases x 2 amp ext for x leq 1 ax 2 bx c amp ext for 1 lt x leq 2 x d amp ext for x gt 2 end cases Find the values for the constants a b c and d so that f is continuous and differentiable everywhere on the real line ,Differentiability,42 If f x R sin frac pi x 2 S f u2019 frac 1 2 sqrt 2 and int_0 1 f x dx frac 2R pi then the constants R and S are frac 2 pi and frac 16 pi frac 2 pi and 0 frac 4 pi and 0 frac 4 pi and frac 16 pi ,Differentiability,42 If f x R sin frac pi x 2 S f u2019 frac 1 2 sqrt 2 and int_0 1 f x dx frac 2R pi then the constants R and S are frac 2 pi and frac 16 pi frac 2 pi and 0 frac 4 pi and 0 frac 4 pi and frac 16 pi ,Differentiability,42 If f x R sin frac pi x 2 S f u2019 frac 1 2 sqrt 2 and int_0 1 f x dx frac 2R pi then the constants R and S are frac 2 pi and frac 16 pi frac 2 pi and 0 frac 4 pi and 0 frac 4 pi and frac 16 pi ,Differentiability,42 Let the function f heta begin vmatrix sin heta amp cos heta amp an heta sin frac pi 6 amp cos frac pi 6 amp an frac pi 6 amp sin frac pi 3 amp cos frac pi 3 amp an frac pi 3 end vmatrix where heta in left frac pi 6 frac pi 3 right and f heta denote the derivative of f with respect to heta Which of the following statements is are TRUE There exists heta in frac pi 6 frac pi 3 such that f heta 0 There exists heta in frac pi 6 frac pi 3 such that f heta eq 0 I only II only Both I and II Neither I Nor II ,Differentiability,42 If f x R sin frac pi x 2 S f u2019 frac 1 2 sqrt 2 and int_0 1 f x dx frac 2R pi then the constants R and S are frac 2 pi and frac 16 pi frac 2 pi and 0 frac 4 pi and 0 frac 4 pi and frac 16 pi ,Differentiability,42 A logic network has two data inputs A and B and two control inputs C_0 and C_1 It implements the function F according to the following table C_1 C_2 F 0 0 overline A B 0 1 A B 1 0 A oplus B Implement the circuit using one 4 to 1 Multiplexer one 2 input Exclusive OR gate one 2 input AND gate one 2 input OR gate and one Inverter ,Digital Circuits,43 In the following truth table V 1 if and only if the input is valid Inputs Outputs D_0 D_1 D_2 D_3 X_0 X_1 V 0 0 0 0 x x 0 1 0 0 0 0 0 1 x 1 0 0 0 1 1 x x 1 0 1 0 1 x x x 1 1 1 1 What function does the truth table represent Priority encoder Decoder Multiplexer Demultiplexer ,Digital Circuits,43 A logic network has two data inputs A and B and two control inputs C_0 and C_1 It implements the function F according to the following table C_1 C_2 F 0 0 overline A B 0 1 A B 1 0 A oplus B Implement the circuit using one 4 to 1 Multiplexer one 2 input Exclusive OR gate one 2 input AND gate one 2 input OR gate and one Inverter ,Digital Circuits,43 Consider the following combinational function block involving four Boolean variables x y a b where x a b are inputs and y is the output f x a b y if x is 1 y a else y b Which one of the following digital logic blocks is the most suitable for implementing this function Full adder Priority encoder Multiplexor Flip flop ,Digital Circuits,43 A logic network has two data inputs A and B and two control inputs C_0 and C_1 It implements the function F according to the following table C_1 C_2 F 0 0 overline A B 0 1 A B 1 0 A oplus B Implement the circuit using one 4 to 1 Multiplexer one 2 input Exclusive OR gate one 2 input AND gate one 2 input OR gate and one Inverter ,Digital Circuits,43 In the following truth table V 1 if and only if the input is valid Inputs Outputs D_0 D_1 D_2 D_3 X_0 X_1 V 0 0 0 0 x x 0 1 0 0 0 0 0 1 x 1 0 0 0 1 1 x x 1 0 1 0 1 x x x 1 1 1 1 What function does the truth table represent Priority encoder Decoder Multiplexer Demultiplexer ,Digital Circuits,43 A logic network has two data inputs A and B and two control inputs C_0 and C_1 It implements the function F according to the following table C_1 C_2 F 0 0 overline A B 0 1 A B 1 0 A oplus B Implement the circuit using one 4 to 1 Multiplexer one 2 input Exclusive OR gate one 2 input AND gate one 2 input OR gate and one Inverter ,Digital Circuits,43 In the following truth table V 1 if and only if the input is valid Inputs Outputs D_0 D_1 D_2 D_3 X_0 X_1 V 0 0 0 0 x x 0 1 0 0 0 0 0 1 x 1 0 0 0 1 1 x x 1 0 1 0 1 x x x 1 1 1 1 What function does the truth table represent Priority encoder Decoder Multiplexer Demultiplexer ,Digital Circuits,43 Consider the following combinational function block involving four Boolean variables x y a b where x a b are inputs and y is the output f x a b y if x is 1 y a else y b Which one of the following digital logic blocks is the most suitable for implementing this function Full adder Priority encoder Multiplexor Flip flop ,Digital Circuits,43 Consider the following combinational function block involving four Boolean variables x y a b where x a b are inputs and y is the output f x a b y if x is 1 y a else y b Which one of the following digital logic blocks is the most suitable for implementing this function Full adder Priority encoder Multiplexor Flip flop ,Digital Circuits,43 In the following truth table V 1 if and only if the input is valid Inputs Outputs D_0 D_1 D_2 D_3 X_0 X_1 V 0 0 0 0 x x 0 1 0 0 0 0 0 1 x 1 0 0 0 1 1 x x 1 0 1 0 1 x x x 1 1 1 1 What function does the truth table represent Priority encoder Decoder Multiplexer Demultiplexer ,Digital Circuits,43 In the following truth table V 1 if and only if the input is valid Inputs Outputs D_0 D_1 D_2 D_3 X_0 X_1 V 0 0 0 0 x x 0 1 0 0 0 0 0 1 x 1 0 0 0 1 1 x x 1 0 1 0 1 x x x 1 1 1 1 What function does the truth table represent Priority encoder Decoder Multiplexer Demultiplexer ,Digital Circuits,43 Consider a 4 bit Johnson counter with an initial value of 0000 The counting sequence of this counter is 0 1 3 7 15 14 12 8 0 0 1 3 5 7 9 11 13 15 0 0 2 4 6 8 10 12 14 0 0 8 12 14 15 7 3 1 0 ,Digital Counter,44 The minimum number of ext D flip flops needed to design a mod 258 counter is 9 8 512 258 ,Digital Counter,44 The next state table of a 2 bit saturating up counter is given below begin array cc cc Q_1 amp Q_0 amp Q_1 amp Q_0 hline 0 amp 0 amp 0 amp 1 0 amp 1 amp 1 amp 0 1 amp 0 amp 1 amp 1 1 amp 1 amp 1 amp 1 end array The counter is built as a synchronous sequential circuit using T flip flops The expressions for T_1 and T_0 are T_1 Q_1Q_0 quad T_0 bar Q_1 bar Q_0 T_1 bar Q_1 Q_0 quad T_0 bar Q_1 bar Q_0 T_1 Q_1 Q_0 quad T_0 bar Q_1 bar Q_0 T_1 bar Q_1 Q_0 quad T_0 Q_1 Q_0 ,Digital Counter,44 The minimum number of JK flip flops required to construct a synchronous counter with the count sequence 0 0 1 1 2 2 3 3 0 0 is _______ ,Digital Counter,44 Let k 2 n A circuit is built by giving the output of an n bit binary counter as input to an n ext to 2 n bit decoder This circuit is equivalent to a k bit binary up counter k bit binary down counter k bit ring counter k bit Johnson counter ,Digital Counter,44 We want to design a synchronous counter that counts the sequence 0 1 0 2 0 3 and then repeats The minimum number of ext J K flip flops required to implement this counter is _____________ ,Digital Counter,44 The next state table of a 2 bit saturating up counter is given below begin array cc cc Q_1 amp Q_0 amp Q_1 amp Q_0 hline 0 amp 0 amp 0 amp 1 0 amp 1 amp 1 amp 0 1 amp 0 amp 1 amp 1 1 amp 1 amp 1 amp 1 end array The counter is built as a synchronous sequential circuit using T flip flops The expressions for T_1 and T_0 are T_1 Q_1Q_0 quad T_0 bar Q_1 bar Q_0 T_1 bar Q_1 Q_0 quad T_0 bar Q_1 bar Q_0 T_1 Q_1 Q_0 quad T_0 bar Q_1 bar Q_0 T_1 bar Q_1 Q_0 quad T_0 Q_1 Q_0 ,Digital Counter,44 Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii ,Dining Philosopher,45 Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii ,Dining Philosopher,45 Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii ,Dining Philosopher,45 Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii ,Dining Philosopher,45 Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii ,Dining Philosopher,45 Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii ,Dining Philosopher,45 Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii ,Dining Philosopher,45 Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii ,Dining Philosopher,45 Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii ,Dining Philosopher,45 Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii ,Dining Philosopher,45 Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii ,Dining Philosopher,45 Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii ,Dining Philosopher,45 Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii ,Dining Philosopher,45 Consider the following two scenarios in the dining philosophers problem First a philosopher has to enter a room with the table that restricts the number of philosophers to four There is no restriction on the number of philosophers entering the room Which of the following is true Deadlock is possible in i and ii Deadlock is possible in i Starvation is possible in i Deadlock is not possible in ii Starvation is not possible in ii ,Dining Philosopher,45 Four branches of a company are located at M N O and P M is north of N at a distance of 4 km P is south of O at a distance of 2 km N is southeast of O by 1 km What is the distance between M and P in km 5 34 6 74 28 5 45 49 ,Direction Sense,46 Four branches of a company are located at M N O and P M is north of N at a distance of 4 km P is south of O at a distance of 2 km N is southeast of O by 1 km What is the distance between M and P in km 5 34 6 74 28 5 45 49 ,Direction Sense,46 There are five buildings called V W X Y and Z in a row not necessarily in that order V is to the West of W Z is to the East of X and the West of V W is to the West of Y Which is the building in the middle V W X Y ,Direction Sense,46 There are five buildings called V W X Y and Z in a row not necessarily in that order V is to the West of W Z is to the East of X and the West of V W is to the West of Y Which is the building in the middle V W X Y ,Direction Sense,46 Four branches of a company are located at M N O and P M is north of N at a distance of 4 km P is south of O at a distance of 2 km N is southeast of O by 1 km What is the distance between M and P in km 5 34 6 74 28 5 45 49 ,Direction Sense,46 Four branches of a company are located at M N O and P M is north of N at a distance of 4 km P is south of O at a distance of 2 km N is southeast of O by 1 km What is the distance between M and P in km 5 34 6 74 28 5 45 49 ,Direction Sense,46 There are five buildings called V W X Y and Z in a row not necessarily in that order V is to the West of W Z is to the East of X and the West of V W is to the West of Y Which is the building in the middle V W X Y ,Direction Sense,46 Four branches of a company are located at M N O and P M is north of N at a distance of 4 km P is south of O at a distance of 2 km N is southeast of O by 1 km What is the distance between M and P in km 5 34 6 74 28 5 45 49 ,Direction Sense,46 Four branches of a company are located at M N O and P M is north of N at a distance of 4 km P is south of O at a distance of 2 km N is southeast of O by 1 km What is the distance between M and P in km 5 34 6 74 28 5 45 49 ,Direction Sense,46 Four branches of a company are located at M N O and P M is north of N at a distance of 4 km P is south of O at a distance of 2 km N is southeast of O by 1 km What is the distance between M and P in km 5 34 6 74 28 5 45 49 ,Direction Sense,46 Four branches of a company are located at M N O and P M is north of N at a distance of 4 km P is south of O at a distance of 2 km N is southeast of O by 1 km What is the distance between M and P in km 5 34 6 74 28 5 45 49 ,Direction Sense,46 Four branches of a company are located at M N O and P M is north of N at a distance of 4 km P is south of O at a distance of 2 km N is southeast of O by 1 km What is the distance between M and P in km 5 34 6 74 28 5 45 49 ,Direction Sense,46 There are five buildings called V W X Y and Z in a row not necessarily in that order V is to the West of W Z is to the East of X and the West of V W is to the West of Y Which is the building in the middle V W X Y ,Direction Sense,46 Suppose a disk has 201 cylinders numbered from 0 to 200 At some time the disk arm is at cylinder 100 and there is a queue of disk access requests for cylinders 30 85 90 100 105 110 135 and 145 If Shortest Seek Time First SSTF is being used for scheduling the disk access the request for cylinder 90 is serviced after servicing ____________ number of requests ,Disk Scheduling,47 The head of a moving head disk with 100 tracks numbered 0 to 99 is currently serving a request at track 55 If the queue of requests kept in FIFO order is 10 70 75 23 65 which of the two disk scheduling algorithms FCFS First Come First Served and SSTF Shortest Seek Time First will require less head movement Find the head movement for each of the algorithms ,Disk Scheduling,47 Suppose a disk has 201 cylinders numbered from 0 to 200 At some time the disk arm is at cylinder 100 and there is a queue of disk access requests for cylinders 30 85 90 100 105 110 135 and 145 If Shortest Seek Time First SSTF is being used for scheduling the disk access the request for cylinder 90 is serviced after servicing ____________ number of requests ,Disk Scheduling,47 Consider an operating system capable of loading and executing a single sequential user process at a time The disk head scheduling algorithm used is First Come First Served FCFS If FCFS is replaced by Shortest Seek Time First SSTF claimed by the vendor to give 50 better benchmark results what is the expected improvement in the I O performance of user programs 50 40 25 0 ,Disk Scheduling,47 The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 ,Dual Function,48 The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 ,Dual Function,48 The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 ,Dual Function,48 The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 ,Dual Function,48 The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 ,Dual Function,48 The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 ,Dual Function,48 The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 ,Dual Function,48 The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 ,Dual Function,48 The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 ,Dual Function,48 The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 ,Dual Function,48 The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 ,Dual Function,48 The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 ,Dual Function,48 The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 ,Dual Function,48 The dual of a Boolean function F x_1 x_2 dots x_n written as F D is the same expression as that of F with and u22c5 swapped F is said to be self dual if F F D The number of self dual functions with n Boolean variables is 2 n 2 n 1 2 2 n 2 2 n 1 ,Dual Function,48 Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds ,Effective Memory Access,49 Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds ,Effective Memory Access,49 Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds ,Effective Memory Access,49 Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds ,Effective Memory Access,49 Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds ,Effective Memory Access,49 Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds ,Effective Memory Access,49 Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds ,Effective Memory Access,49 Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds ,Effective Memory Access,49 Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds ,Effective Memory Access,49 Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds ,Effective Memory Access,49 Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds ,Effective Memory Access,49 Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds ,Effective Memory Access,49 Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds ,Effective Memory Access,49 Suppose the time to service a page fault is on the average 10 milliseconds while a memory access takes 1 microsecond Then a 99 99 hit ratio results in average memory access time of 1 9999 milliseconds 1 millisecond 9 999 microseconds 1 9999 microseconds ,Effective Memory Access,49 The product of the non zero eigenvalues of the matrix is ____ begin pmatrix 1 amp 0 amp 0 amp 0 amp 1 0 amp 1 amp 1 amp 1 amp 0 0 amp 1 amp 1 amp 1 amp 0 0 amp 1 amp 1 amp 1 amp 0 1 amp 0 amp 0 amp 0 amp 1 end pmatrix ,Eigen Value,50 Didn t you buy ____ when you went shopping any paper much paper no paper a few paper ,English Grammar,51 Saturn is ___________ to be seen on a clear night with the naked eye enough bright bright enough as enough bright bright as enough ,English Grammar,51 Archimedes said Give me a lever long enough and a fulcrum on which to place it and I will move the world The sentence above is an example of a ____________ statement figurative collateral literal figurine ,English Grammar,51 Out of the following 4 sentences select the most suitable sentence with respect to grammar and usage Since the report lacked needed information it was of no use to them The report was useless to them because there were no needed information in it Since the report did not contain the needed information it was not real useful to them Since the report lacked needed information it would not had been useful to them ,English Grammar,51 Which one of the parts A B C D in the sentence contains an ERROR No sooner had the doctor seen the results of the blood test than he suggested the patient to see the specialist A no sooner had B results of the blood test C suggested the patient D see the specialist ,English Grammar,51 Choose the grammatically CORRECT sentence He laid in bed till 8 o u2019clock in the morning He layed in bed till 8 o u2019clock in the morning He lain in bed till 8 o u2019clock in the morning He lay in bed till 8 o u2019clock in the morning ,English Grammar,51 Consider an Entity Relationship ER model in which entity sets E _ 1 and E _ 2 are connected by an m n relationship R _ 12 E _ 1 and E _ 3 are connected by a 1 n 1 on the side of E _ 1 and n on the side of E _ 3 relationship R _ 13 E _ 1 has two singled attributes a _ 11 and a _ 12 of which a _ 11 is the key attribute E _ 2 has two singled valued attributes a _ 21 and a _ 22 of which a _ 21 is the key attribute E _ 3 has two single valued attributes a _ 31 and a _ 32 of which a _ 31 is the key attribute The relationships do not have any attributes If a relational model is derived from the above ER model then the minimum number of relations that would be generated if all relation are in 3NF is________________ ,Er Diagram,52 Consider the entities hotel room and person with a many to many relationship lodging as shown below If we wish to store information about the rent payment to be made by person s occupying different hotel rooms then this information should appear as an attribute of Person Hotel Room Lodging None of these ,Er Diagram,52 Consider the following ER diagram The minimum number of tables needed to represent M N P R1 R2 is 2 3 4 5 ,Er Diagram,52 Consider the entities hotel room and person with a many to many relationship lodging as shown below If we wish to store information about the rent payment to be made by person s occupying different hotel rooms then this information should appear as an attribute of Person Hotel Room Lodging None of these ,Er Diagram,52 Consider the following ER diagram The minimum number of tables needed to represent M N P R1 R2 is 2 3 4 5 ,Er Diagram,52 Consider an Entity Relationship ER model in which entity sets E _ 1 and E _ 2 are connected by an m n relationship R _ 12 E _ 1 and E _ 3 are connected by a 1 n 1 on the side of E _ 1 and n on the side of E _ 3 relationship R _ 13 E _ 1 has two singled attributes a _ 11 and a _ 12 of which a _ 11 is the key attribute E _ 2 has two singled valued attributes a _ 21 and a _ 22 of which a _ 21 is the key attribute E _ 3 has two single valued attributes a _ 31 and a _ 32 of which a _ 31 is the key attribute The relationships do not have any attributes If a relational model is derived from the above ER model then the minimum number of relations that would be generated if all relation are in 3NF is________________ ,Er Diagram,52 Consider the following ER diagram The minimum number of tables needed to represent M N P R1 R2 is Which of the following is a correct attribute set for one of the tables for the minimum number of tables needed to represent M N P R1 R2 M1 M2 M3 P1 M1 P1 N1 N2 M1 P1 N1 M1 P1 ,Er Diagram,52 Consider the following ER diagram The minimum number of tables needed to represent M N P R1 R2 is Which of the following is a correct attribute set for one of the tables for the minimum number of tables needed to represent M N P R1 R2 M1 M2 M3 P1 M1 P1 N1 N2 M1 P1 N1 M1 P1 ,Er Diagram,52 Suppose that the expectation of a random variable X is 5 Which of the following statements is true There is a sample point at which X has the value 5 There is a sample point at which X has value greater than 5 There is a sample point at which X has a value greater than equal to 5 None of the above ,Expectation,53 We are given a set X X_1 X_n where X_i 2 i A sample S subseteq X is drawn by selecting each X_i independently with probability P_i frac 1 2 The expected value of the smallest number in sample S is left frac 1 n right 2 sqrt n n ,Expectation,53 Assume that you are flipping a fair coin i e probability of heads or tails is equal Then the expected number of coin flips required to obtain two consecutive heads for the first time is 4 3 6 10 5 ,Expectation,53 We are given a set X X_1 X_n where X_i 2 i A sample S subseteq X is drawn by selecting each X_i independently with probability P_i frac 1 2 The expected value of the smallest number in sample S is left frac 1 n right 2 sqrt n n ,Expectation,53 Suppose that the expectation of a random variable X is 5 Which of the following statements is true There is a sample point at which X has the value 5 There is a sample point at which X has value greater than 5 There is a sample point at which X has a value greater than equal to 5 None of the above ,Expectation,53 Consider an undirected random graph of eight vertices The probability that there is an edge between a pair of vertices is dfrac 1 2 What is the expected number of unordered cycles of length three dfrac 1 8 1 7 8 ,Expectation,53 Consider an undirected random graph of eight vertices The probability that there is an edge between a pair of vertices is dfrac 1 2 What is the expected number of unordered cycles of length three dfrac 1 8 1 7 8 ,Expectation,53 We are given a set X X_1 X_n where X_i 2 i A sample S subseteq X is drawn by selecting each X_i independently with probability P_i frac 1 2 The expected value of the smallest number in sample S is left frac 1 n right 2 sqrt n n ,Expectation,53 Assume that you are flipping a fair coin i e probability of heads or tails is equal Then the expected number of coin flips required to obtain two consecutive heads for the first time is 4 3 6 10 5 ,Expectation,53 Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta ,Exponential Distribution,54 Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta ,Exponential Distribution,54 Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta ,Exponential Distribution,54 Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta ,Exponential Distribution,54 Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta ,Exponential Distribution,54 Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta ,Exponential Distribution,54 Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta ,Exponential Distribution,54 Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta ,Exponential Distribution,54 Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta ,Exponential Distribution,54 Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta ,Exponential Distribution,54 Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta ,Exponential Distribution,54 Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta ,Exponential Distribution,54 Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta ,Exponential Distribution,54 Let X and Y be two exponentially distributed and independent random variables with mean u03b1 and u03b2 respectively If Z min X Y then the mean of Z is given by left dfrac 1 alpha beta right min alpha beta left dfrac alpha beta alpha beta right alpha beta ,Exponential Distribution,54 What is the average of all multiples of 10 from 2 to 198 90 100 110 120 ,Factors,55 Out of all the 2 digit integers between 1 and 100 a 2 digit number has to be selected at random What is the probability that the selected number is not divisible by 7 left dfrac 13 90 right left dfrac 12 90 right left dfrac 78 90 right left dfrac 77 90 right ,Factors,55 What is the average of all multiples of 10 from 2 to 198 90 100 110 120 ,Factors,55 What is the average of all multiples of 10 from 2 to 198 90 100 110 120 ,Factors,55 What is the average of all multiples of 10 from 2 to 198 90 100 110 120 ,Factors,55 What is the average of all multiples of 10 from 2 to 198 90 100 110 120 ,Factors,55 What is the average of all multiples of 10 from 2 to 198 90 100 110 120 ,Factors,55 Out of all the 2 digit integers between 1 and 100 a 2 digit number has to be selected at random What is the probability that the selected number is not divisible by 7 left dfrac 13 90 right left dfrac 12 90 right left dfrac 78 90 right left dfrac 77 90 right ,Factors,55 Out of all the 2 digit integers between 1 and 100 a 2 digit number has to be selected at random What is the probability that the selected number is not divisible by 7 left dfrac 13 90 right left dfrac 12 90 right left dfrac 78 90 right left dfrac 77 90 right ,Factors,55 What is the average of all multiples of 10 from 2 to 198 90 100 110 120 ,Factors,55 What is the average of all multiples of 10 from 2 to 198 90 100 110 120 ,Factors,55 Out of all the 2 digit integers between 1 and 100 a 2 digit number has to be selected at random What is the probability that the selected number is not divisible by 7 left dfrac 13 90 right left dfrac 12 90 right left dfrac 78 90 right left dfrac 77 90 right ,Factors,55 Out of all the 2 digit integers between 1 and 100 a 2 digit number has to be selected at random What is the probability that the selected number is not divisible by 7 left dfrac 13 90 right left dfrac 12 90 right left dfrac 78 90 right left dfrac 77 90 right ,Factors,55 Consider the field C of complex numbers with addition and multiplication Which of the following form s a subfield of C with addition and multiplication S1 the set of real numbers S2 a ib a and b are rational numbers S3 a ib a2 b2 u2264 1 S4 ia a is real only S1 S1 and S3 S2 and S3 S1 and S2 ,Fields,56 Consider the field C of complex numbers with addition and multiplication Which of the following form s a subfield of C with addition and multiplication S1 the set of real numbers S2 a ib a and b are rational numbers S3 a ib a2 b2 u2264 1 S4 ia a is real only S1 S1 and S3 S2 and S3 S1 and S2 ,Fields,56 Consider the field C of complex numbers with addition and multiplication Which of the following form s a subfield of C with addition and multiplication S1 the set of real numbers S2 a ib a and b are rational numbers S3 a ib a2 b2 u2264 1 S4 ia a is real only S1 S1 and S3 S2 and S3 S1 and S2 ,Fields,56 Consider the field C of complex numbers with addition and multiplication Which of the following form s a subfield of C with addition and multiplication S1 the set of real numbers S2 a ib a and b are rational numbers S3 a ib a2 b2 u2264 1 S4 ia a is real only S1 S1 and S3 S2 and S3 S1 and S2 ,Fields,56 Consider the field C of complex numbers with addition and multiplication Which of the following form s a subfield of C with addition and multiplication S1 the set of real numbers S2 a ib a and b are rational numbers S3 a ib a2 b2 u2264 1 S4 ia a is real only S1 S1 and S3 S2 and S3 S1 and S2 ,Fields,56 Consider the field C of complex numbers with addition and multiplication Which of the following form s a subfield of C with addition and multiplication S1 the set of real numbers S2 a ib a and b are rational numbers S3 a ib a2 b2 u2264 1 S4 ia a is real only S1 S1 and S3 S2 and S3 S1 and S2 ,Fields,56 Consider the field C of complex numbers with addition and multiplication Which of the following form s a subfield of C with addition and multiplication S1 the set of real numbers S2 a ib a and b are rational numbers S3 a ib a2 b2 u2264 1 S4 ia a is real only S1 S1 and S3 S2 and S3 S1 and S2 ,Fields,56 Consider the field C of complex numbers with addition and multiplication Which of the following form s a subfield of C with addition and multiplication S1 the set of real numbers S2 a ib a and b are rational numbers S3 a ib a2 b2 u2264 1 S4 ia a is real only S1 S1 and S3 S2 and S3 S1 and S2 ,Fields,56 Consider the field C of complex numbers with addition and multiplication Which of the following form s a subfield of C with addition and multiplication S1 the set of real numbers S2 a ib a and b are rational numbers S3 a ib a2 b2 u2264 1 S4 ia a is real only S1 S1 and S3 S2 and S3 S1 and S2 ,Fields,56 Consider the field C of complex numbers with addition and multiplication Which of the following form s a subfield of C with addition and multiplication S1 the set of real numbers S2 a ib a and b are rational numbers S3 a ib a2 b2 u2264 1 S4 ia a is real only S1 S1 and S3 S2 and S3 S1 and S2 ,Fields,56 Consider the field C of complex numbers with addition and multiplication Which of the following form s a subfield of C with addition and multiplication S1 the set of real numbers S2 a ib a and b are rational numbers S3 a ib a2 b2 u2264 1 S4 ia a is real only S1 S1 and S3 S2 and S3 S1 and S2 ,Fields,56 Consider the field C of complex numbers with addition and multiplication Which of the following form s a subfield of C with addition and multiplication S1 the set of real numbers S2 a ib a and b are rational numbers S3 a ib a2 b2 u2264 1 S4 ia a is real only S1 S1 and S3 S2 and S3 S1 and S2 ,Fields,56 Consider the field C of complex numbers with addition and multiplication Which of the following form s a subfield of C with addition and multiplication S1 the set of real numbers S2 a ib a and b are rational numbers S3 a ib a2 b2 u2264 1 S4 ia a is real only S1 S1 and S3 S2 and S3 S1 and S2 ,Fields,56 Consider the field C of complex numbers with addition and multiplication Which of the following form s a subfield of C with addition and multiplication S1 the set of real numbers S2 a ib a and b are rational numbers S3 a ib a2 b2 u2264 1 S4 ia a is real only S1 S1 and S3 S2 and S3 S1 and S2 ,Fields,56 A FAT file allocation table based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size Given a 100 imes 10 6 bytes disk on which the file system is stored and data block size is 10 3 bytes the maximum size of a file that can be stored on this disk in units of 10 6 bytes is _________ ,File,57 A FAT file allocation table based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size Given a 100 imes 10 6 bytes disk on which the file system is stored and data block size is 10 3 bytes the maximum size of a file that can be stored on this disk in units of 10 6 bytes is _________ ,File,57 A FAT file allocation table based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size Given a 100 imes 10 6 bytes disk on which the file system is stored and data block size is 10 3 bytes the maximum size of a file that can be stored on this disk in units of 10 6 bytes is _________ ,File,57 A FAT file allocation table based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size Given a 100 imes 10 6 bytes disk on which the file system is stored and data block size is 10 3 bytes the maximum size of a file that can be stored on this disk in units of 10 6 bytes is _________ ,File,57 A FAT file allocation table based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size Given a 100 imes 10 6 bytes disk on which the file system is stored and data block size is 10 3 bytes the maximum size of a file that can be stored on this disk in units of 10 6 bytes is _________ ,File,57 A FAT file allocation table based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size Given a 100 imes 10 6 bytes disk on which the file system is stored and data block size is 10 3 bytes the maximum size of a file that can be stored on this disk in units of 10 6 bytes is _________ ,File,57 A FAT file allocation table based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size Given a 100 imes 10 6 bytes disk on which the file system is stored and data block size is 10 3 bytes the maximum size of a file that can be stored on this disk in units of 10 6 bytes is _________ ,File,57 A FAT file allocation table based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size Given a 100 imes 10 6 bytes disk on which the file system is stored and data block size is 10 3 bytes the maximum size of a file that can be stored on this disk in units of 10 6 bytes is _________ ,File,57 A FAT file allocation table based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size Given a 100 imes 10 6 bytes disk on which the file system is stored and data block size is 10 3 bytes the maximum size of a file that can be stored on this disk in units of 10 6 bytes is _________ ,File,57 A FAT file allocation table based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size Given a 100 imes 10 6 bytes disk on which the file system is stored and data block size is 10 3 bytes the maximum size of a file that can be stored on this disk in units of 10 6 bytes is _________ ,File,57 A FAT file allocation table based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size Given a 100 imes 10 6 bytes disk on which the file system is stored and data block size is 10 3 bytes the maximum size of a file that can be stored on this disk in units of 10 6 bytes is _________ ,File,57 A FAT file allocation table based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size Given a 100 imes 10 6 bytes disk on which the file system is stored and data block size is 10 3 bytes the maximum size of a file that can be stored on this disk in units of 10 6 bytes is _________ ,File,57 A FAT file allocation table based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size Given a 100 imes 10 6 bytes disk on which the file system is stored and data block size is 10 3 bytes the maximum size of a file that can be stored on this disk in units of 10 6 bytes is _________ ,File,57 A FAT file allocation table based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size Given a 100 imes 10 6 bytes disk on which the file system is stored and data block size is 10 3 bytes the maximum size of a file that can be stored on this disk in units of 10 6 bytes is _________ ,File,57 In a particular Unix OS each data block is of size 1024 bytes each node has 10 direct data block addresses and three additional addresses one for single indirect block one for double indirect block and one for triple indirect block Also each block can contain addresses for 128 blocks Which one of the following is approximately the maximum size of a file in the file system 512 MB 2 GB 8 GB 16 GB ,File System,58 In a file allocation system which of the following allocation scheme s can be used if no external fragmentation is allowed Contiguous Linked Indexed 1 and 3 only 2 only 3 only 2 and 3 only ,File System,58 In the index allocation scheme of blocks to a file the maximum possible size of the file depends on the size of the blocks and the size of the address of the blocks the number of blocks used for the index and the size of the blocks the size of the blocks the number of blocks used for the index and the size of the address of the blocks None of the above ,File System,58 In a particular Unix OS each data block is of size 1024 bytes each node has 10 direct data block addresses and three additional addresses one for single indirect block one for double indirect block and one for triple indirect block Also each block can contain addresses for 128 blocks Which one of the following is approximately the maximum size of a file in the file system 512 MB 2 GB 8 GB 16 GB ,File System,58 A file system with a one level directory structure is implemented on a disk with disk block size of 4K bytes The disk is used as follows Disk block 0 File Allocation Table consisting of one 8 bit entry per data block representing the data block address of the next data block in the file Disk block 1 Directory with one 32 bit entry per file Disk block 2 Data block 1 Disk block 3 Data block 2 etc What is the maximum possible number of files What is the maximum possible file size in blocks ,File System,58 In a file allocation system which of the following allocation scheme s can be used if no external fragmentation is allowed Contiguous Linked Indexed 1 and 3 only 2 only 3 only 2 and 3 only ,File System,58 In a particular Unix OS each data block is of size 1024 bytes each node has 10 direct data block addresses and three additional addresses one for single indirect block one for double indirect block and one for triple indirect block Also each block can contain addresses for 128 blocks Which one of the following is approximately the maximum size of a file in the file system 512 MB 2 GB 8 GB 16 GB ,File System,58 In a file allocation system which of the following allocation scheme s can be used if no external fragmentation is allowed Contiguous Linked Indexed 1 and 3 only 2 only 3 only 2 and 3 only ,File System,58 In a file allocation system which of the following allocation scheme s can be used if no external fragmentation is allowed Contiguous Linked Indexed 1 and 3 only 2 only 3 only 2 and 3 only ,File System,58 In the index allocation scheme of blocks to a file the maximum possible size of the file depends on the size of the blocks and the size of the address of the blocks the number of blocks used for the index and the size of the blocks the size of the blocks the number of blocks used for the index and the size of the address of the blocks None of the above ,File System,58 Indicate whether the following statement is true or false providing a short explanation to substantiate your answers If a language L is accepted by an NFA with n states then there is a DFA with no more than 2 n states accepting L ,Finite Automata,59 Consider the following first order logic formula in which R is a binary relation symbol u2200x u2200y R x y implies R y x The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable ,First Order Logic,60 def graph ext Graph def connected ext Connected Let graph x be a predicate which denotes that x is a graph Let connected x be a predicate which denotes that x is connected Which of the following first order logic sentences DOES NOT represent the statement qquad ext Not every graph is connected lnot forall x Bigl graph x implies connected x Bigr exists x Bigl graph x land lnot connected x Bigr lnot forall x Bigl lnot graph x lor connected x Bigr forall x Bigl graph x implies lnot connected x Bigr ,First Order Logic,60 Let a x y b x y and c x y be three statements with variables x and y chosen from some universe Consider the following statement qquad exists x forall y a x y wedge b x y wedge eg c x y Which one of the following is its equivalent forall x exists y a x y vee b x y o c x y exists x forall y a x y vee b x y wedge eg c x y eg forall x exists y a x y wedge b x y o c x y eg forall x exists y a x y vee b x y o c x y ,First Order Logic,60 b Consider the following first order formula left matrix forall x exists y R x y 1em Large land 1em forall x forall y Bigl R x y implies lnot R y x Bigr 1em Large land 1em forall x forall y forall z Bigl R x y land R y z implies R x z Bigr 1em Large land 1em forall x lnot R x x right Does it have finite models Is it satisfiable If so give a countable model for it ,First Order Logic,60 Consider the following first order logic formula in which R is a binary relation symbol u2200x u2200y R x y implies R y x The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable ,First Order Logic,60 What is the first order predicate calculus statement equivalent to the following Every teacher is liked by some student u2200 x left ext teacher left x right u2192 u2203 y left ext student left y right u2192 ext likes left y x right right right u2200 x left ext teacher left x right u2192 u2203 y left ext student left y right u2227 ext likes left y x right right right u2203 y u2200 x left ext teacher left x right u2192 left ext student left y right u2227 ext likes left y x right right right u2200 x left ext teacher left x right u2227 u2203 y left ext student left y right u2192 ext likes left y x right right right ,First Order Logic,60 The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right ,Fixed Point Representation,61 The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right ,Fixed Point Representation,61 The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right ,Fixed Point Representation,61 The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right ,Fixed Point Representation,61 The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right ,Fixed Point Representation,61 The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right ,Fixed Point Representation,61 The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right ,Fixed Point Representation,61 The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right ,Fixed Point Representation,61 The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right ,Fixed Point Representation,61 The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right ,Fixed Point Representation,61 The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right ,Fixed Point Representation,61 The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right ,Fixed Point Representation,61 The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right ,Fixed Point Representation,61 The n bit fixed point representation of an unsigned real number X uses f bits for the fraction part Let i n f The range of decimal values for X in this representation is 2 f to 2 i 2 f to left 2 i 2 f right 0 to 2 i 0 to left 2 i 2 f right ,Fixed Point Representation,61 Consider a combination of T and D flip flops connected as shown below The output of the D flip flop is connected to the input of the T flip flop and the output of the T flip flop is connected to the input of the D flip flop Initially both Q_ 0 and Q_ 1 are set to 1 before the 1st clock cycle The outputs Q_ 1 Q_ 0 after the 3rd cycle are 11 and after the 4th cycle are 00 respectively Q_ 1 Q_ 0 after the 3rd cycle are 11 and after the 4th cycle are 01 respectively Q_ 1 Q_ 0 after the 3rd cycle are 00 and after the 4th cycle are 11 respectively Q_ 1 Q_ 0 after the 3rd cycle are 01 and after the 4th cycle are 01 respectively ,Flip Flop,62 Consider a combination of T and D flip flops connected as shown below The output of the D flip flop is connected to the input of the T flip flop and the output of the T flip flop is connected to the input of the D flip flop Initially both Q_ 0 and Q_ 1 are set to 1 before the 1st clock cycle The outputs Q_ 1 Q_ 0 after the 3rd cycle are 11 and after the 4th cycle are 00 respectively Q_ 1 Q_ 0 after the 3rd cycle are 11 and after the 4th cycle are 01 respectively Q_ 1 Q_ 0 after the 3rd cycle are 00 and after the 4th cycle are 11 respectively Q_ 1 Q_ 0 after the 3rd cycle are 01 and after the 4th cycle are 01 respectively ,Flip Flop,62 In an SR latch made by cross coupling two NAND gates if both S and R inputs are set to 0 then it will result in Q 0 Q 1 Q 1 Q 0 Q 1 Q 1 Indeterminate states ,Flip Flop,62 A positive edge triggered D flip flop is connected to a positive edge triggered JK flip flop as follows The Q output of the D flip flop is connected to both the J and K inputs of the JK flip flop while the Q output of the JK flip flop is connected to the input of the D flip flop Initially the output of the D flip flop is set to logic one and the output of the JK flip flop is cleared Which one of the following is the bit sequence including the initial state generated at the Q output of the JK flip flop when the flip flops are connected to a free running common clock Assume that J K 1 is the toggle mode and J K 0 is the state holding mode of the JK flip flops Both the flip flops have non zero propagation delays 0110110 0100100 011101110 011001100 ,Flip Flop,62 A positive edge triggered D flip flop is connected to a positive edge triggered JK flip flop as follows The Q output of the D flip flop is connected to both the J and K inputs of the JK flip flop while the Q output of the JK flip flop is connected to the input of the D flip flop Initially the output of the D flip flop is set to logic one and the output of the JK flip flop is cleared Which one of the following is the bit sequence including the initial state generated at the Q output of the JK flip flop when the flip flops are connected to a free running common clock Assume that J K 1 is the toggle mode and J K 0 is the state holding mode of the JK flip flops Both the flip flops have non zero propagation delays 0110110 0100100 011101110 011001100 ,Flip Flop,62 A positive edge triggered D flip flop is connected to a positive edge triggered JK flip flop as follows The Q output of the D flip flop is connected to both the J and K inputs of the JK flip flop while the Q output of the JK flip flop is connected to the input of the D flip flop Initially the output of the D flip flop is set to logic one and the output of the JK flip flop is cleared Which one of the following is the bit sequence including the initial state generated at the Q output of the JK flip flop when the flip flops are connected to a free running common clock Assume that J K 1 is the toggle mode and J K 0 is the state holding mode of the JK flip flops Both the flip flops have non zero propagation delays 0110110 0100100 011101110 011001100 ,Flip Flop,62 A sequential circuit takes an input stream of 0 s and 1 s and produces an output stream of 0 s and 1 s Initially it replicates the input on its output until two consecutive 0 s are encountered on the input From then onward it produces an output stream which is the bit wise complement of input stream until it encounters two consecutive 1 s whereupon the process repeats An example input and output stream is shown below The input stream 101100 01001011 0 11 The desired output 101100 10110100 0 11 J K master slave flip flops are to be used to design the circuit Give the state transition diagram,Flip Flop,62 A positive edge triggered D flip flop is connected to a positive edge triggered JK flip flop as follows The Q output of the D flip flop is connected to both the J and K inputs of the JK flip flop while the Q output of the JK flip flop is connected to the input of the D flip flop Initially the output of the D flip flop is set to logic one and the output of the JK flip flop is cleared Which one of the following is the bit sequence including the initial state generated at the Q output of the JK flip flop when the flip flops are connected to a free running common clock Assume that J K 1 is the toggle mode and J K 0 is the state holding mode of the JK flip flops Both the flip flops have non zero propagation delays 0110110 0100100 011101110 011001100 ,Flip Flop,62 A positive edge triggered D flip flop is connected to a positive edge triggered JK flip flop as follows The Q output of the D flip flop is connected to both the J and K inputs of the JK flip flop while the Q output of the JK flip flop is connected to the input of the D flip flop Initially the output of the D flip flop is set to logic one and the output of the JK flip flop is cleared Which one of the following is the bit sequence including the initial state generated at the Q output of the JK flip flop when the flip flops are connected to a free running common clock Assume that J K 1 is the toggle mode and J K 0 is the state holding mode of the JK flip flops Both the flip flops have non zero propagation delays 0110110 0100100 011101110 011001100 ,Flip Flop,62 The exponent of a floating point number is represented in excess N code so that The dynamic range is large The precision is high The smallest number is represented by all zeros Overflow is avoided ,Floating Point Representation,63 A 32 bit floating point number is represented by a 7 bit signed exponent and a 24 bit fractional mantissa The base of the scale factor is 16 The range of the exponent is ___________,Floating Point Representation,63 Given the following binary number in 32 bit single precision IEEE 754 format large 00111110011011010000000000000000 The decimal value closest to this floating point number is 1 45 10 1 1 45 10 1 2 27 10 1 2 27 10 1 ,Floating Point Representation,63 Given the following binary number in 32 bit single precision IEEE 754 format large 00111110011011010000000000000000 The decimal value closest to this floating point number is 1 45 10 1 1 45 10 1 2 27 10 1 2 27 10 1 ,Floating Point Representation,63 Consider the following floating point format Mantissa is a pure fraction in sign magnitude form The normalized representation for the above format is specified as follows The mantissa has an implicit 1 preceding the binary radix point Assume that only 0 u2019s are padded in while shifting a field The normalized representation of the above number 0 239 imes 2 13 is 0A 20 11 34 49 D0 4A E8 ,Floating Point Representation,63 Given the following binary number in 32 bit single precision IEEE 754 format large 00111110011011010000000000000000 The decimal value closest to this floating point number is 1 45 10 1 1 45 10 1 2 27 10 1 2 27 10 1 ,Floating Point Representation,63 The exponent of a floating point number is represented in excess N code so that The dynamic range is large The precision is high The smallest number is represented by all zeros Overflow is avoided ,Floating Point Representation,63 The following is a scheme for floating point number representation using 16 bits Bit Position 15 14 9 8 0 s e m Sign Exponent Mantissa Let s e and m be the numbers represented in binary in the sign exponent and mantissa fields respectively Then the floating point number represented is begin cases 1 s left 1 m imes 2 9 right 2 e 31 amp ext if the exponent eq 111111 0 amp ext otherwise end cases What is the maximum difference between two successive real numbers representable in this system 2 40 2 9 2 22 2 31 ,Floating Point Representation,63 The exponent of a floating point number is represented in excess N code so that The dynamic range is large The precision is high The smallest number is represented by all zeros Overflow is avoided ,Floating Point Representation,63 A process executes the following segment of code for i 1 i lt n i fork The number of new processes created is n n n 1 2 2 n 1 3 n 1 ,Fork,64 A process executes the following segment of code for i 1 i lt n i fork The number of new processes created is n n n 1 2 2 n 1 3 n 1 ,Fork,64 Consider the following code fragment if fork 0 a a 5 printf d p n a amp a else a a 5 printf d p n a amp a Let u v be the values printed by the parent process and x y be the values printed by the child process Which one of the following is TRUE u x 10 and v y u x 10 and v y u 10 x and v y u 10 x and v y ,Fork,64 A process executes the code fork fork fork The total number of child processes created is 3 4 7 8 ,Fork,64 A process executes the code fork fork fork The total number of child processes created is 3 4 7 8 ,Fork,64 A process executes the code fork fork fork The total number of child processes created is 3 4 7 8 ,Fork,64 A process executes the following code for i 0 i lt n i fork The total number of child processes created is n 2n 1 2n 2n 1 1 ,Fork,64 A process executes the code fork fork fork The total number of child processes created is 3 4 7 8 ,Fork,64 A process executes the following segment of code for i 1 i lt n i fork The number of new processes created is n n n 1 2 2 n 1 3 n 1 ,Fork,64 A process executes the following segment of code for i 1 i lt n i fork The number of new processes created is n n n 1 2 2 n 1 3 n 1 ,Fork,64 A process executes the following code for i 0 i lt n i fork The total number of child processes created is n 2n 1 2n 2n 1 1 ,Fork,64 A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND ,Functional Completeness,65 A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND ,Functional Completeness,65 The implication gate shown below has two inputs x ext and y the output is 1 except when x 1 ext and y 0 ext realize f bar x y x bar y using only four implication gates Show that the implication gate is functionally complete ,Functional Completeness,65 The implication gate shown below has two inputs x ext and y the output is 1 except when x 1 ext and y 0 ext realize f bar x y x bar y using only four implication gates Show that the implication gate is functionally complete ,Functional Completeness,65 A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND ,Functional Completeness,65 A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND ,Functional Completeness,65 The implication gate shown below has two inputs x ext and y the output is 1 except when x 1 ext and y 0 ext realize f bar x y x bar y using only four implication gates Show that the implication gate is functionally complete ,Functional Completeness,65 The implication gate shown below has two inputs x ext and y the output is 1 except when x 1 ext and y 0 ext realize f bar x y x bar y using only four implication gates Show that the implication gate is functionally complete ,Functional Completeness,65 A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND ,Functional Completeness,65 A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND ,Functional Completeness,65 The implication gate shown below has two inputs x ext and y the output is 1 except when x 1 ext and y 0 ext realize f bar x y x bar y using only four implication gates Show that the implication gate is functionally complete ,Functional Completeness,65 A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND ,Functional Completeness,65 A set of Boolean connectives is functionally complete if all Boolean functions can be synthesized using those Which of the following sets of connectives is NOT functionally complete EX NOR implication negation OR negation NAND ,Functional Completeness,65 Form the following instance of a relation schema R A B C we can conclude that A B C 1 1 1 1 1 0 2 3 2 2 3 2 A functionally determines B and B functionally determines C A functionally determines B and B does not functionally determine C B does not functionally determine C A does not functionally determine B and B does not functionally determine C ,Functional Dependencies,66 Relation R has eight attributes ext ABCDEFGH Fields of R contain only atomic values F ext CH u2192G A u2192BC B u2192CFH E u2192A F u2192EG is a set of functional dependencies FDs so that F is exactly the set of FDs that hold for R How many candidate keys does the relation R have 3 4 5 6 ,Functional Dependencies,66 What is the generating function G z for the sequence of Fibonacci numbers ,Generating Functions,68 The coefficient of x 12 in left x 3 x 4 x 5 x 6 dots right 3 is ___________ ,Generating Functions,68 The coefficient of x 3 in the expansion of 1 x 3 2 x 2 10 is 2 14 31 left frac 3 3 right left frac 10 1 right left frac 3 3 right 2 left frac 10 1 right left frac 3 3 right left frac 10 1 right 2 9 ,Generating Functions,68 The coefficient of x 3 in the expansion of 1 x 3 2 x 2 10 is 2 14 31 left frac 3 3 right left frac 10 1 right left frac 3 3 right 2 left frac 10 1 right left frac 3 3 right left frac 10 1 right 2 9 ,Generating Functions,68 The coefficient of x 12 in left x 3 x 4 x 5 x 6 dots right 3 is ___________ ,Generating Functions,68 The coefficient of x 12 in left x 3 x 4 x 5 x 6 dots right 3 is ___________ ,Generating Functions,68 If the ordinary generating function of a sequence big a_n big _ n 0 infty is large frac 1 z 1 z 3 then a_3 a_0 is equal to ___________ ,Generating Functions,68 If the ordinary generating function of a sequence big a_n big _ n 0 infty is large frac 1 z 1 z 3 then a_3 a_0 is equal to ___________ ,Generating Functions,68 The coefficient of x 12 in left x 3 x 4 x 5 x 6 dots right 3 is ___________ ,Generating Functions,68 The coefficient of x 3 in the expansion of 1 x 3 2 x 2 10 is 2 14 31 left frac 3 3 right left frac 10 1 right left frac 3 3 right 2 left frac 10 1 right left frac 3 3 right left frac 10 1 right 2 9 ,Generating Functions,68 If the ordinary generating function of a sequence big a_n big _ n 0 infty is large frac 1 z 1 z 3 then a_3 a_0 is equal to ___________ ,Generating Functions,68 A cube is built using 64 cubic blocks of side one unit After it is built one cubic block is removed from every corner of the cube The resulting surface area of the body in square units after the removal is ________ 56 64 72 96 ,Geometry,69 A cube is built using 64 cubic blocks of side one unit After it is built one cubic block is removed from every corner of the cube The resulting surface area of the body in square units after the removal is ________ 56 64 72 96 ,Geometry,69 In a triangle PQR PS is the angle bisector of angle QPR ext and angle QPS 60 circ What is the length of PS left dfrac q r qr right left dfrac qr q r right large sqrt q 2 r 2 left dfrac q r 2 qr right ,Geometry,69 In a triangle PQR PS is the angle bisector of angle QPR ext and angle QPS 60 circ What is the length of PS left dfrac q r qr right left dfrac qr q r right large sqrt q 2 r 2 left dfrac q r 2 qr right ,Geometry,69 When a point inside of a tetrahedron a solid with four triangular surfaces is connected by straight lines to its corners how many new internal planes are created with these lines ,Geometry,69 A cube is built using 64 cubic blocks of side one unit After it is built one cubic block is removed from every corner of the cube The resulting surface area of the body in square units after the removal is ________ 56 64 72 96 ,Geometry,69 A cube is built using 64 cubic blocks of side one unit After it is built one cubic block is removed from every corner of the cube The resulting surface area of the body in square units after the removal is ________ 56 64 72 96 ,Geometry,69 A cube is built using 64 cubic blocks of side one unit After it is built one cubic block is removed from every corner of the cube The resulting surface area of the body in square units after the removal is ________ 56 64 72 96 ,Geometry,69 A cube is built using 64 cubic blocks of side one unit After it is built one cubic block is removed from every corner of the cube The resulting surface area of the body in square units after the removal is ________ 56 64 72 96 ,Geometry,69 In a triangle PQR PS is the angle bisector of angle QPR ext and angle QPS 60 circ What is the length of PS left dfrac q r qr right left dfrac qr q r right large sqrt q 2 r 2 left dfrac q r 2 qr right ,Geometry,69 A cube is built using 64 cubic blocks of side one unit After it is built one cubic block is removed from every corner of the cube The resulting surface area of the body in square units after the removal is ________ 56 64 72 96 ,Geometry,69 When a point inside of a tetrahedron a solid with four triangular surfaces is connected by straight lines to its corners how many new internal planes are created with these lines ,Geometry,69 An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code ,Goto,70 An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code ,Goto,70 An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code ,Goto,70 An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code ,Goto,70 An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code ,Goto,70 An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code ,Goto,70 An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code ,Goto,70 An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code ,Goto,70 An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code ,Goto,70 An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code ,Goto,70 An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code ,Goto,70 An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code ,Goto,70 An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code ,Goto,70 An unrestricted use of the goto statement is harmful because it makes it more difficult to verify programs it increases the running time of the programs it increases the memory required for the programs it results in the compiler generating longer machine code ,Goto,70 A vertex colouring of a graph G V E with k coulours is a mapping c V rightarrow 1 dots k such that c u eq c v for every u v in E Consider the following statements If every vertex in G has degree at most d then G admits a vertex coulouring using d 1 colours Every cycle admits a vertex colouring using 2 colours Every tree admits a vertex colouring using 2 colours Which of the above statements is are TRUE Choose from the following options only i only i and ii only i and iii only ii and iii i ii and iii ,Graph Coloring,71 What is the chromatic number of an n vertex simple connected graph which does not contain any odd length cycle Assume n gt 2 2 3 n 1 n ,Graph Coloring,71 The minimum number of colours required to colour the following graph such that no two adjacent vertices are assigned the same color is 2 3 4 5 ,Graph Coloring,71 What is the chromatic number of an n vertex simple connected graph which does not contain any odd length cycle Assume n gt 2 2 3 n 1 n ,Graph Coloring,71 The minimum number of colours required to colour the following graph such that no two adjacent vertices are assigned the same color is 2 3 4 5 ,Graph Coloring,71 A cycle on n vertices is isomorphic to its complement The value of n is _____ ,Graph Isomorphism,73 A cycle on n vertices is isomorphic to its complement The value of n is _____ ,Graph Isomorphism,73 Which of the following graphs is isomorphic to ,Graph Isomorphism,73 Which of the following graphs is isomorphic to ,Graph Isomorphism,73 A cycle on n vertices is isomorphic to its complement The value of n is _____ ,Graph Isomorphism,73 A cycle on n vertices is isomorphic to its complement The value of n is _____ ,Graph Isomorphism,73 A cycle on n vertices is isomorphic to its complement The value of n is _____ ,Graph Isomorphism,73 A cycle on n vertices is isomorphic to its complement The value of n is _____ ,Graph Isomorphism,73 A cycle on n vertices is isomorphic to its complement The value of n is _____ ,Graph Isomorphism,73 Which of the following graphs is isomorphic to ,Graph Isomorphism,73 Which of the following graphs is isomorphic to ,Graph Isomorphism,73 Which of the following graphs is isomorphic to ,Graph Isomorphism,73 A cycle on n vertices is isomorphic to its complement The value of n is _____ ,Graph Isomorphism,73 How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 ,Graph Matching,74 How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 ,Graph Matching,74 How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 ,Graph Matching,74 How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 ,Graph Matching,74 How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 ,Graph Matching,74 How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 ,Graph Matching,74 How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 ,Graph Matching,74 How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 ,Graph Matching,74 How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 ,Graph Matching,74 How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 ,Graph Matching,74 How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 ,Graph Matching,74 How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 ,Graph Matching,74 How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 ,Graph Matching,74 How many perfect matching are there in a complete graph of 6 vertices 15 24 30 60 ,Graph Matching,74 Choose the correct alternatives More than one may be correct A graph is planar if and only if It does not contain subgraphs homeomorphic to k_ 5 and k_ 3 3 It does not contain subgraphs isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph homeomorphic to k_ 5 or k_ 3 3 ,Graph Planarity,75 Answer the following Which of the following graphs is are planner see Fig 2 ,Graph Planarity,75 Choose the correct alternatives More than one may be correct A graph is planar if and only if It does not contain subgraphs homeomorphic to k_ 5 and k_ 3 3 It does not contain subgraphs isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph homeomorphic to k_ 5 or k_ 3 3 ,Graph Planarity,75 Choose the correct alternatives More than one may be correct A graph is planar if and only if It does not contain subgraphs homeomorphic to k_ 5 and k_ 3 3 It does not contain subgraphs isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph homeomorphic to k_ 5 or k_ 3 3 ,Graph Planarity,75 Answer the following Which of the following graphs is are planner see Fig 2 ,Graph Planarity,75 Answer the following Which of the following graphs is are planner see Fig 2 ,Graph Planarity,75 Answer the following Which of the following graphs is are planner see Fig 2 ,Graph Planarity,75 Choose the correct alternatives More than one may be correct A graph is planar if and only if It does not contain subgraphs homeomorphic to k_ 5 and k_ 3 3 It does not contain subgraphs isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph homeomorphic to k_ 5 or k_ 3 3 ,Graph Planarity,75 Choose the correct alternatives More than one may be correct A graph is planar if and only if It does not contain subgraphs homeomorphic to k_ 5 and k_ 3 3 It does not contain subgraphs isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph homeomorphic to k_ 5 or k_ 3 3 ,Graph Planarity,75 Choose the correct alternatives More than one may be correct A graph is planar if and only if It does not contain subgraphs homeomorphic to k_ 5 and k_ 3 3 It does not contain subgraphs isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph homeomorphic to k_ 5 or k_ 3 3 ,Graph Planarity,75 Choose the correct alternatives More than one may be correct A graph is planar if and only if It does not contain subgraphs homeomorphic to k_ 5 and k_ 3 3 It does not contain subgraphs isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph homeomorphic to k_ 5 or k_ 3 3 ,Graph Planarity,75 Answer the following Which of the following graphs is are planner see Fig 2 ,Graph Planarity,75 Choose the correct alternatives More than one may be correct A graph is planar if and only if It does not contain subgraphs homeomorphic to k_ 5 and k_ 3 3 It does not contain subgraphs isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph isomorphic to k_ 5 or k_ 3 3 It does not contain a subgraph homeomorphic to k_ 5 or k_ 3 3 ,Graph Planarity,75 Let G V E be a directed graph where V is the set of vertices and E the set of edges Then which one of the following graphs has the same strongly connected components as G G_1 V E_1 where E_1 left u v mid u v otin E right G_2 V E_2 where E_2 left u v mid v u in E right G_3 V E_3 where E_3 u v mid there is a path of length leq2 from u to v in E G_4 V_4 E where V_4 is the set of vertices in G which are not isolated ,Graphs,76 G is a graph on n vertices and 2n 2 edges The edges of G can be partitioned into two edge disjoint spanning trees Which of the following is NOT true for G For every subset of k vertices the induced subgraph has at most 2k 2 edges The minimum cut in G has at least 2 edges There are at least 2 edge disjoint paths between every pair of vertices There are at least 2 vertex disjoint paths between every pair of vertices ,Graphs,76 What is the size of the smallest MIS Maximal Independent Set of a chain of nine nodes 5 4 3 2 ,Graphs,76 G is a graph on n vertices and 2n 2 edges The edges of G can be partitioned into two edge disjoint spanning trees Which of the following is NOT true for G For every subset of k vertices the induced subgraph has at most 2k 2 edges The minimum cut in G has at least 2 edges There are at least 2 edge disjoint paths between every pair of vertices There are at least 2 vertex disjoint paths between every pair of vertices ,Graphs,76 What is the size of the smallest MIS Maximal Independent Set of a chain of nine nodes 5 4 3 2 ,Graphs,76 What is the size of the smallest MIS Maximal Independent Set of a chain of nine nodes 5 4 3 2 ,Graphs,76 Let G be the graph with 100 vertices numbered 1 to 100 Two vertices i and j are adjacent if vert i j vert 8 or vert i j vert 12 The number of connected components in G is 8 4 12 25 ,Graphs,76 Let G V E be a directed graph where V is the set of vertices and E the set of edges Then which one of the following graphs has the same strongly connected components as G G_1 V E_1 where E_1 left u v mid u v otin E right G_2 V E_2 where E_2 left u v mid v u in E right G_3 V E_3 where E_3 u v mid there is a path of length leq2 from u to v in E G_4 V_4 E where V_4 is the set of vertices in G which are not isolated ,Graphs,76 Let G be the graph with 100 vertices numbered 1 to 100 Two vertices i and j are adjacent if vert i j vert 8 or vert i j vert 12 The number of connected components in G is 8 4 12 25 ,Graphs,76 Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 ,Gray Code,77 Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 ,Gray Code,77 Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 ,Gray Code,77 Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 ,Gray Code,77 Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 ,Gray Code,77 Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 ,Gray Code,77 Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 ,Gray Code,77 Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 ,Gray Code,77 Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 ,Gray Code,77 Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 ,Gray Code,77 Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 ,Gray Code,77 Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 ,Gray Code,77 Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 ,Gray Code,77 Consider numbers represented in 4 bit Gray code Let h_ 3 h_ 2 h_ 1 h_ 0 be the Gray code representation of a number n and let g_ 3 g_ 2 g_ 1 g_ 0 be the Gray code of n 1 modulo 16 value of the number Which one of the following functions is correct g_ 0 h_ 3 h_ 2 h_ 1 h_ 0 sum 1 2 3 6 10 13 14 15 g_ 1 h_ 3 h_ 2 h_ 1 h_ 0 sum 4 9 10 11 12 13 14 15 g_ 2 h_ 3 h_ 2 h_ 1 h_ 0 sum 2 4 5 6 7 12 13 15 g_ 3 h_ 3 h_ 2 h_ 1 h_ 0 sum 0 1 6 7 10 11 12 13 ,Gray Code,77 Consider the set H of all 3 3 matrices of the type left begin array ccc a amp f amp e 0 amp b amp d 0 amp 0 amp c end array right where a b c d e and f are real numbers and abc u2260 0 under the matrix multiplication operation the set H is a group a monoid but not a group a semi group but not a monoid neither a group nor a semi group ,Groups,78 A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ ,Half Adder,79 A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ ,Half Adder,79 A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ ,Half Adder,79 A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ ,Half Adder,79 A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ ,Half Adder,79 A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ ,Half Adder,79 A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ ,Half Adder,79 A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ ,Half Adder,79 A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ ,Half Adder,79 A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ ,Half Adder,79 A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ ,Half Adder,79 A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ ,Half Adder,79 A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ ,Half Adder,79 A half adder is implemented with XOR and AND gates A full adder is implemented with two half adders and one OR gate The propagation delay of an XOR gate is twice that of an AND OR gate The propagation delay of an AND OR gate is 1 2 microseconds A 4 bit ripple carry binary adder is implemented by using four full adders The total propagation time of this 4 bit binary adder in microseconds is ______ ,Half Adder,79 An advantage of chained hash table external hashing over the open addressing scheme is Worst case complexity of search operations is less Space used is less Deletion is easier None of the above ,Hashing,80 In a binary max heap containing n numbers the smallest element can be found in time O n O log n O log log n O 1 ,Heap,81 Let L denote the languages generated by the grammar S o 0S0 mid 00 Which of the following is TRUE L 0 L is regular but not 0 L is context free but not regular L is not context free ,Identify Class Language,82 The following bit pattern represents a floating point number in IEEE 754 single precision format 1 10000011 101000000000000000000000 The value of the number in decimal form is 10 13 26 None of the above ,Ieee Representation,83 The decimal value 0 5 in IEEE single precision floating point representation has fraction bits of 000 dots 000 and exponent value of 0 fraction bits of 000 dots 000 and exponent value of u22121 fraction bits of 100 dots 000 and exponent value of 0 no exact representation ,Ieee Representation,83 In the IEEE floating point representation the hexadecimal value 0 ext x 00000000 corresponds to The normalized value 2 127 The normalized value 2 126 The normalized value 0 The special value 0 ,Ieee Representation,83 In the IEEE floating point representation the hexadecimal value 0 ext x 00000000 corresponds to The normalized value 2 127 The normalized value 2 126 The normalized value 0 The special value 0 ,Ieee Representation,83 In the IEEE floating point representation the hexadecimal value 0 ext x 00000000 corresponds to The normalized value 2 127 The normalized value 2 126 The normalized value 0 The special value 0 ,Ieee Representation,83 The decimal value 0 5 in IEEE single precision floating point representation has fraction bits of 000 dots 000 and exponent value of 0 fraction bits of 000 dots 000 and exponent value of u22121 fraction bits of 100 dots 000 and exponent value of 0 no exact representation ,Ieee Representation,83 The following bit pattern represents a floating point number in IEEE 754 single precision format 1 10000011 101000000000000000000000 The value of the number in decimal form is 10 13 26 None of the above ,Ieee Representation,83 In the IEEE floating point representation the hexadecimal value 0 ext x 00000000 corresponds to The normalized value 2 127 The normalized value 2 126 The normalized value 0 The special value 0 ,Ieee Representation,83 The decimal value 0 5 in IEEE single precision floating point representation has fraction bits of 000 dots 000 and exponent value of 0 fraction bits of 000 dots 000 and exponent value of u22121 fraction bits of 100 dots 000 and exponent value of 0 no exact representation ,Ieee Representation,83 In the IEEE floating point representation the hexadecimal value 0 ext x 00000000 corresponds to The normalized value 2 127 The normalized value 2 126 The normalized value 0 The special value 0 ,Ieee Representation,83 The following bit pattern represents a floating point number in IEEE 754 single precision format 1 10000011 101000000000000000000000 The value of the number in decimal form is 10 13 26 None of the above ,Ieee Representation,83 In the IEEE floating point representation the hexadecimal value 0 ext x 00000000 corresponds to The normalized value 2 127 The normalized value 2 126 The normalized value 0 The special value 0 ,Ieee Representation,83 An index is clustered if it is on a set of fields that form a candidate key it is on a set of fields that include the primary key the data records of the file are organized in the same order as the data entries of the index the data records of the file are organized not in the same order as the data entries of the index ,Indexing,84 A file is organized so that the ordering of the data records is the same as or close to the ordering of data entries in some index Than that index is called Dense Sparse Clustered Unclustered ,Indexing,84 There are five records in a database Name Age Occupation Category Rama 27 CON A Abdul 22 ENG A Jennifer 28 DOC B Maya 32 SER D Dev 24 MUS C There is an index file associated with this and it contains the values 1 3 2 5 and 4 Which one of the fields is the index built from Age Name Occupation Category ,Indexing,84 A clustering index is defined on the fields which are of type non key and ordering non key and non ordering key and ordering key and non ordering ,Indexing,84 There are five records in a database Name Age Occupation Category Rama 27 CON A Abdul 22 ENG A Jennifer 28 DOC B Maya 32 SER D Dev 24 MUS C There is an index file associated with this and it contains the values 1 3 2 5 and 4 Which one of the fields is the index built from Age Name Occupation Category ,Indexing,84 An ext ISAM indexed sequential file consists of records of size 64 bytes each including key field of size 14 bytes An address of a disk block takes 2 bytes If the disk block size is 512 bytes and there are 16 K records compute the size of the data and index areas in terms of number blocks How many levels of ext tree do you have for the index ,Indexing,84 Consider a file of 16384 records Each record is 32 bytes long and its key field is of size 6 bytes The file is ordered on a non key field and the file organization is unspanned The file is stored in a file system with block size 1024 bytes and the size of a block pointer is 10 bytes If the secondary index is built on the key field of the file and a multi level index scheme is used to store the secondary index the number of first level and second level blocks in the multi level index are respectively 8 and 0 128 and 6 256 and 4 512 and 5 ,Indexing,84 Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG ,Inference,85 Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG ,Inference,85 Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG ,Inference,85 Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG ,Inference,85 Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG ,Inference,85 Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG ,Inference,85 Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG ,Inference,85 Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG ,Inference,85 Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG ,Inference,85 Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG ,Inference,85 Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG ,Inference,85 Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG ,Inference,85 Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG ,Inference,85 Hari H Gita G Irfan I and Saira S are siblings i e brothers and sisters All were born on 1st January The age difference between any two successive siblings that is born one after another is less than three years Given the following facts Hari s age Gita s age gt Irfan s age Saira s age The age difference between Gita and Saira is one year However Gita is not the oldest and Saira is not the youngest There are no twins In what order they were born oldest first HSIG SGHI IGSH IHSG ,Inference,85 int pi 4 _0 1 an x 1 an x dx 0 1 ln 2 1 2 ln 2 ,Integration,86 The value of the integral given below is int limits_0 pi x 2 cos x dx 2 pi pi pi 2 pi ,Integration,86 Compute the value of large int_ frac 1 pi frac 2 pi frac cos 1 x x 2 dx ,Integration,86 Compute the value of large int_ frac 1 pi frac 2 pi frac cos 1 x x 2 dx ,Integration,86 The value of the integral given below is int limits_0 pi x 2 cos x dx 2 pi pi pi 2 pi ,Integration,86 Let S sum_ i 3 100 i log_ 2 i and T int_ 2 100 x log_ 2 x dx Which of the following statements is true S gt T S T S lt T and 2S gt T 2S u2264 T ,Integration,86 The value of the integral given below is int limits_0 pi x 2 cos x dx 2 pi pi pi 2 pi ,Integration,86 Let S sum_ i 3 100 i log_ 2 i and T int_ 2 100 x log_ 2 x dx Which of the following statements is true S gt T S T S lt T and 2S gt T 2S u2264 T ,Integration,86 I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above ,Inter Process Communication,87 I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above ,Inter Process Communication,87 I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above ,Inter Process Communication,87 I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above ,Inter Process Communication,87 I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above ,Inter Process Communication,87 I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above ,Inter Process Communication,87 I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above ,Inter Process Communication,87 I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above ,Inter Process Communication,87 I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above ,Inter Process Communication,87 I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above ,Inter Process Communication,87 I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above ,Inter Process Communication,87 I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above ,Inter Process Communication,87 I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above ,Inter Process Communication,87 I O redirection implies changing the name of a file can be employed to use an existing file as input file for a program implies connecting 2 programs through a pipe None of the above ,Inter Process Communication,87 Consider the following relation schema pertaining to a students database Students rollno name address Enroll rollno courseno coursename where the primary keys are shown underlined The number of tuples in the student and Enroll tables are 120 and 8 respectively What are the maximum and minimum number of tuples that can be present in Student Enroll where u2018 u2019 denotes natural join 8 8 120 8 960 8 960 120 ,Joins,88 A database table T_1 has 2000 records and occupies 80 disk blocks Another table T_2 has 400 records and occupies 20 disk blocks These two tables have to be joined as per a specified join condition that needs to be evaluated for every pair of records from these two tables The memory buffer space available can hold exactly one block of records for T_1 and one block of records for T_2 simultaneously at any point in time No index is available on either table If instead of Nested loop join Block nested loop join is used again with the most appropriate choice of table in the outer loop the reduction in number of block accesses required for reading the data will be 0 30400 38400 798400 ,Joins,88 Consider the following relation schemas b Schema b name b city assets a Schema a num b name bal d Schema c name a number Let branch account and depositor be respectively instances of the above schemas Assume that account and depositor relations are much bigger than the branch relation Consider the following query u041fc name u03c3b city Agra u22c0 bal lt 0 branch u22c8 account u22c8 depositor Which one of the following queries is the most efficient version of the above query u041fc name u03c3bal lt 0 u03c3b city Agra branch u22c8 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3bal lt 0 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3b city Agra u22c0 bal lt 0 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3b city Agra u22c0 bal lt 0 account u22c8 depositor ,Joins,88 Consider the following relation schemas b Schema b name b city assets a Schema a num b name bal d Schema c name a number Let branch account and depositor be respectively instances of the above schemas Assume that account and depositor relations are much bigger than the branch relation Consider the following query u041fc name u03c3b city Agra u22c0 bal lt 0 branch u22c8 account u22c8 depositor Which one of the following queries is the most efficient version of the above query u041fc name u03c3bal lt 0 u03c3b city Agra branch u22c8 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3bal lt 0 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3b city Agra u22c0 bal lt 0 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3b city Agra u22c0 bal lt 0 account u22c8 depositor ,Joins,88 A database table T_1 has 2000 records and occupies 80 disk blocks Another table T_2 has 400 records and occupies 20 disk blocks These two tables have to be joined as per a specified join condition that needs to be evaluated for every pair of records from these two tables The memory buffer space available can hold exactly one block of records for T_1 and one block of records for T_2 simultaneously at any point in time No index is available on either table If Nested loop join algorithm is employed to perform the join with the most appropriate choice of table to be used in outer loop the number of block accesses required for reading the data are 800000 40080 32020 100 ,Joins,88 Consider the following relation schemas b Schema b name b city assets a Schema a num b name bal d Schema c name a number Let branch account and depositor be respectively instances of the above schemas Assume that account and depositor relations are much bigger than the branch relation Consider the following query u041fc name u03c3b city Agra u22c0 bal lt 0 branch u22c8 account u22c8 depositor Which one of the following queries is the most efficient version of the above query u041fc name u03c3bal lt 0 u03c3b city Agra branch u22c8 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3bal lt 0 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3b city Agra u22c0 bal lt 0 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3b city Agra u22c0 bal lt 0 account u22c8 depositor ,Joins,88 Consider the following relation schemas b Schema b name b city assets a Schema a num b name bal d Schema c name a number Let branch account and depositor be respectively instances of the above schemas Assume that account and depositor relations are much bigger than the branch relation Consider the following query u041fc name u03c3b city Agra u22c0 bal lt 0 branch u22c8 account u22c8 depositor Which one of the following queries is the most efficient version of the above query u041fc name u03c3bal lt 0 u03c3b city Agra branch u22c8 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3bal lt 0 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3b city Agra u22c0 bal lt 0 account u22c8 depositor u041fc name u03c3b city Agra branch u22c8 u03c3b city Agra u22c0 bal lt 0 account u22c8 depositor ,Joins,88 A database table T_1 has 2000 records and occupies 80 disk blocks Another table T_2 has 400 records and occupies 20 disk blocks These two tables have to be joined as per a specified join condition that needs to be evaluated for every pair of records from these two tables The memory buffer space available can hold exactly one block of records for T_1 and one block of records for T_2 simultaneously at any point in time No index is available on either table If instead of Nested loop join Block nested loop join is used again with the most appropriate choice of table in the outer loop the reduction in number of block accesses required for reading the data will be 0 30400 38400 798400 ,Joins,88 The literal count of a Boolean expression is the sum of the number of times each literal appears in the expression For example the literal count of left xy xz right is 4 What are the minimum possible literal counts of the product of sum and sum of product representations respectively of the function given by the following Karnaugh map Here X denotes don t care 11 9 9 13 9 10 11 11 ,K Map,89 Let wedge vee denote the meet and join operations of lattice A lattice is called distributive if for all x y z x wedge left y vee z right left x wedge y right vee left x wedge z right It is called complete if meet and join exist for every subset It is called modular if for all x y z z leq x Rightarrow x wedge left y vee z right left x wedge y right vee z The positive integers under divisibility ordering i e p leq q if p divides q forms a Complete lattice Modular but not distributive lattice Distributive lattice Lattice but not a complete lattice Under the give ordering positive integers do not form a lattice ,Lattice,90 Suppose L left p q r s t right is a lattice represented by the following Hasse diagram For any x y isin L not necessarily distinct x or y and x and y are join and meet of x y respectively Let L 3 left left x y z right x y z isin L right be the set of all ordered triplets of the elements of L Let p_ r be the probability that an element left x y z right isin L 3 chosen equiprobably satisfies x or y and z x or y and x or z Then p_r 0 p_r 1 0 lt p_r le frac 1 5 frac 1 5 lt p_r lt 1 ,Lattice,90 In the lattice defined by the Hasse diagram given in following figure how many complements does the element u2018e u2019 have 2 3 0 1 ,Lattice,90 S 1 2 2 1 is binary relation on set A 1 2 3 Is it irreflexive Add the minimum number of ordered pairs to S to make it an equivalence relation Give the modified S Let S a b and let square S be the powerset of S Consider the binary relation subseteq set inclusion on square S Draw the Hasse diagram corresponding to the lattice square S subseteq ,Lattice,90 Suppose L left p q r s t right is a lattice represented by the following Hasse diagram For any x y isin L not necessarily distinct x or y and x and y are join and meet of x y respectively Let L 3 left left x y z right x y z isin L right be the set of all ordered triplets of the elements of L Let p_ r be the probability that an element left x y z right isin L 3 chosen equiprobably satisfies x or y and z x or y and x or z Then p_r 0 p_r 1 0 lt p_r le frac 1 5 frac 1 5 lt p_r lt 1 ,Lattice,90 In the lattice defined by the Hasse diagram given in following figure how many complements does the element u2018e u2019 have 2 3 0 1 ,Lattice,90 The following is the Hasse diagram of the poset a b c d e u227a The poset is not a lattice a lattice but not a distributive lattice a distributive lattice but not a Boolean algebra a Boolean algebra ,Lattice,90 Suppose L left p q r s t right is a lattice represented by the following Hasse diagram For any x y isin L not necessarily distinct x or y and x and y are join and meet of x y respectively Let L 3 left left x y z right x y z isin L right be the set of all ordered triplets of the elements of L Let p_ r be the probability that an element left x y z right isin L 3 chosen equiprobably satisfies x or y and z x or y and x or z Then p_r 0 p_r 1 0 lt p_r le frac 1 5 frac 1 5 lt p_r lt 1 ,Lattice,90 What is the value of lim_ n o infty left 1 frac 1 n right 2n 0 e 2 e 1 2 1 ,Limits,91 lim _ x rightarrow 4 frac sin x 4 x 4 ____ ,Limits,91 The value of lim_ x rightarrow 1 frac x 7 2x 5 1 x 3 3x 2 2 is 0 is 1 is 1 does not exist ,Limits,91 lim _ x rightarrow 4 frac sin x 4 x 4 ____ ,Limits,91 lim _ x rightarrow 4 frac sin x 4 x 4 ____ ,Limits,91 The value of lim_ x rightarrow 1 frac x 7 2x 5 1 x 3 3x 2 2 is 0 is 1 is 1 does not exist ,Limits,91 The value of lim_ x rightarrow infty 1 x 2 e x is u00a0 0 frac 1 2 1 infty ,Limits,91 lim_ x rightarrow infty x frac 1 x is infty 0 1 Not defined ,Limits,91 lim_ x o infty frac x sin x x cos x equals 1 1 infty infty ,Limits,91 The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only,Line Graph,92 The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only,Line Graph,92 The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only,Line Graph,92 The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only,Line Graph,92 The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only,Line Graph,92 The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only,Line Graph,92 The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only,Line Graph,92 The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only,Line Graph,92 The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only,Line Graph,92 The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only,Line Graph,92 The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only,Line Graph,92 The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only,Line Graph,92 The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only,Line Graph,92 The line graph L G of a simple graph G is defined as follows There is exactly one vertex v e in L G for each edge e in G For any two edges e and e in G L G has an edge between v e and v e if and only if e and e are incident with the same vertex in G Which of the following statements is are TRUE P The line graph of a cycle is a cycle Q The line graph of a clique is a clique R The line graph of a planar graph is planar S The line graph of a tree is a tree A P only B P and R only C R only D P Q and S only,Line Graph,92 In a circular linked list oraganisation insertion of a record involves modification of One pointer Two pointers Multiple pointers No pointer ,Linked Lists,93 A circularly linked list is used to represent a Queue A single variable p is used to access the Queue To which node should p point such that both the operations ext enQueue and ext deQueue can be performed in constant time rear node front node not possible with a single pointer node next to front ,Linked Lists,93 Consider the following circuit composed of XOR gates and non inverting buffers The non inverting buffers have delays delta_1 2 ns and delta_2 4 ns as shown in the figure Both XOR gates and all wires have zero delay Assume that all gate inputs outputs and wires are stable at logic level 0 at time 0 If the following waveform is applied at input A how many transition s change of logic levels occur s at B during the interval from 0 to 10 ns 1 2 3 4 ,Logic Gates,94 The Boolean function obtained by adding an inverter to each and every input of an AND gate is OR XOR NAND NOR None of the above ,Logic Gates,94 Choose the correct alternatives more than one may be correct and write the corresponding letters only All digital circuits can be realized using only Ex OR gates Multiplexers Half adders OR gates ,Logic Gates,94 Choose the correct alternatives more than one may be correct and write the corresponding letters only All digital circuits can be realized using only Ex OR gates Multiplexers Half adders OR gates ,Logic Gates,94 The Boolean function obtained by adding an inverter to each and every input of an AND gate is OR XOR NAND NOR None of the above ,Logic Gates,94 Choose the correct alternatives more than one may be correct and write the corresponding letters only All digital circuits can be realized using only Ex OR gates Multiplexers Half adders OR gates ,Logic Gates,94 Express the function f x y z xy yz with only one complement operation and one or more AND OR operations Draw the logic circuit implementing the expression obtained using a single NOT gate and one or more AND OR gates Transform the following logic circuit without expressing its switching function into an equivalent logic circuit that employs only 6 NAND gates each with 2 inputs ,Logic Gates,94 Choose the correct alternatives more than one may be correct and write the corresponding letters only All digital circuits can be realized using only Ex OR gates Multiplexers Half adders OR gates ,Logic Gates,94 The Boolean function obtained by adding an inverter to each and every input of an AND gate is OR XOR NAND NOR None of the above ,Logic Gates,94 The Boolean function obtained by adding an inverter to each and every input of an AND gate is OR XOR NAND NOR None of the above ,Logic Gates,94 Express the function f x y z xy yz with only one complement operation and one or more AND OR operations Draw the logic circuit implementing the expression obtained using a single NOT gate and one or more AND OR gates Transform the following logic circuit without expressing its switching function into an equivalent logic circuit that employs only 6 NAND gates each with 2 inputs ,Logic Gates,94 Consider the following program fragment for reversing the digits in a given integer to obtain a new integer Let n d_1 d_2 ldots d_m int n rev rev 0 while n gt 0 rev rev 10 n 10 n n 10 The loop invariant condition at the end of the i th iteration is n d_1 d_2 ldots d_ m i qquad mathbf and qquad ext rev d_m d_ m 1 ldots d_ m i 1 n d_ m i 1 ldots d_ m 1 d_m qquad mathbf or qquad ext rev d_ m i ldots d_2 d_1 n eq ext rev n d_1 d_2 ldots d_m qquad mathbf or qquad ext rev d_m ldots d_2 d_1 ,Loop Invariants,96 The following function computes X Y for positive integers X and Y int exp int X int Y int res 1 a X b Y while b 0 if b 2 0 a a a b b 2 else res res a b b 1 return res Which one of the following conditions is TRUE before every iteration of the loop X Y a b res a Y res X b X Y res a b X Y res a b ,Loop Invariants,96 Consider the following program fragment for reversing the digits in a given integer to obtain a new integer Let n d_1 d_2 ldots d_m int n rev rev 0 while n gt 0 rev rev 10 n 10 n n 10 The loop invariant condition at the end of the i th iteration is n d_1 d_2 ldots d_ m i qquad mathbf and qquad ext rev d_m d_ m 1 ldots d_ m i 1 n d_ m i 1 ldots d_ m 1 d_m qquad mathbf or qquad ext rev d_ m i ldots d_2 d_1 n eq ext rev n d_1 d_2 ldots d_m qquad mathbf or qquad ext rev d_m ldots d_2 d_1 ,Loop Invariants,96 Consider the following pseudo code where x and y are positive integers begin q 0 r x while r u2265 y do begin r r y q q 1 end end The post condition that needs to be satisfied after the program terminates is r qx y wedge r lt y x qy r wedge r lt y y qx r wedge 0 lt r lt y q 1 lt r y wedge y gt 0 ,Loop Invariants,96 Consider the following program fragment for reversing the digits in a given integer to obtain a new integer Let n d_1 d_2 ldots d_m int n rev rev 0 while n gt 0 rev rev 10 n 10 n n 10 The loop invariant condition at the end of the i th iteration is n d_1 d_2 ldots d_ m i qquad mathbf and qquad ext rev d_m d_ m 1 ldots d_ m i 1 n d_ m i 1 ldots d_ m 1 d_m qquad mathbf or qquad ext rev d_ m i ldots d_2 d_1 n eq ext rev n d_1 d_2 ldots d_m qquad mathbf or qquad ext rev d_m ldots d_2 d_1 ,Loop Invariants,96 Consider the program where a b are integers with b gt 0 x a y b z 0 while y gt 0 do if odd x then z z x y y 1 else y y 2 x 2 x fi Invariant of the loop is a condition which is true before and after every iteration of the loop In the above program the loop invariant is given by 0 leq y and z x y a b Which of the following is true of the program The program will not terminate for some values of a b The program will terminate with z 2 b The program will terminate with z a b The program will not terminate for some values of a b but when it does terminate the condition z a b will hold The program will terminate with z a b ,Loop Invariants,96 Consider the C program fragment below which is meant to divide x by y using repeated subtractions The variables x y q and r are all unsigned int while r gt y r r y q q 1 Which of the following conditions on the variables x y q and r before the execution of the fragment will ensure that the loop terminated in a state satisfying the condition x y q r q r amp amp r 0 x gt 0 amp amp r x amp amp y gt 0 q 0 amp amp r x amp amp y gt 0 q 0 amp amp y gt 0 ,Loop Invariants,96 Consider the following pseudo code where x and y are positive integers begin q 0 r x while r u2265 y do begin r r y q q 1 end end The post condition that needs to be satisfied after the program terminates is r qx y wedge r lt y x qy r wedge r lt y y qx r wedge 0 lt r lt y q 1 lt r y wedge y gt 0 ,Loop Invariants,96 Solve min x 2 y 2 subject to x y geq 10 2x 3y geq 20 x geq 4 y geq 4 32 50 52 100 None of the above ,Maxima Minima,98 Find the minimum value of 3 4x 2x 2 Determine the number of positive integers amp le 720 which are not divisible by any of 2 3 or 5 ,Maxima Minima,98 Consider the function f x sin x in the interval x left frac pi 4 frac 7 pi 4 right The number and location s of the local minima of this function are A One at dfrac pi 2 B One at dfrac 3 pi 2 C Two at dfrac pi 2 and dfrac 3 pi 2 D Two at dfrac pi 4 and dfrac 3 pi 2 ,Maxima Minima,98 A point on a curve is said to be an extremum if it is a local minimum or a local maximum The number of distinct extrema for the curve 3x 4 16x 3 24x 2 37 is 0 1 2 3 ,Maxima Minima,98 Find the minimum value of 3 4x 2x 2 Determine the number of positive integers amp le 720 which are not divisible by any of 2 3 or 5 ,Maxima Minima,98 A point on a curve is said to be an extremum if it is a local minimum or a local maximum The number of distinct extrema for the curve 3x 4 16x 3 24x 2 37 is 0 1 2 3 ,Maxima Minima,98 Solve min x 2 y 2 subject to x y geq 10 2x 3y geq 20 x geq 4 y geq 4 32 50 52 100 None of the above ,Maxima Minima,98 Consider the function f x sin x in the interval x left frac pi 4 frac 7 pi 4 right The number and location s of the local minima of this function are A One at dfrac pi 2 B One at dfrac 3 pi 2 C Two at dfrac pi 2 and dfrac 3 pi 2 D Two at dfrac pi 4 and dfrac 3 pi 2 ,Maxima Minima,98 Solve min x 2 y 2 subject to x y geq 10 2x 3y geq 20 x geq 4 y geq 4 32 50 52 100 None of the above ,Maxima Minima,98 Consider the function f x sin x in the interval x left frac pi 4 frac 7 pi 4 right The number and location s of the local minima of this function are A One at dfrac pi 2 B One at dfrac 3 pi 2 C Two at dfrac pi 2 and dfrac 3 pi 2 D Two at dfrac pi 4 and dfrac 3 pi 2 ,Maxima Minima,98 Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB ,Memory Allocation,99 Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB ,Memory Allocation,99 Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB ,Memory Allocation,99 Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB ,Memory Allocation,99 Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB ,Memory Allocation,99 Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB ,Memory Allocation,99 Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB ,Memory Allocation,99 Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB ,Memory Allocation,99 Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB ,Memory Allocation,99 Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB ,Memory Allocation,99 Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB ,Memory Allocation,99 Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB ,Memory Allocation,99 Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB ,Memory Allocation,99 Consider 6 memory partitions of sizes 200 KB 400 KB 600 KB 500 KB 300 KB and 250 KB where KB refers to kilobyte These partitions need to be allotted to four processes of sizes 357 KB 210 KB 468 KB 491 KB in that order If the best fit algorithm is used which partitions are NOT allotted to any process 200 KB and 300 KB 200 KB and 250 KB 250 KB and 300 KB 300 KB and 400 KB ,Memory Allocation,99 Let the page reference and the working set window be c c d b c e c e a d and 4 respectively The initial working set at time t 0 contains the pages a d e where a was referenced at time t 0 d was referenced at time t 1 and e was referenced at time t 2 Determine the total number of page faults and the average number of page frames used by computing the working set at each reference ,Memory Management,100 Let a memory have four free blocks of sizes 4k 8k 20k 2k These blocks are allocated following the best fit strategy The allocation requests are stored in a queue as shown below Request No J1 J2 J3 J4 J5 J6 J7 J8 Request Sizes 2k 14k 3k 6k 6k 10k 7k 20k Usage Time 4 10 2 8 4 1 8 6 The time at which the request for J7 will be completed will be 16 19 20 37 ,Memory Management,100 A 1000 Kbyte memory is managed using variable partitions but no compaction It currently has two partitions of sizes 200 Kbytes and 260 Kbytes respectively The smallest allocation request in Kbytes that could be denied is for 151 181 231 541 ,Memory Management,100 Consider a main memory system that consists of 8 memory modules attached to the system bus which is one word wide When a write request is made the bus is occupied for 100 nanoseconds ns by the data address and control signals During the same 100 ns and for 500 ns thereafter the addressed memory module executes one cycle accepting and storing the data The internal operation of different memory modules may overlap in time but only one request can be on the bus at any time The maximum number of stores of one word each that can be initiated in 1 millisecond is ________,Memory Management,100 Let a memory have four free blocks of sizes 4k 8k 20k 2k These blocks are allocated following the best fit strategy The allocation requests are stored in a queue as shown below Request No J1 J2 J3 J4 J5 J6 J7 J8 Request Sizes 2k 14k 3k 6k 6k 10k 7k 20k Usage Time 4 10 2 8 4 1 8 6 The time at which the request for J7 will be completed will be 16 19 20 37 ,Memory Management,100 Let a memory have four free blocks of sizes 4k 8k 20k 2k These blocks are allocated following the best fit strategy The allocation requests are stored in a queue as shown below Request No J1 J2 J3 J4 J5 J6 J7 J8 Request Sizes 2k 14k 3k 6k 6k 10k 7k 20k Usage Time 4 10 2 8 4 1 8 6 The time at which the request for J7 will be completed will be 16 19 20 37 ,Memory Management,100 Let a memory have four free blocks of sizes 4k 8k 20k 2k These blocks are allocated following the best fit strategy The allocation requests are stored in a queue as shown below Request No J1 J2 J3 J4 J5 J6 J7 J8 Request Sizes 2k 14k 3k 6k 6k 10k 7k 20k Usage Time 4 10 2 8 4 1 8 6 The time at which the request for J7 will be completed will be 16 19 20 37 ,Memory Management,100 Let the page reference and the working set window be c c d b c e c e a d and 4 respectively The initial working set at time t 0 contains the pages a d e where a was referenced at time t 0 d was referenced at time t 1 and e was referenced at time t 2 Determine the total number of page faults and the average number of page frames used by computing the working set at each reference ,Memory Management,100 Let a memory have four free blocks of sizes 4k 8k 20k 2k These blocks are allocated following the best fit strategy The allocation requests are stored in a queue as shown below Request No J1 J2 J3 J4 J5 J6 J7 J8 Request Sizes 2k 14k 3k 6k 6k 10k 7k 20k Usage Time 4 10 2 8 4 1 8 6 The time at which the request for J7 will be completed will be 16 19 20 37 ,Memory Management,100 What is the minimum number of NAND gates required to implement a 2 input EXCLUSIVE OR function without using any other logic gate 2 4 5 6 ,Min No Gates,101 Design a logic circuit to convert a single digit BCD number to the number modulo six as follows Do not detect illegal input Write the truth table for all bits Label the input bits I1 I2 with I1 as the least significant bit Label the output bits R1 R2 with R1 as the least significant bit Use 1 to signify truth Draw one circuit for each output bit using altogether two two input AND gates one two input OR gate and two NOT gates ,Min No Gates,101 A circuit outputs a digit in the form of 4 bits 0 is represented by 0000 1 by 0001 u2026 9 by 1001 A combinational circuit is to be designed which takes these 4 bits as input and outputs 1 if the digit geq 5 and 0 otherwise If only AND OR and NOT gates may be used what is the minimum number of gates required 2 3 4 5 ,Min No Gates,101 A circuit outputs a digit in the form of 4 bits 0 is represented by 0000 1 by 0001 u2026 9 by 1001 A combinational circuit is to be designed which takes these 4 bits as input and outputs 1 if the digit geq 5 and 0 otherwise If only AND OR and NOT gates may be used what is the minimum number of gates required 2 3 4 5 ,Min No Gates,101 A circuit outputs a digit in the form of 4 bits 0 is represented by 0000 1 by 0001 u2026 9 by 1001 A combinational circuit is to be designed which takes these 4 bits as input and outputs 1 if the digit geq 5 and 0 otherwise If only AND OR and NOT gates may be used what is the minimum number of gates required 2 3 4 5 ,Min No Gates,101 What is the minimum number of gates required to implement the Boolean function AB C if we have to use only 2 input NOR gates 2 3 4 5 ,Min No Gates,101 What is the minimum number of NAND gates required to implement a 2 input EXCLUSIVE OR function without using any other logic gate 2 4 5 6 ,Min No Gates,101 Design a logic circuit to convert a single digit BCD number to the number modulo six as follows Do not detect illegal input Write the truth table for all bits Label the input bits I1 I2 with I1 as the least significant bit Label the output bits R1 R2 with R1 as the least significant bit Use 1 to signify truth Draw one circuit for each output bit using altogether two two input AND gates one two input OR gate and two NOT gates ,Min No Gates,101 What is the minimum number of gates required to implement the Boolean function AB C if we have to use only 2 input NOR gates 2 3 4 5 ,Min No Gates,101 What is the minimum number of NAND gates required to implement a 2 input EXCLUSIVE OR function without using any other logic gate 2 4 5 6 ,Min No Gates,101 What is the minimum number of gates required to implement the Boolean function AB C if we have to use only 2 input NOR gates 2 3 4 5 ,Min No Gates,101 Given f w x y z Sigma_m 0 1 2 3 7 8 10 Sigma_d 5 6 11 15 where d represents the don t care condition in Karnaugh maps Which of the following is a minimum product of sums POS form of f w x y z f bar w bar z bar x z f bar w z x z f w z bar x z f w bar z bar x z ,Min Product Of Sums,102 Given f w x y z Sigma_m 0 1 2 3 7 8 10 Sigma_d 5 6 11 15 where d represents the don t care condition in Karnaugh maps Which of the following is a minimum product of sums POS form of f w x y z f bar w bar z bar x z f bar w z x z f w z bar x z f w bar z bar x z ,Min Product Of Sums,102 Given f w x y z Sigma_m 0 1 2 3 7 8 10 Sigma_d 5 6 11 15 where d represents the don t care condition in Karnaugh maps Which of the following is a minimum product of sums POS form of f w x y z f bar w bar z bar x z f bar w z x z f w z bar x z f w bar z bar x z ,Min Product Of Sums,102 Given f w x y z Sigma_m 0 1 2 3 7 8 10 Sigma_d 5 6 11 15 where d represents the don t care condition in Karnaugh maps Which of the following is a minimum product of sums POS form of f w x y z f bar w bar z bar x z f bar w z x z f w z bar x z f w bar z bar x z ,Min Product Of Sums,102 Given f w x y z Sigma_m 0 1 2 3 7 8 10 Sigma_d 5 6 11 15 where d represents the don t care condition in Karnaugh maps Which of the following is a minimum product of sums POS form of f w x y z f bar w bar z bar x z f bar w z x z f w z bar x z f w bar z bar x z ,Min Product Of Sums,102 Given f w x y z Sigma_m 0 1 2 3 7 8 10 Sigma_d 5 6 11 15 where d represents the don t care condition in Karnaugh maps Which of the following is a minimum product of sums POS form of f w x y z f bar w bar z bar x z f bar w z x z f w z bar x z f w bar z bar x z ,Min Product Of Sums,102 Given f w x y z Sigma_m 0 1 2 3 7 8 10 Sigma_d 5 6 11 15 where d represents the don t care condition in Karnaugh maps Which of the following is a minimum product of sums POS form of f w x y z f bar w bar z bar x z f bar w z x z f w z bar x z f w bar z bar x z ,Min Product Of Sums,102 Given f w x y z Sigma_m 0 1 2 3 7 8 10 Sigma_d 5 6 11 15 where d represents the don t care condition in Karnaugh maps Which of the following is a minimum product of sums POS form of f w x y z f bar w bar z bar x z f bar w z x z f w z bar x z f w bar z bar x z ,Min Product Of Sums,102 Given f w x y z Sigma_m 0 1 2 3 7 8 10 Sigma_d 5 6 11 15 where d represents the don t care condition in Karnaugh maps Which of the following is a minimum product of sums POS form of f w x y z f bar w bar z bar x z f bar w z x z f w z bar x z f w bar z bar x z ,Min Product Of Sums,102 Given f w x y z Sigma_m 0 1 2 3 7 8 10 Sigma_d 5 6 11 15 where d represents the don t care condition in Karnaugh maps Which of the following is a minimum product of sums POS form of f w x y z f bar w bar z bar x z f bar w z x z f w z bar x z f w bar z bar x z ,Min Product Of Sums,102 Given f w x y z Sigma_m 0 1 2 3 7 8 10 Sigma_d 5 6 11 15 where d represents the don t care condition in Karnaugh maps Which of the following is a minimum product of sums POS form of f w x y z f bar w bar z bar x z f bar w z x z f w z bar x z f w bar z bar x z ,Min Product Of Sums,102 Given f w x y z Sigma_m 0 1 2 3 7 8 10 Sigma_d 5 6 11 15 where d represents the don t care condition in Karnaugh maps Which of the following is a minimum product of sums POS form of f w x y z f bar w bar z bar x z f bar w z x z f w z bar x z f w bar z bar x z ,Min Product Of Sums,102 Given f w x y z Sigma_m 0 1 2 3 7 8 10 Sigma_d 5 6 11 15 where d represents the don t care condition in Karnaugh maps Which of the following is a minimum product of sums POS form of f w x y z f bar w bar z bar x z f bar w z x z f w z bar x z f w bar z bar x z ,Min Product Of Sums,102 Given f w x y z Sigma_m 0 1 2 3 7 8 10 Sigma_d 5 6 11 15 where d represents the don t care condition in Karnaugh maps Which of the following is a minimum product of sums POS form of f w x y z f bar w bar z bar x z f bar w z x z f w z bar x z f w bar z bar x z ,Min Product Of Sums,102 Consider the following minterm expression for F F P Q R S sum 0 2 5 7 8 10 13 15 The minterms 2 7 8 and 13 are do not care terms The minimal sum of products form for F is Q bar S bar QS bar Q bar S QS bar Q bar R bar S bar QR bar S Q bar R S QRS bar P bar Q bar S bar P QS PQS P bar Q bar S ,Min Sum Of Products Form,103 Consider the following Boolean function of four variables f w x y z Sigma 1 3 4 6 9 11 12 14 The function is independent of one variables independent of two variables independent of three variables dependent on all variables ,Min Sum Of Products Form,103 Consider the 4 to 1 multiplexer with two select lines S_1 and S_0 given below The minimal sum of products form of the Boolean expression for the output F of the multiplexer is bar P Q Q bar R P bar Q R bar P Q bar P Q bar R PQ bar R P bar Q R bar P QR bar P Q bar R Q bar R P bar Q R PQ bar R ,Min Sum Of Products Form,103 Consider the following Boolean expression for F F P Q R S PQ bar P QR bar P Q bar R S The minimal sum of products form of F is PQ QR QS P Q R S bar P bar Q bar R bar S bar P R bar R bar P S P ,Min Sum Of Products Form,103 Following is a state table for time finite state machine Present State Next State Output Input 0 Input 1 A B C D E F G H B 1 F 1 D 0 C 0 D 1 C 1 C 1 C 0 H 1 D 1 E 1 F 1 C 1 C 1 D 1 A 1 Find the equivalence partition on the states of the machine Give the state table for the minimal machine Use appropriate names for the equivalent states For example if states X and Y are equivalent then use XY as the name for the equivalent state in the minimal machine ,Minimal State Automata,104 Following is a state table for time finite state machine Present State Next State Output Input 0 Input 1 A B C D E F G H B 1 F 1 D 0 C 0 D 1 C 1 C 1 C 0 H 1 D 1 E 1 F 1 C 1 C 1 D 1 A 1 Find the equivalence partition on the states of the machine Give the state table for the minimal machine Use appropriate names for the equivalent states For example if states X and Y are equivalent then use XY as the name for the equivalent state in the minimal machine ,Minimal State Automata,104 A 1 input 2 output synchronous sequential circuit behaves as follows Let z_k n_k denote the number of 0 u2019s and 1 u2019s respectively in initial k bits of the input z_k n_k k The circuit outputs 00 until one of the following conditions holds z_k n_k 2 In this case the output at the k th and all subsequent clock ticks is 10 n_k z_k 2 In this case the output at the k th and all subsequent clock ticks is 01 What is the minimum number of states required in the state transition graph of the above circuit 5 6 7 8 ,Minimal State Automata,104 Following is a state table for time finite state machine Present State Next State Output Input 0 Input 1 A B C D E F G H B 1 F 1 D 0 C 0 D 1 C 1 C 1 C 0 H 1 D 1 E 1 F 1 C 1 C 1 D 1 A 1 Find the equivalence partition on the states of the machine Give the state table for the minimal machine Use appropriate names for the equivalent states For example if states X and Y are equivalent then use XY as the name for the equivalent state in the minimal machine ,Minimal State Automata,104 A 1 input 2 output synchronous sequential circuit behaves as follows Let z_k n_k denote the number of 0 u2019s and 1 u2019s respectively in initial k bits of the input z_k n_k k The circuit outputs 00 until one of the following conditions holds z_k n_k 2 In this case the output at the k th and all subsequent clock ticks is 10 n_k z_k 2 In this case the output at the k th and all subsequent clock ticks is 01 What is the minimum number of states required in the state transition graph of the above circuit 5 6 7 8 ,Minimal State Automata,104 A 1 input 2 output synchronous sequential circuit behaves as follows Let z_k n_k denote the number of 0 u2019s and 1 u2019s respectively in initial k bits of the input z_k n_k k The circuit outputs 00 until one of the following conditions holds z_k n_k 2 In this case the output at the k th and all subsequent clock ticks is 10 n_k z_k 2 In this case the output at the k th and all subsequent clock ticks is 01 What is the minimum number of states required in the state transition graph of the above circuit 5 6 7 8 ,Minimal State Automata,104 Following is a state table for time finite state machine Present State Next State Output Input 0 Input 1 A B C D E F G H B 1 F 1 D 0 C 0 D 1 C 1 C 1 C 0 H 1 D 1 E 1 F 1 C 1 C 1 D 1 A 1 Find the equivalence partition on the states of the machine Give the state table for the minimal machine Use appropriate names for the equivalent states For example if states X and Y are equivalent then use XY as the name for the equivalent state in the minimal machine ,Minimal State Automata,104 A 1 input 2 output synchronous sequential circuit behaves as follows Let z_k n_k denote the number of 0 u2019s and 1 u2019s respectively in initial k bits of the input z_k n_k k The circuit outputs 00 until one of the following conditions holds z_k n_k 2 In this case the output at the k th and all subsequent clock ticks is 10 n_k z_k 2 In this case the output at the k th and all subsequent clock ticks is 01 What is the minimum number of states required in the state transition graph of the above circuit 5 6 7 8 ,Minimal State Automata,104 A 1 input 2 output synchronous sequential circuit behaves as follows Let z_k n_k denote the number of 0 u2019s and 1 u2019s respectively in initial k bits of the input z_k n_k k The circuit outputs 00 until one of the following conditions holds z_k n_k 2 In this case the output at the k th and all subsequent clock ticks is 10 n_k z_k 2 In this case the output at the k th and all subsequent clock ticks is 01 What is the minimum number of states required in the state transition graph of the above circuit 5 6 7 8 ,Minimal State Automata,104 Following is a state table for time finite state machine Present State Next State Output Input 0 Input 1 A B C D E F G H B 1 F 1 D 0 C 0 D 1 C 1 C 1 C 0 H 1 D 1 E 1 F 1 C 1 C 1 D 1 A 1 Find the equivalence partition on the states of the machine Give the state table for the minimal machine Use appropriate names for the equivalent states For example if states X and Y are equivalent then use XY as the name for the equivalent state in the minimal machine ,Minimal State Automata,104 A 1 input 2 output synchronous sequential circuit behaves as follows Let z_k n_k denote the number of 0 u2019s and 1 u2019s respectively in initial k bits of the input z_k n_k k The circuit outputs 00 until one of the following conditions holds z_k n_k 2 In this case the output at the k th and all subsequent clock ticks is 10 n_k z_k 2 In this case the output at the k th and all subsequent clock ticks is 01 What is the minimum number of states required in the state transition graph of the above circuit 5 6 7 8 ,Minimal State Automata,104 A 1 input 2 output synchronous sequential circuit behaves as follows Let z_k n_k denote the number of 0 u2019s and 1 u2019s respectively in initial k bits of the input z_k n_k k The circuit outputs 00 until one of the following conditions holds z_k n_k 2 In this case the output at the k th and all subsequent clock ticks is 10 n_k z_k 2 In this case the output at the k th and all subsequent clock ticks is 01 What is the minimum number of states required in the state transition graph of the above circuit 5 6 7 8 ,Minimal State Automata,104 Following is a state table for time finite state machine Present State Next State Output Input 0 Input 1 A B C D E F G H B 1 F 1 D 0 C 0 D 1 C 1 C 1 C 0 H 1 D 1 E 1 F 1 C 1 C 1 D 1 A 1 Find the equivalence partition on the states of the machine Give the state table for the minimal machine Use appropriate names for the equivalent states For example if states X and Y are equivalent then use XY as the name for the equivalent state in the minimal machine ,Minimal State Automata,104 The value of the expression 13 99 pmod 17 in the range 0 to 16 is ________ ,Modular Arithmetic,105 The value of the expression 13 99 pmod 17 in the range 0 to 16 is ________ ,Modular Arithmetic,105 The value of the expression 13 99 pmod 17 in the range 0 to 16 is ________ ,Modular Arithmetic,105 The value of the expression 13 99 pmod 17 in the range 0 to 16 is ________ ,Modular Arithmetic,105 The value of the expression 13 99 pmod 17 in the range 0 to 16 is ________ ,Modular Arithmetic,105 The value of the expression 13 99 pmod 17 in the range 0 to 16 is ________ ,Modular Arithmetic,105 The value of the expression 13 99 pmod 17 in the range 0 to 16 is ________ ,Modular Arithmetic,105 The value of the expression 13 99 pmod 17 in the range 0 to 16 is ________ ,Modular Arithmetic,105 The value of the expression 13 99 pmod 17 in the range 0 to 16 is ________ ,Modular Arithmetic,105 The value of the expression 13 99 pmod 17 in the range 0 to 16 is ________ ,Modular Arithmetic,105 The value of the expression 13 99 pmod 17 in the range 0 to 16 is ________ ,Modular Arithmetic,105 The value of the expression 13 99 pmod 17 in the range 0 to 16 is ________ ,Modular Arithmetic,105 The value of the expression 13 99 pmod 17 in the range 0 to 16 is ________ ,Modular Arithmetic,105 The value of the expression 13 99 pmod 17 in the range 0 to 16 is ________ ,Modular Arithmetic,105 The following circuit implements a two input AND gate using two 2 1 multiplexers What are the values of X1 X2 X3 X1 b X2 0 X3 a X1 b X2 1 X3 b X1 a X2 b X3 1 X1 a X2 0 X3 b ,Multiplexer,106 The following circuit implements a two input AND gate using two 2 1 multiplexers What are the values of X1 X2 X3 X1 b X2 0 X3 a X1 b X2 1 X3 b X1 a X2 b X3 1 X1 a X2 0 X3 b ,Multiplexer,106 Consider the two cascade 2 to 1 multiplexers as shown in the figure The minimal sum of products form of the output X is overline P overline Q PQR overline P Q QR PQ overline P overline Q R overline Q overline R PQR ,Multiplexer,106 Consider the two cascade 2 to 1 multiplexers as shown in the figure The minimal sum of products form of the output X is overline P overline Q PQR overline P Q QR PQ overline P overline Q R overline Q overline R PQR ,Multiplexer,106 Consider a multiplexer with X and Y as data inputs and Z the as control input Z 0 selects input X and Z 1 selects input Y What are the connections required to realize the 2 variable Boolean function f T R without using any additional hardware R to X 1 to Y T to Z T to X R to Y T to Z T to X R to Y 0 to Z R to X 0 to Y T to Z ,Multiplexer,106 The circuit shown below implements a 2 input NOR gate using two 2 4 MUX control signal 1 selects the upper input What are the values of signals x y and z 1 0 B 1 0 A 0 1 B 0 1 A ,Multiplexer,106 Consider a multiplexer with X and Y as data inputs and Z the as control input Z 0 selects input X and Z 1 selects input Y What are the connections required to realize the 2 variable Boolean function f T R without using any additional hardware R to X 1 to Y T to Z T to X R to Y T to Z T to X R to Y 0 to Z R to X 0 to Y T to Z ,Multiplexer,106 Consider the following implications relating to functional and multivalued dependencies given below which may or may not be correct If A u2192 u2192 B and A u2192 u2192 C then A u2192 BC If A u2192 B and A u2192 C then A u2192 u2192 BC If A u2192 u2192 BC and A u2192 B then A u2192 C If A u2192 BC and A u2192 B then A u2192 u2192 C Exactly how many of the above implications are valid 0 1 2 3 ,Multivalued Dependency 4nf,107 Consider the following implications relating to functional and multivalued dependencies given below which may or may not be correct If A u2192 u2192 B and A u2192 u2192 C then A u2192 BC If A u2192 B and A u2192 C then A u2192 u2192 BC If A u2192 u2192 BC and A u2192 B then A u2192 C If A u2192 BC and A u2192 B then A u2192 u2192 C Exactly how many of the above implications are valid 0 1 2 3 ,Multivalued Dependency 4nf,107 Consider the following implications relating to functional and multivalued dependencies given below which may or may not be correct If A u2192 u2192 B and A u2192 u2192 C then A u2192 BC If A u2192 B and A u2192 C then A u2192 u2192 BC If A u2192 u2192 BC and A u2192 B then A u2192 C If A u2192 BC and A u2192 B then A u2192 u2192 C Exactly how many of the above implications are valid 0 1 2 3 ,Multivalued Dependency 4nf,107 Consider the following implications relating to functional and multivalued dependencies given below which may or may not be correct If A u2192 u2192 B and A u2192 u2192 C then A u2192 BC If A u2192 B and A u2192 C then A u2192 u2192 BC If A u2192 u2192 BC and A u2192 B then A u2192 C If A u2192 BC and A u2192 B then A u2192 u2192 C Exactly how many of the above implications are valid 0 1 2 3 ,Multivalued Dependency 4nf,107 Consider the following implications relating to functional and multivalued dependencies given below which may or may not be correct If A u2192 u2192 B and A u2192 u2192 C then A u2192 BC If A u2192 B and A u2192 C then A u2192 u2192 BC If A u2192 u2192 BC and A u2192 B then A u2192 C If A u2192 BC and A u2192 B then A u2192 u2192 C Exactly how many of the above implications are valid 0 1 2 3 ,Multivalued Dependency 4nf,107 Consider the following implications relating to functional and multivalued dependencies given below which may or may not be correct If A u2192 u2192 B and A u2192 u2192 C then A u2192 BC If A u2192 B and A u2192 C then A u2192 u2192 BC If A u2192 u2192 BC and A u2192 B then A u2192 C If A u2192 BC and A u2192 B then A u2192 u2192 C Exactly how many of the above implications are valid 0 1 2 3 ,Multivalued Dependency 4nf,107 Consider the following implications relating to functional and multivalued dependencies given below which may or may not be correct If A u2192 u2192 B and A u2192 u2192 C then A u2192 BC If A u2192 B and A u2192 C then A u2192 u2192 BC If A u2192 u2192 BC and A u2192 B then A u2192 C If A u2192 BC and A u2192 B then A u2192 u2192 C Exactly how many of the above implications are valid 0 1 2 3 ,Multivalued Dependency 4nf,107 Consider the following implications relating to functional and multivalued dependencies given below which may or may not be correct If A u2192 u2192 B and A u2192 u2192 C then A u2192 BC If A u2192 B and A u2192 C then A u2192 u2192 BC If A u2192 u2192 BC and A u2192 B then A u2192 C If A u2192 BC and A u2192 B then A u2192 u2192 C Exactly how many of the above implications are valid 0 1 2 3 ,Multivalued Dependency 4nf,107 Consider the following implications relating to functional and multivalued dependencies given below which may or may not be correct If A u2192 u2192 B and A u2192 u2192 C then A u2192 BC If A u2192 B and A u2192 C then A u2192 u2192 BC If A u2192 u2192 BC and A u2192 B then A u2192 C If A u2192 BC and A u2192 B then A u2192 u2192 C Exactly how many of the above implications are valid 0 1 2 3 ,Multivalued Dependency 4nf,107 Consider the following implications relating to functional and multivalued dependencies given below which may or may not be correct If A u2192 u2192 B and A u2192 u2192 C then A u2192 BC If A u2192 B and A u2192 C then A u2192 u2192 BC If A u2192 u2192 BC and A u2192 B then A u2192 C If A u2192 BC and A u2192 B then A u2192 u2192 C Exactly how many of the above implications are valid 0 1 2 3 ,Multivalued Dependency 4nf,107 Consider the following implications relating to functional and multivalued dependencies given below which may or may not be correct If A u2192 u2192 B and A u2192 u2192 C then A u2192 BC If A u2192 B and A u2192 C then A u2192 u2192 BC If A u2192 u2192 BC and A u2192 B then A u2192 C If A u2192 BC and A u2192 B then A u2192 u2192 C Exactly how many of the above implications are valid 0 1 2 3 ,Multivalued Dependency 4nf,107 Consider the following implications relating to functional and multivalued dependencies given below which may or may not be correct If A u2192 u2192 B and A u2192 u2192 C then A u2192 BC If A u2192 B and A u2192 C then A u2192 u2192 BC If A u2192 u2192 BC and A u2192 B then A u2192 C If A u2192 BC and A u2192 B then A u2192 u2192 C Exactly how many of the above implications are valid 0 1 2 3 ,Multivalued Dependency 4nf,107 Consider the following implications relating to functional and multivalued dependencies given below which may or may not be correct If A u2192 u2192 B and A u2192 u2192 C then A u2192 BC If A u2192 B and A u2192 C then A u2192 u2192 BC If A u2192 u2192 BC and A u2192 B then A u2192 C If A u2192 BC and A u2192 B then A u2192 u2192 C Exactly how many of the above implications are valid 0 1 2 3 ,Multivalued Dependency 4nf,107 Consider the following implications relating to functional and multivalued dependencies given below which may or may not be correct If A u2192 u2192 B and A u2192 u2192 C then A u2192 BC If A u2192 B and A u2192 C then A u2192 u2192 BC If A u2192 u2192 BC and A u2192 B then A u2192 C If A u2192 BC and A u2192 B then A u2192 u2192 C Exactly how many of the above implications are valid 0 1 2 3 ,Multivalued Dependency 4nf,107 Consider two relations R_1 A B with the tuples 1 5 3 7 and R_2 A C 1 7 4 9 Assume that R A B C is the full natural outer join of R_1 and R_2 Consider the following tuples of the form A B C a 1 5 null b 1 null 7 c 3 null 9 d 4 7 null e 1 5 7 f 3 7 null g 4 null 9 Which one of the following statements is correct R contains a b e f g but not c d R contains all a b c d e f g R contains e f g but not a b R contains e but not f g ,Natural Join,108 The following functional dependencies hold for relations R A B C and S B D E B o A A o C The relation R contains 200 tuples and the relation S contains 100 tuples What is the maximum number of tuples possible in the natural join R bowtie S 100 200 300 2000 ,Natural Join,108 Consider two relations R_1 A B with the tuples 1 5 3 7 and R_2 A C 1 7 4 9 Assume that R A B C is the full natural outer join of R_1 and R_2 Consider the following tuples of the form A B C a 1 5 null b 1 null 7 c 3 null 9 d 4 7 null e 1 5 7 f 3 7 null g 4 null 9 Which one of the following statements is correct R contains a b e f g but not c d R contains all a b c d e f g R contains e f g but not a b R contains e but not f g ,Natural Join,108 Consider two relations R_1 A B with the tuples 1 5 3 7 and R_2 A C 1 7 4 9 Assume that R A B C is the full natural outer join of R_1 and R_2 Consider the following tuples of the form A B C a 1 5 null b 1 null 7 c 3 null 9 d 4 7 null e 1 5 7 f 3 7 null g 4 null 9 Which one of the following statements is correct R contains a b e f g but not c d R contains all a b c d e f g R contains e f g but not a b R contains e but not f g ,Natural Join,108 Let r be a relation instance with schema R A B C D We define r_1 pi_ A B C R and r_2 pi_ A D r Let s r_1 r_2 where denotes natural join Given that the decomposition of r into r_1 and r_2 is lossy which one of the following is TRUE s subset r r cup s r r subset s r s s ,Natural Join,108 Consider two relations R_1 A B with the tuples 1 5 3 7 and R_2 A C 1 7 4 9 Assume that R A B C is the full natural outer join of R_1 and R_2 Consider the following tuples of the form A B C a 1 5 null b 1 null 7 c 3 null 9 d 4 7 null e 1 5 7 f 3 7 null g 4 null 9 Which one of the following statements is correct R contains a b e f g but not c d R contains all a b c d e f g R contains e f g but not a b R contains e but not f g ,Natural Join,108 Consider two relations R_1 A B with the tuples 1 5 3 7 and R_2 A C 1 7 4 9 Assume that R A B C is the full natural outer join of R_1 and R_2 Consider the following tuples of the form A B C a 1 5 null b 1 null 7 c 3 null 9 d 4 7 null e 1 5 7 f 3 7 null g 4 null 9 Which one of the following statements is correct R contains a b e f g but not c d R contains all a b c d e f g R contains e f g but not a b R contains e but not f g ,Natural Join,108 Let r be a relation instance with schema R A B C D We define r_1 pi_ A B C R and r_2 pi_ A D r Let s r_1 r_2 where denotes natural join Given that the decomposition of r into r_1 and r_2 is lossy which one of the following is TRUE s subset r r cup s r r subset s r s s ,Natural Join,108 Let r be a relation instance with schema R A B C D We define r_1 pi_ A B C R and r_2 pi_ A D r Let s r_1 r_2 where denotes natural join Given that the decomposition of r into r_1 and r_2 is lossy which one of the following is TRUE s subset r r cup s r r subset s r s s ,Natural Join,108 The following functional dependencies hold for relations R A B C and S B D E B o A A o C The relation R contains 200 tuples and the relation S contains 100 tuples What is the maximum number of tuples possible in the natural join R bowtie S 100 200 300 2000 ,Natural Join,108 Consider two relations R_1 A B with the tuples 1 5 3 7 and R_2 A C 1 7 4 9 Assume that R A B C is the full natural outer join of R_1 and R_2 Consider the following tuples of the form A B C a 1 5 null b 1 null 7 c 3 null 9 d 4 7 null e 1 5 7 f 3 7 null g 4 null 9 Which one of the following statements is correct R contains a b e f g but not c d R contains all a b c d e f g R contains e f g but not a b R contains e but not f g ,Natural Join,108 Let r be a relation instance with schema R A B C D We define r_1 pi_ A B C R and r_2 pi_ A D r Let s r_1 r_2 where denotes natural join Given that the decomposition of r into r_1 and r_2 is lossy which one of the following is TRUE s subset r r cup s r r subset s r s s ,Natural Join,108 Consider two hosts X and Y connected by a single direct link of rate 10 6 bits sec The distance between the two hosts is 10 000 km and the propagation speed along the link is 2 imes 10 8 m sec Host X sends a file of 50 000 bytes as one large message to host Y continuously Let the transmission and propagation delays be p milliseconds and q milliseconds respectively Then the value of p and q are p 50 and q 100 p 50 and q 400 p 100 and q 50 p 400 and q 50 ,Network Communication,109 Consider two hosts X and Y connected by a single direct link of rate 10 6 bits sec The distance between the two hosts is 10 000 km and the propagation speed along the link is 2 imes 10 8 m sec Host X sends a file of 50 000 bytes as one large message to host Y continuously Let the transmission and propagation delays be p milliseconds and q milliseconds respectively Then the value of p and q are p 50 and q 100 p 50 and q 400 p 100 and q 50 p 400 and q 50 ,Network Communication,109 Consider two hosts X and Y connected by a single direct link of rate 10 6 bits sec The distance between the two hosts is 10 000 km and the propagation speed along the link is 2 imes 10 8 m sec Host X sends a file of 50 000 bytes as one large message to host Y continuously Let the transmission and propagation delays be p milliseconds and q milliseconds respectively Then the value of p and q are p 50 and q 100 p 50 and q 400 p 100 and q 50 p 400 and q 50 ,Network Communication,109 Consider two hosts X and Y connected by a single direct link of rate 10 6 bits sec The distance between the two hosts is 10 000 km and the propagation speed along the link is 2 imes 10 8 m sec Host X sends a file of 50 000 bytes as one large message to host Y continuously Let the transmission and propagation delays be p milliseconds and q milliseconds respectively Then the value of p and q are p 50 and q 100 p 50 and q 400 p 100 and q 50 p 400 and q 50 ,Network Communication,109 Consider two hosts X and Y connected by a single direct link of rate 10 6 bits sec The distance between the two hosts is 10 000 km and the propagation speed along the link is 2 imes 10 8 m sec Host X sends a file of 50 000 bytes as one large message to host Y continuously Let the transmission and propagation delays be p milliseconds and q milliseconds respectively Then the value of p and q are p 50 and q 100 p 50 and q 400 p 100 and q 50 p 400 and q 50 ,Network Communication,109 Consider two hosts X and Y connected by a single direct link of rate 10 6 bits sec The distance between the two hosts is 10 000 km and the propagation speed along the link is 2 imes 10 8 m sec Host X sends a file of 50 000 bytes as one large message to host Y continuously Let the transmission and propagation delays be p milliseconds and q milliseconds respectively Then the value of p and q are p 50 and q 100 p 50 and q 400 p 100 and q 50 p 400 and q 50 ,Network Communication,109 Consider two hosts X and Y connected by a single direct link of rate 10 6 bits sec The distance between the two hosts is 10 000 km and the propagation speed along the link is 2 imes 10 8 m sec Host X sends a file of 50 000 bytes as one large message to host Y continuously Let the transmission and propagation delays be p milliseconds and q milliseconds respectively Then the value of p and q are p 50 and q 100 p 50 and q 400 p 100 and q 50 p 400 and q 50 ,Network Communication,109 Consider two hosts X and Y connected by a single direct link of rate 10 6 bits sec The distance between the two hosts is 10 000 km and the propagation speed along the link is 2 imes 10 8 m sec Host X sends a file of 50 000 bytes as one large message to host Y continuously Let the transmission and propagation delays be p milliseconds and q milliseconds respectively Then the value of p and q are p 50 and q 100 p 50 and q 400 p 100 and q 50 p 400 and q 50 ,Network Communication,109 Consider two hosts X and Y connected by a single direct link of rate 10 6 bits sec The distance between the two hosts is 10 000 km and the propagation speed along the link is 2 imes 10 8 m sec Host X sends a file of 50 000 bytes as one large message to host Y continuously Let the transmission and propagation delays be p milliseconds and q milliseconds respectively Then the value of p and q are p 50 and q 100 p 50 and q 400 p 100 and q 50 p 400 and q 50 ,Network Communication,109 Consider two hosts X and Y connected by a single direct link of rate 10 6 bits sec The distance between the two hosts is 10 000 km and the propagation speed along the link is 2 imes 10 8 m sec Host X sends a file of 50 000 bytes as one large message to host Y continuously Let the transmission and propagation delays be p milliseconds and q milliseconds respectively Then the value of p and q are p 50 and q 100 p 50 and q 400 p 100 and q 50 p 400 and q 50 ,Network Communication,109 Consider two hosts X and Y connected by a single direct link of rate 10 6 bits sec The distance between the two hosts is 10 000 km and the propagation speed along the link is 2 imes 10 8 m sec Host X sends a file of 50 000 bytes as one large message to host Y continuously Let the transmission and propagation delays be p milliseconds and q milliseconds respectively Then the value of p and q are p 50 and q 100 p 50 and q 400 p 100 and q 50 p 400 and q 50 ,Network Communication,109 Consider two hosts X and Y connected by a single direct link of rate 10 6 bits sec The distance between the two hosts is 10 000 km and the propagation speed along the link is 2 imes 10 8 m sec Host X sends a file of 50 000 bytes as one large message to host Y continuously Let the transmission and propagation delays be p milliseconds and q milliseconds respectively Then the value of p and q are p 50 and q 100 p 50 and q 400 p 100 and q 50 p 400 and q 50 ,Network Communication,109 Consider two hosts X and Y connected by a single direct link of rate 10 6 bits sec The distance between the two hosts is 10 000 km and the propagation speed along the link is 2 imes 10 8 m sec Host X sends a file of 50 000 bytes as one large message to host Y continuously Let the transmission and propagation delays be p milliseconds and q milliseconds respectively Then the value of p and q are p 50 and q 100 p 50 and q 400 p 100 and q 50 p 400 and q 50 ,Network Communication,109 Consider two hosts X and Y connected by a single direct link of rate 10 6 bits sec The distance between the two hosts is 10 000 km and the propagation speed along the link is 2 imes 10 8 m sec Host X sends a file of 50 000 bytes as one large message to host Y continuously Let the transmission and propagation delays be p milliseconds and q milliseconds respectively Then the value of p and q are p 50 and q 100 p 50 and q 400 p 100 and q 50 p 400 and q 50 ,Network Communication,109 A TCP message consisting of 2100 bytes is passed to IP for delivery across two networks The first network can carry a maximum payload of 1200 bytes per frame and the second network can carry a maximum payload of 400 bytes per frame excluding network overhead Assume that IP overhead per packet is 20 bytes What is the total IP overhead in the second network for this transmission 40 bytes 80 bytes 120 bytes 160 bytes ,Network Flow,110 A link of capacity 100 Mbps is carrying traffic from a number of sources Each source generates an on off traffic stream when the source is on the rate of traffic is 10 Mbps and when the source is off the rate of traffic is zero The duty cycle which is the ratio of on time to off time is 1 2 When there is no buffer at the link the minimum number of sources that can be multiplexed on the link so that link capacity is not wasted and no data loss occurs is S1 Assuming that all sources are synchronized and that the link is provided with a large buffer the maximum number of sources that can be multiplexed so that no data loss occurs is S2 The values of S1 and S2 are respectively 10 and 30 12 and 25 5 and 33 15 and 22 ,Network Flow,110 In a data link protocol the frame delimiter flag is given by 0111 Assuming that bit stuffing is employed the transmitter sends the data sequence 01110110 as 01101011 011010110 011101100 0110101100 ,Network Flow,110 A TCP message consisting of 2100 bytes is passed to IP for delivery across two networks The first network can carry a maximum payload of 1200 bytes per frame and the second network can carry a maximum payload of 400 bytes per frame excluding network overhead Assume that IP overhead per packet is 20 bytes What is the total IP overhead in the second network for this transmission 40 bytes 80 bytes 120 bytes 160 bytes ,Network Flow,110 A link of capacity 100 Mbps is carrying traffic from a number of sources Each source generates an on off traffic stream when the source is on the rate of traffic is 10 Mbps and when the source is off the rate of traffic is zero The duty cycle which is the ratio of on time to off time is 1 2 When there is no buffer at the link the minimum number of sources that can be multiplexed on the link so that link capacity is not wasted and no data loss occurs is S1 Assuming that all sources are synchronized and that the link is provided with a large buffer the maximum number of sources that can be multiplexed so that no data loss occurs is S2 The values of S1 and S2 are respectively 10 and 30 12 and 25 5 and 33 15 and 22 ,Network Flow,110 A channel has a bit rate of 4 kbps and one way propagation delay of 20 ms The channel uses stop and wait protocol The transmission time of the acknowledgement frame is negligible To get a channel efficiency of at least 50 the minimum frame size should be 80 bytes 80 bits 160 bytes 160 bits ,Network Flow,110 A TCP message consisting of 2100 bytes is passed to IP for delivery across two networks The first network can carry a maximum payload of 1200 bytes per frame and the second network can carry a maximum payload of 400 bytes per frame excluding network overhead Assume that IP overhead per packet is 20 bytes What is the total IP overhead in the second network for this transmission 40 bytes 80 bytes 120 bytes 160 bytes ,Network Flow,110 A link of capacity 100 Mbps is carrying traffic from a number of sources Each source generates an on off traffic stream when the source is on the rate of traffic is 10 Mbps and when the source is off the rate of traffic is zero The duty cycle which is the ratio of on time to off time is 1 2 When there is no buffer at the link the minimum number of sources that can be multiplexed on the link so that link capacity is not wasted and no data loss occurs is S1 Assuming that all sources are synchronized and that the link is provided with a large buffer the maximum number of sources that can be multiplexed so that no data loss occurs is S2 The values of S1 and S2 are respectively 10 and 30 12 and 25 5 and 33 15 and 22 ,Network Flow,110 A TCP message consisting of 2100 bytes is passed to IP for delivery across two networks The first network can carry a maximum payload of 1200 bytes per frame and the second network can carry a maximum payload of 400 bytes per frame excluding network overhead Assume that IP overhead per packet is 20 bytes What is the total IP overhead in the second network for this transmission 40 bytes 80 bytes 120 bytes 160 bytes ,Network Flow,110 A channel has a bit rate of 4 kbps and one way propagation delay of 20 ms The channel uses stop and wait protocol The transmission time of the acknowledgement frame is negligible To get a channel efficiency of at least 50 the minimum frame size should be 80 bytes 80 bits 160 bytes 160 bits ,Network Flow,110 A link of capacity 100 Mbps is carrying traffic from a number of sources Each source generates an on off traffic stream when the source is on the rate of traffic is 10 Mbps and when the source is off the rate of traffic is zero The duty cycle which is the ratio of on time to off time is 1 2 When there is no buffer at the link the minimum number of sources that can be multiplexed on the link so that link capacity is not wasted and no data loss occurs is S1 Assuming that all sources are synchronized and that the link is provided with a large buffer the maximum number of sources that can be multiplexed so that no data loss occurs is S2 The values of S1 and S2 are respectively 10 and 30 12 and 25 5 and 33 15 and 22 ,Network Flow,110 Assume that source S and destination D are connected through two intermediate routers labeled R Determine how many times each packet has to visit the network layer and the data link layer during a transmission from S to D A Network layer u2013 4 times and Data link layer u2013 4 times B Network layer u2013 4 times and Data link layer u2013 3 times C Network layer u2013 4 times and Data link layer u2013 6 times D Network layer u2013 2 times and Data link layer u2013 6 times,Network Layering,111 Choose the best matching between ext Group 1 and ext Group 2 Group 1 Group 2 P Data link layer 1 Ensures reliable transport of data over a physical point to point link Q Network layer 2 Encodes decodes data for physical transmission R Transport layer 3 Allows end to end communication between two processes 4 Routes data from one network node to the next P 1 Q 4 R 3 P 2 Q 4 R 1 P 2 Q 3 R 1 P 1 Q 3 R 2 ,Network Layering,111 Choose the best matching between ext Group 1 and ext Group 2 Group 1 Group 2 P Data link layer 1 Ensures reliable transport of data over a physical point to point link Q Network layer 2 Encodes decodes data for physical transmission R Transport layer 3 Allows end to end communication between two processes 4 Routes data from one network node to the next P 1 Q 4 R 3 P 2 Q 4 R 1 P 2 Q 3 R 1 P 1 Q 3 R 2 ,Network Layering,111 Assume that source S and destination D are connected through two intermediate routers labeled R Determine how many times each packet has to visit the network layer and the data link layer during a transmission from S to D A Network layer u2013 4 times and Data link layer u2013 4 times B Network layer u2013 4 times and Data link layer u2013 3 times C Network layer u2013 4 times and Data link layer u2013 6 times D Network layer u2013 2 times and Data link layer u2013 6 times,Network Layering,111 Choose the best matching between ext Group 1 and ext Group 2 Group 1 Group 2 P Data link layer 1 Ensures reliable transport of data over a physical point to point link Q Network layer 2 Encodes decodes data for physical transmission R Transport layer 3 Allows end to end communication between two processes 4 Routes data from one network node to the next P 1 Q 4 R 3 P 2 Q 4 R 1 P 2 Q 3 R 1 P 1 Q 3 R 2 ,Network Layering,111 Assume that source S and destination D are connected through two intermediate routers labeled R Determine how many times each packet has to visit the network layer and the data link layer during a transmission from S to D A Network layer u2013 4 times and Data link layer u2013 4 times B Network layer u2013 4 times and Data link layer u2013 3 times C Network layer u2013 4 times and Data link layer u2013 6 times D Network layer u2013 2 times and Data link layer u2013 6 times,Network Layering,111 Assume that source S and destination D are connected through two intermediate routers labeled R Determine how many times each packet has to visit the network layer and the data link layer during a transmission from S to D A Network layer u2013 4 times and Data link layer u2013 4 times B Network layer u2013 4 times and Data link layer u2013 3 times C Network layer u2013 4 times and Data link layer u2013 6 times D Network layer u2013 2 times and Data link layer u2013 6 times,Network Layering,111 Choose the best matching between ext Group 1 and ext Group 2 Group 1 Group 2 P Data link layer 1 Ensures reliable transport of data over a physical point to point link Q Network layer 2 Encodes decodes data for physical transmission R Transport layer 3 Allows end to end communication between two processes 4 Routes data from one network node to the next P 1 Q 4 R 3 P 2 Q 4 R 1 P 2 Q 3 R 1 P 1 Q 3 R 2 ,Network Layering,111 Assume that source S and destination D are connected through two intermediate routers labeled R Determine how many times each packet has to visit the network layer and the data link layer during a transmission from S to D A Network layer u2013 4 times and Data link layer u2013 4 times B Network layer u2013 4 times and Data link layer u2013 3 times C Network layer u2013 4 times and Data link layer u2013 6 times D Network layer u2013 2 times and Data link layer u2013 6 times,Network Layering,111 Assume that source S and destination D are connected through two intermediate routers labeled R Determine how many times each packet has to visit the network layer and the data link layer during a transmission from S to D A Network layer u2013 4 times and Data link layer u2013 4 times B Network layer u2013 4 times and Data link layer u2013 3 times C Network layer u2013 4 times and Data link layer u2013 6 times D Network layer u2013 2 times and Data link layer u2013 6 times,Network Layering,111 Assume that source S and destination D are connected through two intermediate routers labeled R Determine how many times each packet has to visit the network layer and the data link layer during a transmission from S to D A Network layer u2013 4 times and Data link layer u2013 4 times B Network layer u2013 4 times and Data link layer u2013 3 times C Network layer u2013 4 times and Data link layer u2013 6 times D Network layer u2013 2 times and Data link layer u2013 6 times,Network Layering,111 Choose the best matching between ext Group 1 and ext Group 2 Group 1 Group 2 P Data link layer 1 Ensures reliable transport of data over a physical point to point link Q Network layer 2 Encodes decodes data for physical transmission R Transport layer 3 Allows end to end communication between two processes 4 Routes data from one network node to the next P 1 Q 4 R 3 P 2 Q 4 R 1 P 2 Q 3 R 1 P 1 Q 3 R 2 ,Network Layering,111 Choose the best matching between ext Group 1 and ext Group 2 Group 1 Group 2 P Data link layer 1 Ensures reliable transport of data over a physical point to point link Q Network layer 2 Encodes decodes data for physical transmission R Transport layer 3 Allows end to end communication between two processes 4 Routes data from one network node to the next P 1 Q 4 R 3 P 2 Q 4 R 1 P 2 Q 3 R 1 P 1 Q 3 R 2 ,Network Layering,111 In one of the pairs of protocols given below both the protocols can use multiple TCP connections between the same client and the server Which one is that HTTP FTP HTTP TELNET FTP SMTP HTTP SMTP ,Network Protocols,112 Match the following P SMTP 1 Application layer Q BGP 2 Transport layer R TCP 3 Data link layer S PPP 4 Network layer 5 Physical layer P 2 Q 1 R 3 S 5 P 1 Q 4 R 2 S 3 P 1 Q 4 R 2 S 5 P 2 Q 4 R 1 S 3 ,Network Protocols,112 Match the following P SMTP 1 Application layer Q BGP 2 Transport layer R TCP 3 Data link layer S PPP 4 Network layer 5 Physical layer P 2 Q 1 R 3 S 5 P 1 Q 4 R 2 S 3 P 1 Q 4 R 2 S 5 P 2 Q 4 R 1 S 3 ,Network Protocols,112 Consider the following clauses Not inherently suitable for client authentication Not a state sensitive protocol Must be operated with more than one server Suitable for structured message organization May need two ports on the serve side for proper operation The option that has the maximum number of correct matches is IMAP i FTP ii HTTP iii DNS iv POP3 v FTP i POP3 ii SMTP iii HTTP iv IMAP v POP3 i SMTP ii DNS iii IMAP iv HTTP v SMTP i HTTP ii IMAP iii DNS iv FTP v ,Network Protocols,112 Consider the following clauses Not inherently suitable for client authentication Not a state sensitive protocol Must be operated with more than one server Suitable for structured message organization May need two ports on the serve side for proper operation The option that has the maximum number of correct matches is IMAP i FTP ii HTTP iii DNS iv POP3 v FTP i POP3 ii SMTP iii HTTP iv IMAP v POP3 i SMTP ii DNS iii IMAP iv HTTP v SMTP i HTTP ii IMAP iii DNS iv FTP v ,Network Protocols,112 In one of the pairs of protocols given below both the protocols can use multiple TCP connections between the same client and the server Which one is that HTTP FTP HTTP TELNET FTP SMTP HTTP SMTP ,Network Protocols,112 Match the following P SMTP 1 Application layer Q BGP 2 Transport layer R TCP 3 Data link layer S PPP 4 Network layer 5 Physical layer P 2 Q 1 R 3 S 5 P 1 Q 4 R 2 S 3 P 1 Q 4 R 2 S 5 P 2 Q 4 R 1 S 3 ,Network Protocols,112 In one of the pairs of protocols given below both the protocols can use multiple TCP connections between the same client and the server Which one is that HTTP FTP HTTP TELNET FTP SMTP HTTP SMTP ,Network Protocols,112 In one of the pairs of protocols given below both the protocols can use multiple TCP connections between the same client and the server Which one is that HTTP FTP HTTP TELNET FTP SMTP HTTP SMTP ,Network Protocols,112 Consider the following clauses Not inherently suitable for client authentication Not a state sensitive protocol Must be operated with more than one server Suitable for structured message organization May need two ports on the serve side for proper operation The option that has the maximum number of correct matches is IMAP i FTP ii HTTP iii DNS iv POP3 v FTP i POP3 ii SMTP iii HTTP iv IMAP v POP3 i SMTP ii DNS iii IMAP iv HTTP v SMTP i HTTP ii IMAP iii DNS iv FTP v ,Network Protocols,112 Consider the following clauses Not inherently suitable for client authentication Not a state sensitive protocol Must be operated with more than one server Suitable for structured message organization May need two ports on the serve side for proper operation The option that has the maximum number of correct matches is IMAP i FTP ii HTTP iii DNS iv POP3 v FTP i POP3 ii SMTP iii HTTP iv IMAP v POP3 i SMTP ii DNS iii IMAP iv HTTP v SMTP i HTTP ii IMAP iii DNS iv FTP v ,Network Protocols,112 Consider the following two statements A hash function these are often used for computing digital signatures is an injective function A encryption technique such as DES performs a permutation on the elements of its input alphabet Which one of the following options is valid for the above two statements Both are false Statement i is true and the other is false Statement ii is true and the other is false Both are true ,Network Security,113 A firewall is to be configured to allow hosts in a private network to freely open TCP connections and send packets on open connections However it will only allow external hosts to send packets on existing open TCP connections or connections that are being opened by internal hosts but not allow them to open TCP connections to hosts in the private network To achieve this the minimum capability of the firewall should be that of A combinational circuit A finite automaton A pushdown automaton with one stack A pushdown automaton with two stacks ,Network Security,113 Suppose that everyone in a group on N people wants to communicate secretly withhe ext N 1 others using symmetric Key cryptographic system The communication between any two person should not be decodable by the others in the group The numbers of keys required in the system as a whole to satisfyhe confidentiality requirement is 2N N N 1 dfrac N N 1 2 N 1 2 ,Network Security,113 Two hosts are connected via a packet switch with 10 7 bits per second links Each link has a propagation delay of 20 microseconds The switch begins forwarding a packet 35 microseconds after it receives the same If 10000 bits of data are to be transmitted between the two hosts using a packet size of 5000 bits the time elapsed between the transmission of the first bit of data and the reception of the last bit of the data in microseconds is ______ ,Network Switching,114 In a packet switching network packets are routed from source to destination along a single path having two intermediate nodes If the message size is 24 bytes and each packet contains a header of 3 bytes then the optimum packet size is 4 6 7 9 ,Network Switching,114 Consider the store and forward packet switched network given below Assume that the bandwidth of each link is 10 6 bytes sec A user on host A sends a file of size 10 3 bytes to host B through routers R1 and R2 in three different ways In the first case a single packet containing the complete file is transmitted from A to B In the second case the file is split into 10 equal parts and these packets are transmitted from A to B In the third case the file is split into 20 equal parts and these packets are sent from A to B Each packet contains 100 bytes of header information along with the user data Consider only transmission time and ignore processing queuing and propagation delays Also assume that there are no errors during transmission Let T1 T2 and T3 be the times taken to transmit the file in the first second and third case respectively Which one of the following is CORRECT T lt T2 lt T3 T1 gt T2 gt T3 T2 T3 T3 lt T1 T1 T3 T3 gt T2 ,Network Switching,114 Consider the store and forward packet switched network given below Assume that the bandwidth of each link is 10 6 bytes sec A user on host A sends a file of size 10 3 bytes to host B through routers R1 and R2 in three different ways In the first case a single packet containing the complete file is transmitted from A to B In the second case the file is split into 10 equal parts and these packets are transmitted from A to B In the third case the file is split into 20 equal parts and these packets are sent from A to B Each packet contains 100 bytes of header information along with the user data Consider only transmission time and ignore processing queuing and propagation delays Also assume that there are no errors during transmission Let T1 T2 and T3 be the times taken to transmit the file in the first second and third case respectively Which one of the following is CORRECT T lt T2 lt T3 T1 gt T2 gt T3 T2 T3 T3 lt T1 T1 T3 T3 gt T2 ,Network Switching,114 Consider the store and forward packet switched network given below Assume that the bandwidth of each link is 10 6 bytes sec A user on host A sends a file of size 10 3 bytes to host B through routers R1 and R2 in three different ways In the first case a single packet containing the complete file is transmitted from A to B In the second case the file is split into 10 equal parts and these packets are transmitted from A to B In the third case the file is split into 20 equal parts and these packets are sent from A to B Each packet contains 100 bytes of header information along with the user data Consider only transmission time and ignore processing queuing and propagation delays Also assume that there are no errors during transmission Let T1 T2 and T3 be the times taken to transmit the file in the first second and third case respectively Which one of the following is CORRECT T lt T2 lt T3 T1 gt T2 gt T3 T2 T3 T3 lt T1 T1 T3 T3 gt T2 ,Network Switching,114 Two hosts are connected via a packet switch with 10 7 bits per second links Each link has a propagation delay of 20 microseconds The switch begins forwarding a packet 35 microseconds after it receives the same If 10000 bits of data are to be transmitted between the two hosts using a packet size of 5000 bits the time elapsed between the transmission of the first bit of data and the reception of the last bit of the data in microseconds is ______ ,Network Switching,114 In a packet switching network packets are routed from source to destination along a single path having two intermediate nodes If the message size is 24 bytes and each packet contains a header of 3 bytes then the optimum packet size is 4 6 7 9 ,Network Switching,114 Two hosts are connected via a packet switch with 10 7 bits per second links Each link has a propagation delay of 20 microseconds The switch begins forwarding a packet 35 microseconds after it receives the same If 10000 bits of data are to be transmitted between the two hosts using a packet size of 5000 bits the time elapsed between the transmission of the first bit of data and the reception of the last bit of the data in microseconds is ______ ,Network Switching,114 Two hosts are connected via a packet switch with 10 7 bits per second links Each link has a propagation delay of 20 microseconds The switch begins forwarding a packet 35 microseconds after it receives the same If 10000 bits of data are to be transmitted between the two hosts using a packet size of 5000 bits the time elapsed between the transmission of the first bit of data and the reception of the last bit of the data in microseconds is ______ ,Network Switching,114 In a packet switching network packets are routed from source to destination along a single path having two intermediate nodes If the message size is 24 bytes and each packet contains a header of 3 bytes then the optimum packet size is 4 6 7 9 ,Network Switching,114 Consider the store and forward packet switched network given below Assume that the bandwidth of each link is 10 6 bytes sec A user on host A sends a file of size 10 3 bytes to host B through routers R1 and R2 in three different ways In the first case a single packet containing the complete file is transmitted from A to B In the second case the file is split into 10 equal parts and these packets are transmitted from A to B In the third case the file is split into 20 equal parts and these packets are sent from A to B Each packet contains 100 bytes of header information along with the user data Consider only transmission time and ignore processing queuing and propagation delays Also assume that there are no errors during transmission Let T1 T2 and T3 be the times taken to transmit the file in the first second and third case respectively Which one of the following is CORRECT T lt T2 lt T3 T1 gt T2 gt T3 T2 T3 T3 lt T1 T1 T3 T3 gt T2 ,Network Switching,114 Consider the store and forward packet switched network given below Assume that the bandwidth of each link is 10 6 bytes sec A user on host A sends a file of size 10 3 bytes to host B through routers R1 and R2 in three different ways In the first case a single packet containing the complete file is transmitted from A to B In the second case the file is split into 10 equal parts and these packets are transmitted from A to B In the third case the file is split into 20 equal parts and these packets are sent from A to B Each packet contains 100 bytes of header information along with the user data Consider only transmission time and ignore processing queuing and propagation delays Also assume that there are no errors during transmission Let T1 T2 and T3 be the times taken to transmit the file in the first second and third case respectively Which one of the following is CORRECT T lt T2 lt T3 T1 gt T2 gt T3 T2 T3 T3 lt T1 T1 T3 T3 gt T2 ,Network Switching,114 X is a 30 digit number starting with the digit 4 followed by the digit 7 Then the number X 3 will have 90 digits 91 digits 92 digits 93 digits ,No Of Digits,115 X is a 30 digit number starting with the digit 4 followed by the digit 7 Then the number X 3 will have 90 digits 91 digits 92 digits 93 digits ,No Of Digits,115 X is a 30 digit number starting with the digit 4 followed by the digit 7 Then the number X 3 will have 90 digits 91 digits 92 digits 93 digits ,No Of Digits,115 X is a 30 digit number starting with the digit 4 followed by the digit 7 Then the number X 3 will have 90 digits 91 digits 92 digits 93 digits ,No Of Digits,115 X is a 30 digit number starting with the digit 4 followed by the digit 7 Then the number X 3 will have 90 digits 91 digits 92 digits 93 digits ,No Of Digits,115 X is a 30 digit number starting with the digit 4 followed by the digit 7 Then the number X 3 will have 90 digits 91 digits 92 digits 93 digits ,No Of Digits,115 X is a 30 digit number starting with the digit 4 followed by the digit 7 Then the number X 3 will have 90 digits 91 digits 92 digits 93 digits ,No Of Digits,115 X is a 30 digit number starting with the digit 4 followed by the digit 7 Then the number X 3 will have 90 digits 91 digits 92 digits 93 digits ,No Of Digits,115 X is a 30 digit number starting with the digit 4 followed by the digit 7 Then the number X 3 will have 90 digits 91 digits 92 digits 93 digits ,No Of Digits,115 X is a 30 digit number starting with the digit 4 followed by the digit 7 Then the number X 3 will have 90 digits 91 digits 92 digits 93 digits ,No Of Digits,115 X is a 30 digit number starting with the digit 4 followed by the digit 7 Then the number X 3 will have 90 digits 91 digits 92 digits 93 digits ,No Of Digits,115 X is a 30 digit number starting with the digit 4 followed by the digit 7 Then the number X 3 will have 90 digits 91 digits 92 digits 93 digits ,No Of Digits,115 X is a 30 digit number starting with the digit 4 followed by the digit 7 Then the number X 3 will have 90 digits 91 digits 92 digits 93 digits ,No Of Digits,115 X is a 30 digit number starting with the digit 4 followed by the digit 7 Then the number X 3 will have 90 digits 91 digits 92 digits 93 digits ,No Of Digits,115 Let N_f and N_p denote the classes of languages accepted by non deterministic finite automata and non deterministic push down automata respectively Let D_f and D_p denote the classes of languages accepted by deterministic finite automata and deterministic push down automata respectively Which one of the following is TRUE D_f subset N_f ext and D_p subset N_p D_f subset N_f ext and D_p N_p D_f N_f ext and D_p N_p D_f N_f ext and D_p subset N_p ,Non Determinism,116 Regarding the power of recognition of languages which of the following statements is false The non deterministic finite state automata are equivalent to deterministic finite state automata Non deterministic Push down automata are equivalent to deterministic Push down automata Non deterministic Turing machines are equivalent to deterministic Push down automata Non deterministic Turing machines are equivalent to deterministic Turing machines Multi tape Turing machines are available are equivalent to Single tape Turing machines ,Non Determinism,116 Regarding the power of recognition of languages which of the following statements is false The non deterministic finite state automata are equivalent to deterministic finite state automata Non deterministic Push down automata are equivalent to deterministic Push down automata Non deterministic Turing machines are equivalent to deterministic Push down automata Non deterministic Turing machines are equivalent to deterministic Turing machines Multi tape Turing machines are available are equivalent to Single tape Turing machines ,Non Determinism,116 Let N_f and N_p denote the classes of languages accepted by non deterministic finite automata and non deterministic push down automata respectively Let D_f and D_p denote the classes of languages accepted by deterministic finite automata and deterministic push down automata respectively Which one of the following is TRUE D_f subset N_f ext and D_p subset N_p D_f subset N_f ext and D_p N_p D_f N_f ext and D_p N_p D_f N_f ext and D_p subset N_p ,Non Determinism,116 02 Choose the correct alternatives more than one may be correct and write the corresponding letters only In which of the cases stated below is the following statement true For every non deterministic machine M_ 1 there exists an equivalent deterministic machine M_ 2 recognizing the same language M_ 1 is non deterministic finite automaton M_ 1 is non deterministic PDA M_ 1 is a non deteministic Turing machine For no machines M_ 1 and M_2 the above statement true ,Non Determinism,116 Regarding the power of recognition of languages which of the following statements is false The non deterministic finite state automata are equivalent to deterministic finite state automata Non deterministic Push down automata are equivalent to deterministic Push down automata Non deterministic Turing machines are equivalent to deterministic Push down automata Non deterministic Turing machines are equivalent to deterministic Turing machines Multi tape Turing machines are available are equivalent to Single tape Turing machines ,Non Determinism,116 Let N_f and N_p denote the classes of languages accepted by non deterministic finite automata and non deterministic push down automata respectively Let D_f and D_p denote the classes of languages accepted by deterministic finite automata and deterministic push down automata respectively Which one of the following is TRUE D_f subset N_f ext and D_p subset N_p D_f subset N_f ext and D_p N_p D_f N_f ext and D_p N_p D_f N_f ext and D_p subset N_p ,Non Determinism,116 Let N_f and N_p denote the classes of languages accepted by non deterministic finite automata and non deterministic push down automata respectively Let D_f and D_p denote the classes of languages accepted by deterministic finite automata and deterministic push down automata respectively Which one of the following is TRUE D_f subset N_f ext and D_p subset N_p D_f subset N_f ext and D_p N_p D_f N_f ext and D_p N_p D_f N_f ext and D_p subset N_p ,Non Determinism,116 Let N_f and N_p denote the classes of languages accepted by non deterministic finite automata and non deterministic push down automata respectively Let D_f and D_p denote the classes of languages accepted by deterministic finite automata and deterministic push down automata respectively Which one of the following is TRUE D_f subset N_f ext and D_p subset N_p D_f subset N_f ext and D_p N_p D_f N_f ext and D_p N_p D_f N_f ext and D_p subset N_p ,Non Determinism,116 02 Choose the correct alternatives more than one may be correct and write the corresponding letters only In which of the cases stated below is the following statement true For every non deterministic machine M_ 1 there exists an equivalent deterministic machine M_ 2 recognizing the same language M_ 1 is non deterministic finite automaton M_ 1 is non deterministic PDA M_ 1 is a non deteministic Turing machine For no machines M_ 1 and M_2 the above statement true ,Non Determinism,116 Let N_f and N_p denote the classes of languages accepted by non deterministic finite automata and non deterministic push down automata respectively Let D_f and D_p denote the classes of languages accepted by deterministic finite automata and deterministic push down automata respectively Which one of the following is TRUE D_f subset N_f ext and D_p subset N_p D_f subset N_f ext and D_p N_p D_f N_f ext and D_p N_p D_f N_f ext and D_p subset N_p ,Non Determinism,116 Regarding the power of recognition of languages which of the following statements is false The non deterministic finite state automata are equivalent to deterministic finite state automata Non deterministic Push down automata are equivalent to deterministic Push down automata Non deterministic Turing machines are equivalent to deterministic Push down automata Non deterministic Turing machines are equivalent to deterministic Turing machines Multi tape Turing machines are available are equivalent to Single tape Turing machines ,Non Determinism,116 Let X be a random variable following normal distribution with mean 1 and variance 4 Let Y be another normal variable with mean 1 and variance unknown If P X u2264 1 P Y u2265 2 the standard deviation of Y is 3 2 sqrt 2 1 ,Normal Distribution,117 Let X be a random variable following normal distribution with mean 1 and variance 4 Let Y be another normal variable with mean 1 and variance unknown If P X u2264 1 P Y u2265 2 the standard deviation of Y is 3 2 sqrt 2 1 ,Normal Distribution,117 Let X be a random variable following normal distribution with mean 1 and variance 4 Let Y be another normal variable with mean 1 and variance unknown If P X u2264 1 P Y u2265 2 the standard deviation of Y is 3 2 sqrt 2 1 ,Normal Distribution,117 Let X be a random variable following normal distribution with mean 1 and variance 4 Let Y be another normal variable with mean 1 and variance unknown If P X u2264 1 P Y u2265 2 the standard deviation of Y is 3 2 sqrt 2 1 ,Normal Distribution,117 Let X be a random variable following normal distribution with mean 1 and variance 4 Let Y be another normal variable with mean 1 and variance unknown If P X u2264 1 P Y u2265 2 the standard deviation of Y is 3 2 sqrt 2 1 ,Normal Distribution,117 Let X be a random variable following normal distribution with mean 1 and variance 4 Let Y be another normal variable with mean 1 and variance unknown If P X u2264 1 P Y u2265 2 the standard deviation of Y is 3 2 sqrt 2 1 ,Normal Distribution,117 Let X be a random variable following normal distribution with mean 1 and variance 4 Let Y be another normal variable with mean 1 and variance unknown If P X u2264 1 P Y u2265 2 the standard deviation of Y is 3 2 sqrt 2 1 ,Normal Distribution,117 Let X be a random variable following normal distribution with mean 1 and variance 4 Let Y be another normal variable with mean 1 and variance unknown If P X u2264 1 P Y u2265 2 the standard deviation of Y is 3 2 sqrt 2 1 ,Normal Distribution,117 Let X be a random variable following normal distribution with mean 1 and variance 4 Let Y be another normal variable with mean 1 and variance unknown If P X u2264 1 P Y u2265 2 the standard deviation of Y is 3 2 sqrt 2 1 ,Normal Distribution,117 Let X be a random variable following normal distribution with mean 1 and variance 4 Let Y be another normal variable with mean 1 and variance unknown If P X u2264 1 P Y u2265 2 the standard deviation of Y is 3 2 sqrt 2 1 ,Normal Distribution,117 Let X be a random variable following normal distribution with mean 1 and variance 4 Let Y be another normal variable with mean 1 and variance unknown If P X u2264 1 P Y u2265 2 the standard deviation of Y is 3 2 sqrt 2 1 ,Normal Distribution,117 Let X be a random variable following normal distribution with mean 1 and variance 4 Let Y be another normal variable with mean 1 and variance unknown If P X u2264 1 P Y u2265 2 the standard deviation of Y is 3 2 sqrt 2 1 ,Normal Distribution,117 Let X be a random variable following normal distribution with mean 1 and variance 4 Let Y be another normal variable with mean 1 and variance unknown If P X u2264 1 P Y u2265 2 the standard deviation of Y is 3 2 sqrt 2 1 ,Normal Distribution,117 Let X be a random variable following normal distribution with mean 1 and variance 4 Let Y be another normal variable with mean 1 and variance unknown If P X u2264 1 P Y u2265 2 the standard deviation of Y is 3 2 sqrt 2 1 ,Normal Distribution,117 Consider the following floating point number representation 31 24 23 0 Exponent Mantissa The exponent is in 2 u2019s complement representation and mantissa is in the sign magnitude representation The range of the magnitude of the normalized numbers in this representation is 0 to 1 0 5 to 1 2 23 to 0 5 0 5 to left 1 2 23 right ,Number Representation,118 Find the sum of the expression frac 1 sqrt 1 sqrt 2 frac 1 sqrt 2 sqrt 3 frac 1 sqrt 3 sqrt 4 frac 1 sqrt 80 sqrt 81 7 8 9 10 ,Number Series,119 The value of sqrt 12 sqrt 12 sqrt 12 dots is 3 464 3 932 4 000 4 444 ,Number Series,119 The value of sqrt 12 sqrt 12 sqrt 12 dots is 3 464 3 932 4 000 4 444 ,Number Series,119 The value of sqrt 12 sqrt 12 sqrt 12 dots is 3 464 3 932 4 000 4 444 ,Number Series,119 Find the sum of the expression frac 1 sqrt 1 sqrt 2 frac 1 sqrt 2 sqrt 3 frac 1 sqrt 3 sqrt 4 frac 1 sqrt 80 sqrt 81 7 8 9 10 ,Number Series,119 The value of sqrt 12 sqrt 12 sqrt 12 dots is 3 464 3 932 4 000 4 444 ,Number Series,119 The value of sqrt 12 sqrt 12 sqrt 12 dots is 3 464 3 932 4 000 4 444 ,Number Series,119 The value of sqrt 12 sqrt 12 sqrt 12 dots is 3 464 3 932 4 000 4 444 ,Number Series,119 The value of sqrt 12 sqrt 12 sqrt 12 dots is 3 464 3 932 4 000 4 444 ,Number Series,119 Find the sum of the expression frac 1 sqrt 1 sqrt 2 frac 1 sqrt 2 sqrt 3 frac 1 sqrt 3 sqrt 4 frac 1 sqrt 80 sqrt 81 7 8 9 10 ,Number Series,119 The value of sqrt 12 sqrt 12 sqrt 12 dots is 3 464 3 932 4 000 4 444 ,Number Series,119 Find the sum of the expression frac 1 sqrt 1 sqrt 2 frac 1 sqrt 2 sqrt 3 frac 1 sqrt 3 sqrt 4 frac 1 sqrt 80 sqrt 81 7 8 9 10 ,Number Series,119 Find the sum of the expression frac 1 sqrt 1 sqrt 2 frac 1 sqrt 2 sqrt 3 frac 1 sqrt 3 sqrt 4 frac 1 sqrt 80 sqrt 81 7 8 9 10 ,Number Series,119 Consider the quadratic equation x 2 13x 36 0 with coefficients in a base b The solutions of this equation in the same base b are x 5 and x 6 Then b _____,Number System,120 Consider the quadratic equation x 2 13x 36 0 with coefficients in a base b The solutions of this equation in the same base b are x 5 and x 6 Then b _____,Number System,120 Consider the quadratic equation x 2 13x 36 0 with coefficients in a base b The solutions of this equation in the same base b are x 5 and x 6 Then b _____,Number System,120 Consider the quadratic equation x 2 13x 36 0 with coefficients in a base b The solutions of this equation in the same base b are x 5 and x 6 Then b _____,Number System,120 Consider the quadratic equation x 2 13x 36 0 with coefficients in a base b The solutions of this equation in the same base b are x 5 and x 6 Then b _____,Number System,120 Consider the quadratic equation x 2 13x 36 0 with coefficients in a base b The solutions of this equation in the same base b are x 5 and x 6 Then b _____,Number System,120 Consider the quadratic equation x 2 13x 36 0 with coefficients in a base b The solutions of this equation in the same base b are x 5 and x 6 Then b _____,Number System,120 Consider the quadratic equation x 2 13x 36 0 with coefficients in a base b The solutions of this equation in the same base b are x 5 and x 6 Then b _____,Number System,120 Consider the quadratic equation x 2 13x 36 0 with coefficients in a base b The solutions of this equation in the same base b are x 5 and x 6 Then b _____,Number System,120 Consider the quadratic equation x 2 13x 36 0 with coefficients in a base b The solutions of this equation in the same base b are x 5 and x 6 Then b _____,Number System,120 Consider the quadratic equation x 2 13x 36 0 with coefficients in a base b The solutions of this equation in the same base b are x 5 and x 6 Then b _____,Number System,120 Consider the quadratic equation x 2 13x 36 0 with coefficients in a base b The solutions of this equation in the same base b are x 5 and x 6 Then b _____,Number System,120 Consider the quadratic equation x 2 13x 36 0 with coefficients in a base b The solutions of this equation in the same base b are x 5 and x 6 Then b _____,Number System,120 Consider the quadratic equation x 2 13x 36 0 with coefficients in a base b The solutions of this equation in the same base b are x 5 and x 6 Then b _____,Number System,120 The minimum positive integer p such that 3 p pmod 17 1 is 5 8 12 16 ,Number Theory,121 The number of distinct positive integral factors of 2014 is _____________,Number Theory,121 Show that the product of the least common multiple and the greatest common divisor of two positive integers a and b is a imes b ,Number Theory,121 The number of divisors of 2100 is ____ ,Number Theory,121 Show that the product of the least common multiple and the greatest common divisor of two positive integers a and b is a imes b ,Number Theory,121 Show that the product of the least common multiple and the greatest common divisor of two positive integers a and b is a imes b ,Number Theory,121 Show that the product of the least common multiple and the greatest common divisor of two positive integers a and b is a imes b ,Number Theory,121 Show that the product of the least common multiple and the greatest common divisor of two positive integers a and b is a imes b ,Number Theory,121 The number of distinct positive integral factors of 2014 is _____________,Number Theory,121 The number of divisors of 2100 is ____ ,Number Theory,121 A CPU has two modes privileged and non privileged In order to change the mode from privileged to non privileged a hardware interrupt is needed a software interrupt is needed a privileged instruction which does not generate an interrupt is needed a non privileged instruction which does not generate an interrupt is needed ,Os Protection,122 A CPU has two modes privileged and non privileged In order to change the mode from privileged to non privileged a hardware interrupt is needed a software interrupt is needed a privileged instruction which does not generate an interrupt is needed a non privileged instruction which does not generate an interrupt is needed ,Os Protection,122 A CPU has two modes privileged and non privileged In order to change the mode from privileged to non privileged a hardware interrupt is needed a software interrupt is needed a privileged instruction which does not generate an interrupt is needed a non privileged instruction which does not generate an interrupt is needed ,Os Protection,122 A CPU has two modes privileged and non privileged In order to change the mode from privileged to non privileged a hardware interrupt is needed a software interrupt is needed a privileged instruction which does not generate an interrupt is needed a non privileged instruction which does not generate an interrupt is needed ,Os Protection,122 A CPU has two modes privileged and non privileged In order to change the mode from privileged to non privileged a hardware interrupt is needed a software interrupt is needed a privileged instruction which does not generate an interrupt is needed a non privileged instruction which does not generate an interrupt is needed ,Os Protection,122 A CPU has two modes privileged and non privileged In order to change the mode from privileged to non privileged a hardware interrupt is needed a software interrupt is needed a privileged instruction which does not generate an interrupt is needed a non privileged instruction which does not generate an interrupt is needed ,Os Protection,122 A CPU has two modes privileged and non privileged In order to change the mode from privileged to non privileged a hardware interrupt is needed a software interrupt is needed a privileged instruction which does not generate an interrupt is needed a non privileged instruction which does not generate an interrupt is needed ,Os Protection,122 A CPU has two modes privileged and non privileged In order to change the mode from privileged to non privileged a hardware interrupt is needed a software interrupt is needed a privileged instruction which does not generate an interrupt is needed a non privileged instruction which does not generate an interrupt is needed ,Os Protection,122 A CPU has two modes privileged and non privileged In order to change the mode from privileged to non privileged a hardware interrupt is needed a software interrupt is needed a privileged instruction which does not generate an interrupt is needed a non privileged instruction which does not generate an interrupt is needed ,Os Protection,122 A CPU has two modes privileged and non privileged In order to change the mode from privileged to non privileged a hardware interrupt is needed a software interrupt is needed a privileged instruction which does not generate an interrupt is needed a non privileged instruction which does not generate an interrupt is needed ,Os Protection,122 A CPU has two modes privileged and non privileged In order to change the mode from privileged to non privileged a hardware interrupt is needed a software interrupt is needed a privileged instruction which does not generate an interrupt is needed a non privileged instruction which does not generate an interrupt is needed ,Os Protection,122 A CPU has two modes privileged and non privileged In order to change the mode from privileged to non privileged a hardware interrupt is needed a software interrupt is needed a privileged instruction which does not generate an interrupt is needed a non privileged instruction which does not generate an interrupt is needed ,Os Protection,122 A CPU has two modes privileged and non privileged In order to change the mode from privileged to non privileged a hardware interrupt is needed a software interrupt is needed a privileged instruction which does not generate an interrupt is needed a non privileged instruction which does not generate an interrupt is needed ,Os Protection,122 A CPU has two modes privileged and non privileged In order to change the mode from privileged to non privileged a hardware interrupt is needed a software interrupt is needed a privileged instruction which does not generate an interrupt is needed a non privileged instruction which does not generate an interrupt is needed ,Os Protection,122 In the following pairs of OSI protocol layer sub layer and its functionality the INCORRECT pair is Network layer and Routing Data Link Layer and Bit synchronization Transport layer and End to end process communication Medium Access Control sub layer and Channel sharing ,Osi Protocol,123 In the following pairs of OSI protocol layer sub layer and its functionality the INCORRECT pair is Network layer and Routing Data Link Layer and Bit synchronization Transport layer and End to end process communication Medium Access Control sub layer and Channel sharing ,Osi Protocol,123 In the following pairs of OSI protocol layer sub layer and its functionality the INCORRECT pair is Network layer and Routing Data Link Layer and Bit synchronization Transport layer and End to end process communication Medium Access Control sub layer and Channel sharing ,Osi Protocol,123 In the following pairs of OSI protocol layer sub layer and its functionality the INCORRECT pair is Network layer and Routing Data Link Layer and Bit synchronization Transport layer and End to end process communication Medium Access Control sub layer and Channel sharing ,Osi Protocol,123 In the following pairs of OSI protocol layer sub layer and its functionality the INCORRECT pair is Network layer and Routing Data Link Layer and Bit synchronization Transport layer and End to end process communication Medium Access Control sub layer and Channel sharing ,Osi Protocol,123 In the following pairs of OSI protocol layer sub layer and its functionality the INCORRECT pair is Network layer and Routing Data Link Layer and Bit synchronization Transport layer and End to end process communication Medium Access Control sub layer and Channel sharing ,Osi Protocol,123 In the following pairs of OSI protocol layer sub layer and its functionality the INCORRECT pair is Network layer and Routing Data Link Layer and Bit synchronization Transport layer and End to end process communication Medium Access Control sub layer and Channel sharing ,Osi Protocol,123 In the following pairs of OSI protocol layer sub layer and its functionality the INCORRECT pair is Network layer and Routing Data Link Layer and Bit synchronization Transport layer and End to end process communication Medium Access Control sub layer and Channel sharing ,Osi Protocol,123 In the following pairs of OSI protocol layer sub layer and its functionality the INCORRECT pair is Network layer and Routing Data Link Layer and Bit synchronization Transport layer and End to end process communication Medium Access Control sub layer and Channel sharing ,Osi Protocol,123 In the following pairs of OSI protocol layer sub layer and its functionality the INCORRECT pair is Network layer and Routing Data Link Layer and Bit synchronization Transport layer and End to end process communication Medium Access Control sub layer and Channel sharing ,Osi Protocol,123 In the following pairs of OSI protocol layer sub layer and its functionality the INCORRECT pair is Network layer and Routing Data Link Layer and Bit synchronization Transport layer and End to end process communication Medium Access Control sub layer and Channel sharing ,Osi Protocol,123 In the following pairs of OSI protocol layer sub layer and its functionality the INCORRECT pair is Network layer and Routing Data Link Layer and Bit synchronization Transport layer and End to end process communication Medium Access Control sub layer and Channel sharing ,Osi Protocol,123 In the following pairs of OSI protocol layer sub layer and its functionality the INCORRECT pair is Network layer and Routing Data Link Layer and Bit synchronization Transport layer and End to end process communication Medium Access Control sub layer and Channel sharing ,Osi Protocol,123 In the following pairs of OSI protocol layer sub layer and its functionality the INCORRECT pair is Network layer and Routing Data Link Layer and Bit synchronization Transport layer and End to end process communication Medium Access Control sub layer and Channel sharing ,Osi Protocol,123 The overlay tree for a program is as shown below What will be the size of the partition in physical memory required to load and run this program 12 KB 14 KB 10 KB 8 KB ,Overlay,124 The overlay tree for a program is as shown below What will be the size of the partition in physical memory required to load and run this program 12 KB 14 KB 10 KB 8 KB ,Overlay,124 The overlay tree for a program is as shown below What will be the size of the partition in physical memory required to load and run this program 12 KB 14 KB 10 KB 8 KB ,Overlay,124 The overlay tree for a program is as shown below What will be the size of the partition in physical memory required to load and run this program 12 KB 14 KB 10 KB 8 KB ,Overlay,124 The overlay tree for a program is as shown below What will be the size of the partition in physical memory required to load and run this program 12 KB 14 KB 10 KB 8 KB ,Overlay,124 The overlay tree for a program is as shown below What will be the size of the partition in physical memory required to load and run this program 12 KB 14 KB 10 KB 8 KB ,Overlay,124 The overlay tree for a program is as shown below What will be the size of the partition in physical memory required to load and run this program 12 KB 14 KB 10 KB 8 KB ,Overlay,124 The overlay tree for a program is as shown below What will be the size of the partition in physical memory required to load and run this program 12 KB 14 KB 10 KB 8 KB ,Overlay,124 The overlay tree for a program is as shown below What will be the size of the partition in physical memory required to load and run this program 12 KB 14 KB 10 KB 8 KB ,Overlay,124 The overlay tree for a program is as shown below What will be the size of the partition in physical memory required to load and run this program 12 KB 14 KB 10 KB 8 KB ,Overlay,124 The overlay tree for a program is as shown below What will be the size of the partition in physical memory required to load and run this program 12 KB 14 KB 10 KB 8 KB ,Overlay,124 The overlay tree for a program is as shown below What will be the size of the partition in physical memory required to load and run this program 12 KB 14 KB 10 KB 8 KB ,Overlay,124 The overlay tree for a program is as shown below What will be the size of the partition in physical memory required to load and run this program 12 KB 14 KB 10 KB 8 KB ,Overlay,124 The overlay tree for a program is as shown below What will be the size of the partition in physical memory required to load and run this program 12 KB 14 KB 10 KB 8 KB ,Overlay,124 The following page addresses in the given sequence were generated by a program 1 2 3 4 1 3 5 2 1 5 4 3 2 3 This program is run on a demand paged virtual memory system with main memory size equal to 4 pages Indicate the page references for which page faults occur for the following page replacement algorithms LRU FIFO Assume that the main memory is initially empty,Page Replacement,125 Let X 2 3 6 12 24 Let leq be the partial order defined by X leq Y if x divides y Number of edges in the Hasse diagram of X leq is 3 4 9 None of the above ,Partial Order,126 The inclusion of which of the following sets into S left left 1 2 right left 1 2 3 right left 1 3 5 right left 1 2 4 right left 1 2 3 4 5 right right is necessary and sufficient to make S a complete lattice under the partial order defined by set containment 1 1 2 3 1 1 3 1 1 3 1 2 3 4 1 2 3 5 ,Partial Order,126 The less than relation lt on reals is a partial ordering since it is asymmetric and reflexive a partial ordering since it is antisymmetric and reflexive not a partial ordering because it is not asymmetric and not reflexive not a partial ordering because it is not antisymmetric and reflexive none of the above ,Partial Order,126 Let S leq be a partial order with two minimal elements a and b and a maximum element c Let P S o True False be a predicate defined on S Suppose that P a True P b False and P x implies P y for all x y in S satisfying x leq y where implies stands for logical implication Which of the following statements CANNOT be true P x True for all x in S such that x u2260 b P x False for all x in S such that x u2260 a and x u2260 c P x False for all x in S such that b u2264 x and x u2260 c P x False for all x in S such that a u2264 x and b u2264 x ,Partial Order,126 A partial order P is defined on the set of natural numbers as follows Here dfrac x y denotes integer division 0 0 in P a b in P if and only if a 10 leq b 10 and frac a 10 frac b 10 in P Consider the following ordered pairs 101 22 22 101 145 265 0 153 Which of these ordered pairs of natural numbers are contained in P i and iii ii and iv i and iv iii and iv ,Partial Order,126 The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined ,Passage Reading,127 The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined ,Passage Reading,127 The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined ,Passage Reading,127 The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined ,Passage Reading,127 The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined ,Passage Reading,127 The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined ,Passage Reading,127 The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined ,Passage Reading,127 The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined ,Passage Reading,127 The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined ,Passage Reading,127 The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined ,Passage Reading,127 The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined ,Passage Reading,127 The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined ,Passage Reading,127 The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined ,Passage Reading,127 The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history Which of the following statements best reflects the author s opinion Nationalists are highly imaginative History is viewed through the filter of nationalism Our colonial past never happened Nationalism has to be both adequately and properly imagined ,Passage Reading,127 Round trip tickets to a tourist destination are eligible for a discount of 10 on the total fare In addition groups of 4 or more get a discount of 5 on the total fare If the one way single person fare is Rs 100 a group of 5 tourists purchasing round trip tickets will be charged Rs __________,Percentage,128 The Gross Domestic Product GDP in Rupees grew at 7 during 2012 2013 For international comparison the GDP is compared in US Dollars USD after conversion based on the market exchange rate During the period 2012 2013 the exchange rate for the USD increased from Rs 50 USD to Rs 60 USD India s GDP in USD during the period 2012 2013 increased by 5 decreased by 13 decreased by 20 decreased by 11 ,Percentage,128 Round trip tickets to a tourist destination are eligible for a discount of 10 on the total fare In addition groups of 4 or more get a discount of 5 on the total fare If the one way single person fare is Rs 100 a group of 5 tourists purchasing round trip tickets will be charged Rs __________,Percentage,128 Round trip tickets to a tourist destination are eligible for a discount of 10 on the total fare In addition groups of 4 or more get a discount of 5 on the total fare If the one way single person fare is Rs 100 a group of 5 tourists purchasing round trip tickets will be charged Rs __________,Percentage,128 Round trip tickets to a tourist destination are eligible for a discount of 10 on the total fare In addition groups of 4 or more get a discount of 5 on the total fare If the one way single person fare is Rs 100 a group of 5 tourists purchasing round trip tickets will be charged Rs __________,Percentage,128 The Gross Domestic Product GDP in Rupees grew at 7 during 2012 2013 For international comparison the GDP is compared in US Dollars USD after conversion based on the market exchange rate During the period 2012 2013 the exchange rate for the USD increased from Rs 50 USD to Rs 60 USD India s GDP in USD during the period 2012 2013 increased by 5 decreased by 13 decreased by 20 decreased by 11 ,Percentage,128 The Gross Domestic Product GDP in Rupees grew at 7 during 2012 2013 For international comparison the GDP is compared in US Dollars USD after conversion based on the market exchange rate During the period 2012 2013 the exchange rate for the USD increased from Rs 50 USD to Rs 60 USD India s GDP in USD during the period 2012 2013 increased by 5 decreased by 13 decreased by 20 decreased by 11 ,Percentage,128 The Gross Domestic Product GDP in Rupees grew at 7 during 2012 2013 For international comparison the GDP is compared in US Dollars USD after conversion based on the market exchange rate During the period 2012 2013 the exchange rate for the USD increased from Rs 50 USD to Rs 60 USD India s GDP in USD during the period 2012 2013 increased by 5 decreased by 13 decreased by 20 decreased by 11 ,Percentage,128 Round trip tickets to a tourist destination are eligible for a discount of 10 on the total fare In addition groups of 4 or more get a discount of 5 on the total fare If the one way single person fare is Rs 100 a group of 5 tourists purchasing round trip tickets will be charged Rs __________,Percentage,128 The Gross Domestic Product GDP in Rupees grew at 7 during 2012 2013 For international comparison the GDP is compared in US Dollars USD after conversion based on the market exchange rate During the period 2012 2013 the exchange rate for the USD increased from Rs 50 USD to Rs 60 USD India s GDP in USD during the period 2012 2013 increased by 5 decreased by 13 decreased by 20 decreased by 11 ,Percentage,128 The Gross Domestic Product GDP in Rupees grew at 7 during 2012 2013 For international comparison the GDP is compared in US Dollars USD after conversion based on the market exchange rate During the period 2012 2013 the exchange rate for the USD increased from Rs 50 USD to Rs 60 USD India s GDP in USD during the period 2012 2013 increased by 5 decreased by 13 decreased by 20 decreased by 11 ,Percentage,128 Round trip tickets to a tourist destination are eligible for a discount of 10 on the total fare In addition groups of 4 or more get a discount of 5 on the total fare If the one way single person fare is Rs 100 a group of 5 tourists purchasing round trip tickets will be charged Rs __________,Percentage,128 Round trip tickets to a tourist destination are eligible for a discount of 10 on the total fare In addition groups of 4 or more get a discount of 5 on the total fare If the one way single person fare is Rs 100 a group of 5 tourists purchasing round trip tickets will be charged Rs __________,Percentage,128 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12 ,Permutation Combination,129 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12 ,Permutation Combination,129 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12 ,Permutation Combination,129 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12 ,Permutation Combination,129 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12 ,Permutation Combination,129 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12 ,Permutation Combination,129 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12 ,Permutation Combination,129 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12 ,Permutation Combination,129 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12 ,Permutation Combination,129 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12 ,Permutation Combination,129 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12 ,Permutation Combination,129 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12 ,Permutation Combination,129 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12 ,Permutation Combination,129 The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit is 3 8 9 12 ,Permutation Combination,129 The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above ,Pigeonhole Principle,131 The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above ,Pigeonhole Principle,131 The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above ,Pigeonhole Principle,131 The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above ,Pigeonhole Principle,131 The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above ,Pigeonhole Principle,131 The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above ,Pigeonhole Principle,131 The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above ,Pigeonhole Principle,131 The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above ,Pigeonhole Principle,131 The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above ,Pigeonhole Principle,131 The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above ,Pigeonhole Principle,131 The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above ,Pigeonhole Principle,131 The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above ,Pigeonhole Principle,131 The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above ,Pigeonhole Principle,131 The rules for the University of Bombay five a side cricket competition specify that the members of each team must have birthdays in the same month What is the minimum number of mathematics students needed to be enrolled in the department to guarantee that they can raise a team of students 23 91 60 49 None of the above ,Pigeonhole Principle,131 Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM and p has a Poisson distribution with mean 3 What is the probability of observing fewer than 3 cars during any given minute in this interval A dfrac 8 2e 3 B dfrac 9 2e 3 C dfrac 17 2e 3 D dfrac 26 2e 3 ,Poisson Distribution,132 Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM and p has a Poisson distribution with mean 3 What is the probability of observing fewer than 3 cars during any given minute in this interval A dfrac 8 2e 3 B dfrac 9 2e 3 C dfrac 17 2e 3 D dfrac 26 2e 3 ,Poisson Distribution,132 In a multi user operating system on an average 20 requests are made to use a particular resource per hour The arrival of requests follows a Poisson distribution The probability that either one three or five requests are made in 45 minutes is given by 6 9 imes 10 6 imes e 20 1 02 imes 10 6 imes e 20 6 9 imes 10 3 imes e 20 1 02 imes 10 3 imes e 20 ,Poisson Distribution,132 Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM and p has a Poisson distribution with mean 3 What is the probability of observing fewer than 3 cars during any given minute in this interval A dfrac 8 2e 3 B dfrac 9 2e 3 C dfrac 17 2e 3 D dfrac 26 2e 3 ,Poisson Distribution,132 Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM and p has a Poisson distribution with mean 3 What is the probability of observing fewer than 3 cars during any given minute in this interval A dfrac 8 2e 3 B dfrac 9 2e 3 C dfrac 17 2e 3 D dfrac 26 2e 3 ,Poisson Distribution,132 In a multi user operating system on an average 20 requests are made to use a particular resource per hour The arrival of requests follows a Poisson distribution The probability that either one three or five requests are made in 45 minutes is given by 6 9 imes 10 6 imes e 20 1 02 imes 10 6 imes e 20 6 9 imes 10 3 imes e 20 1 02 imes 10 3 imes e 20 ,Poisson Distribution,132 In a multi user operating system on an average 20 requests are made to use a particular resource per hour The arrival of requests follows a Poisson distribution The probability that either one three or five requests are made in 45 minutes is given by 6 9 imes 10 6 imes e 20 1 02 imes 10 6 imes e 20 6 9 imes 10 3 imes e 20 1 02 imes 10 3 imes e 20 ,Poisson Distribution,132 If a random variable X has a Poisson distribution with mean 5 then the expectation E X 2 2 equals ___ ,Poisson Distribution,132 In a multi user operating system on an average 20 requests are made to use a particular resource per hour The arrival of requests follows a Poisson distribution The probability that either one three or five requests are made in 45 minutes is given by 6 9 imes 10 6 imes e 20 1 02 imes 10 6 imes e 20 6 9 imes 10 3 imes e 20 1 02 imes 10 3 imes e 20 ,Poisson Distribution,132 In a multi user operating system on an average 20 requests are made to use a particular resource per hour The arrival of requests follows a Poisson distribution The probability that either one three or five requests are made in 45 minutes is given by 6 9 imes 10 6 imes e 20 1 02 imes 10 6 imes e 20 6 9 imes 10 3 imes e 20 1 02 imes 10 3 imes e 20 ,Poisson Distribution,132 If a random variable X has a Poisson distribution with mean 5 then the expectation E X 2 2 equals ___ ,Poisson Distribution,132 Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM and p has a Poisson distribution with mean 3 What is the probability of observing fewer than 3 cars during any given minute in this interval A dfrac 8 2e 3 B dfrac 9 2e 3 C dfrac 17 2e 3 D dfrac 26 2e 3 ,Poisson Distribution,132 If the cube roots of unity are 1 omega and omega 2 then the roots of the following equation are x 1 3 8 0 1 1 2 omega 1 2 omega 2 1 1 2 omega 1 2 omega 2 1 1 2 omega 1 2 omega 2 1 1 2 omega 1 2 omega 2 ,Polynomials,133 A polynomial p x is such that p 0 5 p 1 4 p 2 9 and p 3 20 The minimum degree it should have is 1 2 3 4 ,Polynomials,133 If the cube roots of unity are 1 omega and omega 2 then the roots of the following equation are x 1 3 8 0 1 1 2 omega 1 2 omega 2 1 1 2 omega 1 2 omega 2 1 1 2 omega 1 2 omega 2 1 1 2 omega 1 2 omega 2 ,Polynomials,133 If f x 2x 7 3x 5 which of the following is a factor of f x left x 3 8 right x 1 2x 5 x 1 ,Polynomials,133 A polynomial p x satisfies the following p 1 p 3 p 5 1 p 2 p 4 1 The minimum degree of such a polynomial is 1 2 3 4 ,Polynomials,133 A polynomial p x satisfies the following p 1 p 3 p 5 1 p 2 p 4 1 The minimum degree of such a polynomial is 1 2 3 4 ,Polynomials,133 A polynomial p x satisfies the following p 1 p 3 p 5 1 p 2 p 4 1 The minimum degree of such a polynomial is 1 2 3 4 ,Polynomials,133 A polynomial p x satisfies the following p 1 p 3 p 5 1 p 2 p 4 1 The minimum degree of such a polynomial is 1 2 3 4 ,Polynomials,133 If the cube roots of unity are 1 omega and omega 2 then the roots of the following equation are x 1 3 8 0 1 1 2 omega 1 2 omega 2 1 1 2 omega 1 2 omega 2 1 1 2 omega 1 2 omega 2 1 1 2 omega 1 2 omega 2 ,Polynomials,133 If f x 2x 7 3x 5 which of the following is a factor of f x left x 3 8 right x 1 2x 5 x 1 ,Polynomials,133 A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______,Precedence Graph,134 A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______,Precedence Graph,134 A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______,Precedence Graph,134 A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______,Precedence Graph,134 A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______,Precedence Graph,134 A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______,Precedence Graph,134 A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______,Precedence Graph,134 A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______,Precedence Graph,134 A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______,Precedence Graph,134 A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______,Precedence Graph,134 A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______,Precedence Graph,134 A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______,Precedence Graph,134 A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______,Precedence Graph,134 A given set of processes can be implemented by using only parbegin parend statement if the precedence graph of these processes is ______,Precedence Graph,134 Let f x y z bar x bar y x xz be a switching function Which one of the following is valid bar y x is a prime implicant of f xz is a minterm of f xz is an implicant of f y is a prime implicant of f ,Prime Implicants,135 Which are the essential prime implicants of the following Boolean function f a b c a c ac b c a c and ac a c and b c a c only ac and bc ,Prime Implicants,135 Which are the essential prime implicants of the following Boolean function f a b c a c ac b c a c and ac a c and b c a c only ac and bc ,Prime Implicants,135 Which are the essential prime implicants of the following Boolean function f a b c a c ac b c a c and ac a c and b c a c only ac and bc ,Prime Implicants,135 Which are the essential prime implicants of the following Boolean function f a b c a c ac b c a c and ac a c and b c a c only ac and bc ,Prime Implicants,135 Which are the essential prime implicants of the following Boolean function f a b c a c ac b c a c and ac a c and b c a c only ac and bc ,Prime Implicants,135 Let f x y z bar x bar y x xz be a switching function Which one of the following is valid bar y x is a prime implicant of f xz is a minterm of f xz is an implicant of f y is a prime implicant of f ,Prime Implicants,135 Let f x y z bar x bar y x xz be a switching function Which one of the following is valid bar y x is a prime implicant of f xz is a minterm of f xz is an implicant of f y is a prime implicant of f ,Prime Implicants,135 Which are the essential prime implicants of the following Boolean function f a b c a c ac b c a c and ac a c and b c a c only ac and bc ,Prime Implicants,135 Which are the essential prime implicants of the following Boolean function f a b c a c ac b c a c and ac a c and b c a c only ac and bc ,Prime Implicants,135 Which are the essential prime implicants of the following Boolean function f a b c a c ac b c a c and ac a c and b c a c only ac and bc ,Prime Implicants,135 Let f x y z bar x bar y x xz be a switching function Which one of the following is valid bar y x is a prime implicant of f xz is a minterm of f xz is an implicant of f y is a prime implicant of f ,Prime Implicants,135 Which are the essential prime implicants of the following Boolean function f a b c a c ac b c a c and ac a c and b c a c only ac and bc ,Prime Implicants,135 A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order ,Priority Queue,136 A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order ,Priority Queue,136 A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order ,Priority Queue,136 A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order ,Priority Queue,136 A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order ,Priority Queue,136 A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order ,Priority Queue,136 A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order ,Priority Queue,136 A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order ,Priority Queue,136 A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order ,Priority Queue,136 A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order ,Priority Queue,136 A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order ,Priority Queue,136 A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order ,Priority Queue,136 A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order ,Priority Queue,136 A priority queue Q is used to implement a stack that stores characters PUSH C is implemented as INSERT Q C K where K is an appropriate integer key chosen by the implementation POP is implemented as DELETEMIN Q For a sequence of operations the keys chosen are in non increasing order non decreasing order strictly increasing order strictly decreasing order ,Priority Queue,136 The process state transition diagram in the below figure is representative of a batch operating system an operating system with a preemptive scheduler an operating system with a non preemptive scheduler a uni programmed operating system ,Process,138 The process state transition diagram in the below figure is representative of a batch operating system an operating system with a preemptive scheduler an operating system with a non preemptive scheduler a uni programmed operating system ,Process,138 The process state transition diagram of an operating system is as given below Which of the following must be FALSE about the above operating system It is a multiprogrammed operating system It uses preemptive scheduling It uses non preemptive scheduling It is a multi user operating system ,Process,138 The process state transition diagram of an operating system is as given below Which of the following must be FALSE about the above operating system It is a multiprogrammed operating system It uses preemptive scheduling It uses non preemptive scheduling It is a multi user operating system ,Process,138 Which combination of the following features will suffice to characterize an OS as a multi programmed OS More than one program may be loaded into main memory at the same time for execution If a program waits for certain events such as I O another program is immediately scheduled for execution If the execution of a program terminates another program is immediately scheduled for execution a a and b a and c a b and c ,Process,138 Which combination of the following features will suffice to characterize an OS as a multi programmed OS More than one program may be loaded into main memory at the same time for execution If a program waits for certain events such as I O another program is immediately scheduled for execution If the execution of a program terminates another program is immediately scheduled for execution a a and b a and c a b and c ,Process,138 Which combination of the following features will suffice to characterize an OS as a multi programmed OS More than one program may be loaded into main memory at the same time for execution If a program waits for certain events such as I O another program is immediately scheduled for execution If the execution of a program terminates another program is immediately scheduled for execution a a and b a and c a b and c ,Process,138 The process state transition diagram in the below figure is representative of a batch operating system an operating system with a preemptive scheduler an operating system with a non preemptive scheduler a uni programmed operating system ,Process,138 Which combination of the following features will suffice to characterize an OS as a multi programmed OS More than one program may be loaded into main memory at the same time for execution If a program waits for certain events such as I O another program is immediately scheduled for execution If the execution of a program terminates another program is immediately scheduled for execution a a and b a and c a b and c ,Process,138 The process state transition diagram in the below figure is representative of a batch operating system an operating system with a preemptive scheduler an operating system with a non preemptive scheduler a uni programmed operating system ,Process,138 The process state transition diagram in the below figure is representative of a batch operating system an operating system with a preemptive scheduler an operating system with a non preemptive scheduler a uni programmed operating system ,Process,138 The process state transition diagram in the below figure is representative of a batch operating system an operating system with a preemptive scheduler an operating system with a non preemptive scheduler a uni programmed operating system ,Process,138 Consider the following set of processes with the arrival times and the CPU burst times gives in milliseconds Process Arrival Time Burst Time P1 P2 P3 P4 0 1 2 4 5 3 3 1 What is the average turnaround time for these processes with the preemptive shortest remaining processing time first SRPT algorithm 5 50 5 75 6 00 6 25 ,Process Schedule,139 Four jobs to be executed on a single processor system arrive at time 0 in the order A B C D Their burst CPU time requirements are 4 1 8 1 time units respectively The completion time of A under round robin scheduling with time slice of one time unit is 10 4 8 9 ,Process Schedule,139 When the result of a computation depends on the speed of the processes involved there is said to be cycle stealing race condition a time lock a deadlock ,Process Synchronization,140 Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii ,Programming Constructs,141 Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii ,Programming Constructs,141 Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii ,Programming Constructs,141 Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii ,Programming Constructs,141 Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii ,Programming Constructs,141 Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii ,Programming Constructs,141 Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii ,Programming Constructs,141 Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii ,Programming Constructs,141 Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii ,Programming Constructs,141 Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii ,Programming Constructs,141 Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii ,Programming Constructs,141 Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii ,Programming Constructs,141 Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii ,Programming Constructs,141 Given the programming constructs assignment for loops where the loop parameter cannot be changed within the loop if then else forward go to arbitrary go to non recursive procedure call recursive procedure function call repeat loop which constructs will you not include in a programming language such that it should be possible to program the terminates i e halting function in the same programming language ii iii iv v vii viii vi vii viii iii vii viii ,Programming Constructs,141 Choose the best matching between the programming styles in Group 1 and their characteristics in Group 2 Group 1 Group 2 P Functional Q Logic R Object oriented S Imperative 1 Common based procedural 2 Imperative abstract data types 3 Side effect free declarative expression evaluations 4 Declarative clausal representation theorem proving P 2 Q 3 R 4 S 1 P 4 Q 3 R 2 S 1 P 3 Q 4 R 1 S 2 P 3 Q 4 R 2 S 1 ,Programming Paradigms,142 Choose the best matching between the programming styles in Group 1 and their characteristics in Group 2 Group 1 Group 2 P Functional Q Logic R Object oriented S Imperative 1 Common based procedural 2 Imperative abstract data types 3 Side effect free declarative expression evaluations 4 Declarative clausal representation theorem proving P 2 Q 3 R 4 S 1 P 4 Q 3 R 2 S 1 P 3 Q 4 R 1 S 2 P 3 Q 4 R 2 S 1 ,Programming Paradigms,142 Choose the best matching between the programming styles in Group 1 and their characteristics in Group 2 Group 1 Group 2 P Functional Q Logic R Object oriented S Imperative 1 Common based procedural 2 Imperative abstract data types 3 Side effect free declarative expression evaluations 4 Declarative clausal representation theorem proving P 2 Q 3 R 4 S 1 P 4 Q 3 R 2 S 1 P 3 Q 4 R 1 S 2 P 3 Q 4 R 2 S 1 ,Programming Paradigms,142 The goal of structured programming is to have well indented programs be able to infer the flow of control from the compiled code be able to infer the flow of control from the program text avoid the use of GOTO statements ,Programming Paradigms,142 The goal of structured programming is to have well indented programs be able to infer the flow of control from the compiled code be able to infer the flow of control from the program text avoid the use of GOTO statements ,Programming Paradigms,142 Choose the best matching between the programming styles in Group 1 and their characteristics in Group 2 Group 1 Group 2 P Functional Q Logic R Object oriented S Imperative 1 Common based procedural 2 Imperative abstract data types 3 Side effect free declarative expression evaluations 4 Declarative clausal representation theorem proving P 2 Q 3 R 4 S 1 P 4 Q 3 R 2 S 1 P 3 Q 4 R 1 S 2 P 3 Q 4 R 2 S 1 ,Programming Paradigms,142 Choose the best matching between the programming styles in Group 1 and their characteristics in Group 2 Group 1 Group 2 P Functional Q Logic R Object oriented S Imperative 1 Common based procedural 2 Imperative abstract data types 3 Side effect free declarative expression evaluations 4 Declarative clausal representation theorem proving P 2 Q 3 R 4 S 1 P 4 Q 3 R 2 S 1 P 3 Q 4 R 1 S 2 P 3 Q 4 R 2 S 1 ,Programming Paradigms,142 Choose the best matching between the programming styles in Group 1 and their characteristics in Group 2 Group 1 Group 2 P Functional Q Logic R Object oriented S Imperative 1 Common based procedural 2 Imperative abstract data types 3 Side effect free declarative expression evaluations 4 Declarative clausal representation theorem proving P 2 Q 3 R 4 S 1 P 4 Q 3 R 2 S 1 P 3 Q 4 R 1 S 2 P 3 Q 4 R 2 S 1 ,Programming Paradigms,142 The goal of structured programming is to have well indented programs be able to infer the flow of control from the compiled code be able to infer the flow of control from the program text avoid the use of GOTO statements ,Programming Paradigms,142 Choose the best matching between the programming styles in Group 1 and their characteristics in Group 2 Group 1 Group 2 P Functional Q Logic R Object oriented S Imperative 1 Common based procedural 2 Imperative abstract data types 3 Side effect free declarative expression evaluations 4 Declarative clausal representation theorem proving P 2 Q 3 R 4 S 1 P 4 Q 3 R 2 S 1 P 3 Q 4 R 1 S 2 P 3 Q 4 R 2 S 1 ,Programming Paradigms,142 The goal of structured programming is to have well indented programs be able to infer the flow of control from the compiled code be able to infer the flow of control from the program text avoid the use of GOTO statements ,Programming Paradigms,142 The goal of structured programming is to have well indented programs be able to infer the flow of control from the compiled code be able to infer the flow of control from the program text avoid the use of GOTO statements ,Programming Paradigms,142 The goal of structured programming is to have well indented programs be able to infer the flow of control from the compiled code be able to infer the flow of control from the program text avoid the use of GOTO statements ,Programming Paradigms,142 In a process the number of cycles to failure decreases exponentially with an increase in load At a load of 80 units it takes 100 cycles for failure When the load is halved it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02 ,Proportions,143 In a process the number of cycles to failure decreases exponentially with an increase in load At a load of 80 units it takes 100 cycles for failure When the load is halved it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02 ,Proportions,143 In a process the number of cycles to failure decreases exponentially with an increase in load At a load of 80 units it takes 100 cycles for failure When the load is halved it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02 ,Proportions,143 In a process the number of cycles to failure decreases exponentially with an increase in load At a load of 80 units it takes 100 cycles for failure When the load is halved it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02 ,Proportions,143 In a process the number of cycles to failure decreases exponentially with an increase in load At a load of 80 units it takes 100 cycles for failure When the load is halved it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02 ,Proportions,143 In a process the number of cycles to failure decreases exponentially with an increase in load At a load of 80 units it takes 100 cycles for failure When the load is halved it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02 ,Proportions,143 In a process the number of cycles to failure decreases exponentially with an increase in load At a load of 80 units it takes 100 cycles for failure When the load is halved it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02 ,Proportions,143 In a process the number of cycles to failure decreases exponentially with an increase in load At a load of 80 units it takes 100 cycles for failure When the load is halved it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02 ,Proportions,143 In a process the number of cycles to failure decreases exponentially with an increase in load At a load of 80 units it takes 100 cycles for failure When the load is halved it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02 ,Proportions,143 In a process the number of cycles to failure decreases exponentially with an increase in load At a load of 80 units it takes 100 cycles for failure When the load is halved it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02 ,Proportions,143 In a process the number of cycles to failure decreases exponentially with an increase in load At a load of 80 units it takes 100 cycles for failure When the load is halved it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02 ,Proportions,143 In a process the number of cycles to failure decreases exponentially with an increase in load At a load of 80 units it takes 100 cycles for failure When the load is halved it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02 ,Proportions,143 In a process the number of cycles to failure decreases exponentially with an increase in load At a load of 80 units it takes 100 cycles for failure When the load is halved it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02 ,Proportions,143 In a process the number of cycles to failure decreases exponentially with an increase in load At a load of 80 units it takes 100 cycles for failure When the load is halved it takes 10000 ext cycles for failure The load for which the failure will happen in 5000 ext cycles is _____________ 40 00 46 02 60 01 92 02 ,Proportions,143 If X then Y unless Z is represented by which of the following formulas in prepositional logic eg is negation land is conjunction and rightarrow is implication X land eg Z rightarrow Y X land Y rightarrow eg Z X rightarrow Y land eg Z X rightarrow Y land eg Z ,Propositional Logic,144 What is the converse of the following assertion I stay only if you go I stay if you go If I stay then you go If you do not go then I do not stay If I do not stay then you go ,Propositional Logic,144 Choose the correct option to fill 1 and 2 so that the program below prints an input string in reverse order Assume that the input string is terminated by a new line character void reverse void int c if 1 reverse 2 main printf Enter text printf reverse printf 1 is getchar u2019 setminus n u2019 2 is getchar c 1 is c getchar u2019 setminus n u2019 2 is getchar c 1 is c u2019 setminus n u2019 2 is putchar c 1 is c getchar u2019 setminus n u2019 2 is putchar c ,Pseudo Code,145 Choose the correct option to fill 1 and 2 so that the program below prints an input string in reverse order Assume that the input string is terminated by a new line character void reverse void int c if 1 reverse 2 main printf Enter text printf reverse printf 1 is getchar u2019 setminus n u2019 2 is getchar c 1 is c getchar u2019 setminus n u2019 2 is getchar c 1 is c u2019 setminus n u2019 2 is putchar c 1 is c getchar u2019 setminus n u2019 2 is putchar c ,Pseudo Code,145 Choose the correct option to fill 1 and 2 so that the program below prints an input string in reverse order Assume that the input string is terminated by a new line character void reverse void int c if 1 reverse 2 main printf Enter text printf reverse printf 1 is getchar u2019 setminus n u2019 2 is getchar c 1 is c getchar u2019 setminus n u2019 2 is getchar c 1 is c u2019 setminus n u2019 2 is putchar c 1 is c getchar u2019 setminus n u2019 2 is putchar c ,Pseudo Code,145 Choose the correct option to fill 1 and 2 so that the program below prints an input string in reverse order Assume that the input string is terminated by a new line character void reverse void int c if 1 reverse 2 main printf Enter text printf reverse printf 1 is getchar u2019 setminus n u2019 2 is getchar c 1 is c getchar u2019 setminus n u2019 2 is getchar c 1 is c u2019 setminus n u2019 2 is putchar c 1 is c getchar u2019 setminus n u2019 2 is putchar c ,Pseudo Code,145 Choose the correct option to fill 1 and 2 so that the program below prints an input string in reverse order Assume that the input string is terminated by a new line character void reverse void int c if 1 reverse 2 main printf Enter text printf reverse printf 1 is getchar u2019 setminus n u2019 2 is getchar c 1 is c getchar u2019 setminus n u2019 2 is getchar c 1 is c u2019 setminus n u2019 2 is putchar c 1 is c getchar u2019 setminus n u2019 2 is putchar c ,Pseudo Code,145 Choose the correct option to fill 1 and 2 so that the program below prints an input string in reverse order Assume that the input string is terminated by a new line character void reverse void int c if 1 reverse 2 main printf Enter text printf reverse printf 1 is getchar u2019 setminus n u2019 2 is getchar c 1 is c getchar u2019 setminus n u2019 2 is getchar c 1 is c u2019 setminus n u2019 2 is putchar c 1 is c getchar u2019 setminus n u2019 2 is putchar c ,Pseudo Code,145 Choose the correct option to fill 1 and 2 so that the program below prints an input string in reverse order Assume that the input string is terminated by a new line character void reverse void int c if 1 reverse 2 main printf Enter text printf reverse printf 1 is getchar u2019 setminus n u2019 2 is getchar c 1 is c getchar u2019 setminus n u2019 2 is getchar c 1 is c u2019 setminus n u2019 2 is putchar c 1 is c getchar u2019 setminus n u2019 2 is putchar c ,Pseudo Code,145 Choose the correct option to fill 1 and 2 so that the program below prints an input string in reverse order Assume that the input string is terminated by a new line character void reverse void int c if 1 reverse 2 main printf Enter text printf reverse printf 1 is getchar u2019 setminus n u2019 2 is getchar c 1 is c getchar u2019 setminus n u2019 2 is getchar c 1 is c u2019 setminus n u2019 2 is putchar c 1 is c getchar u2019 setminus n u2019 2 is putchar c ,Pseudo Code,145 Choose the correct option to fill 1 and 2 so that the program below prints an input string in reverse order Assume that the input string is terminated by a new line character void reverse void int c if 1 reverse 2 main printf Enter text printf reverse printf 1 is getchar u2019 setminus n u2019 2 is getchar c 1 is c getchar u2019 setminus n u2019 2 is getchar c 1 is c u2019 setminus n u2019 2 is putchar c 1 is c getchar u2019 setminus n u2019 2 is putchar c ,Pseudo Code,145 Choose the correct option to fill 1 and 2 so that the program below prints an input string in reverse order Assume that the input string is terminated by a new line character void reverse void int c if 1 reverse 2 main printf Enter text printf reverse printf 1 is getchar u2019 setminus n u2019 2 is getchar c 1 is c getchar u2019 setminus n u2019 2 is getchar c 1 is c u2019 setminus n u2019 2 is putchar c 1 is c getchar u2019 setminus n u2019 2 is putchar c ,Pseudo Code,145 Choose the correct option to fill 1 and 2 so that the program below prints an input string in reverse order Assume that the input string is terminated by a new line character void reverse void int c if 1 reverse 2 main printf Enter text printf reverse printf 1 is getchar u2019 setminus n u2019 2 is getchar c 1 is c getchar u2019 setminus n u2019 2 is getchar c 1 is c u2019 setminus n u2019 2 is putchar c 1 is c getchar u2019 setminus n u2019 2 is putchar c ,Pseudo Code,145 Choose the correct option to fill 1 and 2 so that the program below prints an input string in reverse order Assume that the input string is terminated by a new line character void reverse void int c if 1 reverse 2 main printf Enter text printf reverse printf 1 is getchar u2019 setminus n u2019 2 is getchar c 1 is c getchar u2019 setminus n u2019 2 is getchar c 1 is c u2019 setminus n u2019 2 is putchar c 1 is c getchar u2019 setminus n u2019 2 is putchar c ,Pseudo Code,145 Choose the correct option to fill 1 and 2 so that the program below prints an input string in reverse order Assume that the input string is terminated by a new line character void reverse void int c if 1 reverse 2 main printf Enter text printf reverse printf 1 is getchar u2019 setminus n u2019 2 is getchar c 1 is c getchar u2019 setminus n u2019 2 is getchar c 1 is c u2019 setminus n u2019 2 is putchar c 1 is c getchar u2019 setminus n u2019 2 is putchar c ,Pseudo Code,145 Choose the correct option to fill 1 and 2 so that the program below prints an input string in reverse order Assume that the input string is terminated by a new line character void reverse void int c if 1 reverse 2 main printf Enter text printf reverse printf 1 is getchar u2019 setminus n u2019 2 is getchar c 1 is c getchar u2019 setminus n u2019 2 is getchar c 1 is c u2019 setminus n u2019 2 is putchar c 1 is c getchar u2019 setminus n u2019 2 is putchar c ,Pseudo Code,145 A language L satisfies the Pumping Lemma for regular languages and also the Pumping Lemma for context free languages Which of the following statements about L is TRUE L is necessarily a regular language L is necessarily a context free language but not necessarily a regular language L is necessarily a non regular language None of the above ,Pumping Lemma,146 A language L satisfies the Pumping Lemma for regular languages and also the Pumping Lemma for context free languages Which of the following statements about L is TRUE L is necessarily a regular language L is necessarily a context free language but not necessarily a regular language L is necessarily a non regular language None of the above ,Pumping Lemma,146 A language L satisfies the Pumping Lemma for regular languages and also the Pumping Lemma for context free languages Which of the following statements about L is TRUE L is necessarily a regular language L is necessarily a context free language but not necessarily a regular language L is necessarily a non regular language None of the above ,Pumping Lemma,146 A language L satisfies the Pumping Lemma for regular languages and also the Pumping Lemma for context free languages Which of the following statements about L is TRUE L is necessarily a regular language L is necessarily a context free language but not necessarily a regular language L is necessarily a non regular language None of the above ,Pumping Lemma,146 A language L satisfies the Pumping Lemma for regular languages and also the Pumping Lemma for context free languages Which of the following statements about L is TRUE L is necessarily a regular language L is necessarily a context free language but not necessarily a regular language L is necessarily a non regular language None of the above ,Pumping Lemma,146 A language L satisfies the Pumping Lemma for regular languages and also the Pumping Lemma for context free languages Which of the following statements about L is TRUE L is necessarily a regular language L is necessarily a context free language but not necessarily a regular language L is necessarily a non regular language None of the above ,Pumping Lemma,146 A language L satisfies the Pumping Lemma for regular languages and also the Pumping Lemma for context free languages Which of the following statements about L is TRUE L is necessarily a regular language L is necessarily a context free language but not necessarily a regular language L is necessarily a non regular language None of the above ,Pumping Lemma,146 A language L satisfies the Pumping Lemma for regular languages and also the Pumping Lemma for context free languages Which of the following statements about L is TRUE L is necessarily a regular language L is necessarily a context free language but not necessarily a regular language L is necessarily a non regular language None of the above ,Pumping Lemma,146 A language L satisfies the Pumping Lemma for regular languages and also the Pumping Lemma for context free languages Which of the following statements about L is TRUE L is necessarily a regular language L is necessarily a context free language but not necessarily a regular language L is necessarily a non regular language None of the above ,Pumping Lemma,146 A language L satisfies the Pumping Lemma for regular languages and also the Pumping Lemma for context free languages Which of the following statements about L is TRUE L is necessarily a regular language L is necessarily a context free language but not necessarily a regular language L is necessarily a non regular language None of the above ,Pumping Lemma,146 A language L satisfies the Pumping Lemma for regular languages and also the Pumping Lemma for context free languages Which of the following statements about L is TRUE L is necessarily a regular language L is necessarily a context free language but not necessarily a regular language L is necessarily a non regular language None of the above ,Pumping Lemma,146 A language L satisfies the Pumping Lemma for regular languages and also the Pumping Lemma for context free languages Which of the following statements about L is TRUE L is necessarily a regular language L is necessarily a context free language but not necessarily a regular language L is necessarily a non regular language None of the above ,Pumping Lemma,146 A language L satisfies the Pumping Lemma for regular languages and also the Pumping Lemma for context free languages Which of the following statements about L is TRUE L is necessarily a regular language L is necessarily a context free language but not necessarily a regular language L is necessarily a non regular language None of the above ,Pumping Lemma,146 A language L satisfies the Pumping Lemma for regular languages and also the Pumping Lemma for context free languages Which of the following statements about L is TRUE L is necessarily a regular language L is necessarily a context free language but not necessarily a regular language L is necessarily a non regular language None of the above ,Pumping Lemma,146 Consider the NPDA left langle Q left q_ 0 q_ 1 q_ 2 right Sigma left 0 1 right Gamma left 0 1 perp right delta q_ 0 perp F left q_ 2 right right rangle where as per usual convention Q is the set of states Sigma is the input alphabet Gamma is the stack alphabet delta is the state transition function q_ 0 is the initial state perp is the initial stack symbol and F is the set of accepting states The state transition is as follows Which one of the following sequences must follow the string 101100 so that the overall string is accepted by the automaton 10110 10010 01010 01001 ,Pushdown Automata,147 Consider the NPDA left langle Q left q_ 0 q_ 1 q_ 2 right Sigma left 0 1 right Gamma left 0 1 perp right delta q_ 0 perp F left q_ 2 right right rangle where as per usual convention Q is the set of states Sigma is the input alphabet Gamma is the stack alphabet delta is the state transition function q_ 0 is the initial state perp is the initial stack symbol and F is the set of accepting states The state transition is as follows Which one of the following sequences must follow the string 101100 so that the overall string is accepted by the automaton 10110 10010 01010 01001 ,Pushdown Automata,147 Let P be a non deterministic push down automaton NPDA with exactly one state q and exactly one symbol Z in its stack alphabet State q is both the starting as well as the accepting state of the PDA The stack is initialized with one Z before the start of the operation of the PDA Let the input alphabet of the PDA be u03a3 Let L P be the language accepted by the PDA by reading a string and reaching its accepting state Let N P be the language accepted by the PDA by reading a string and emptying its stack Which of the following statements is TRUE L P is necessarily u03a3 but N P is not necessarily u03a3 N P is necessarily u03a3 but L P is not necessarily u03a3 Both L P and N P are necessarily u03a3 Neither L P nor N P are necessarily u03a3 ,Pushdown Automata,147 Let M K u03a3 u0413 u0394 s F be a pushdown automaton where K s f F f Sigma a b u0413 a and u0394 s a epsilon s a s b epsilon s a s a epsilon f epsilon f a a f epsilon f b a f epsilon Which one of the following strings is not a member of L M aaa aabab baaba bab ,Pushdown Automata,147 A push down automation pda is given in the following extended notation of finite state diagram The nodes denote the states while the edges denote the moves of the pda The edge labels are of the form d s s where d is the input symbol read and s s are the stack contents before and after the move For example the edge labeled 1 s 1 s denotes the move from state q_0 to q_0 in which the input symbol 1 is read and pushed to the stack Introduce two edges with appropriate labels in the above diagram so that the resulting pda accepts the language left x2x R mid x in left 0 1 right x R ext denotes reverse of x right by empty stack Describe a non deterministic pda with three states in the above notation that accept the language left 0 n 1 m mid n leq m leq 2n right by empty stack ,Pushdown Automata,147 The set of values of p for which the roots of the equation 3x 2 2x p p u20131 0 are of opposite sign is A u2013 u221e 0 B 0 1 C 1 u221e D 0 u221e ,Quadratic Equations,148 The roots of ax2 bx c 0 are real and positive a b and c are real Then ax2 b x c 0 has no roots 2 real roots 3 real roots 4 real roots ,Quadratic Equations,148 In a quadratic function the value of the product of the roots alpha beta is 4 Find the value of dfrac alpha n beta n alpha n beta n n 4 4 n 2 2n 1 4 n 1 ,Quadratic Equations,148 The set of values of p for which the roots of the equation 3x 2 2x p p u20131 0 are of opposite sign is A u2013 u221e 0 B 0 1 C 1 u221e D 0 u221e ,Quadratic Equations,148 In a quadratic function the value of the product of the roots alpha beta is 4 Find the value of dfrac alpha n beta n alpha n beta n n 4 4 n 2 2n 1 4 n 1 ,Quadratic Equations,148 The roots of ax2 bx c 0 are real and positive a b and c are real Then ax2 b x c 0 has no roots 2 real roots 3 real roots 4 real roots ,Quadratic Equations,148 The set of values of p for which the roots of the equation 3x 2 2x p p u20131 0 are of opposite sign is A u2013 u221e 0 B 0 1 C 1 u221e D 0 u221e ,Quadratic Equations,148 The set of values of p for which the roots of the equation 3x 2 2x p p u20131 0 are of opposite sign is A u2013 u221e 0 B 0 1 C 1 u221e D 0 u221e ,Quadratic Equations,148 The set of values of p for which the roots of the equation 3x 2 2x p p u20131 0 are of opposite sign is A u2013 u221e 0 B 0 1 C 1 u221e D 0 u221e ,Quadratic Equations,148 The roots of ax2 bx c 0 are real and positive a b and c are real Then ax2 b x c 0 has no roots 2 real roots 3 real roots 4 real roots ,Quadratic Equations,148 The set of values of p for which the roots of the equation 3x 2 2x p p u20131 0 are of opposite sign is A u2013 u221e 0 B 0 1 C 1 u221e D 0 u221e ,Quadratic Equations,148 The roots of ax2 bx c 0 are real and positive a b and c are real Then ax2 b x c 0 has no roots 2 real roots 3 real roots 4 real roots ,Quadratic Equations,148 What is the minimum number of stacks of size n required to implement a queue of size n One Two Three Four ,Queues,149 Suggest a data structure for representing a subset S of integers from 1 to n Following operations on the set S are to be performed in constant time independent of cardinality of S i MEMBER X Check whether X is in the set S or not ii FIND ONE S If S is not empty return one element of the set S any arbitrary element will do iii ADD X Add integer X to set S iv DELETE X Delete integer X from S Give pictorial examples of your data structure Give routines for these operations in an English like language You may assume that the data structure has been suitable initialized Clearly state your assumptions regarding initialization ,Queues,149 Let Q denote a queue containing sixteen numbers and S be an empty stack Head Q returns the element at the head of the queue Q without removing it from Q Similarly Top S returns the element at the top of S without removing it from S Consider the algorithm given below while Q is not Empty do if S is Empty OR Top S u2264 Head Q then x Dequeue Q Push S x else x Pop S Enqueue Q x end end The maximum possible number of iterations of the while loop in the algorithm is _______ ,Queues,149 Suggest a data structure for representing a subset S of integers from 1 to n Following operations on the set S are to be performed in constant time independent of cardinality of S i MEMBER X Check whether X is in the set S or not ii FIND ONE S If S is not empty return one element of the set S any arbitrary element will do iii ADD X Add integer X to set S iv DELETE X Delete integer X from S Give pictorial examples of your data structure Give routines for these operations in an English like language You may assume that the data structure has been suitable initialized Clearly state your assumptions regarding initialization ,Queues,149 A main memory unit with a capacity of 4 megabytes is built using 1M imes 1 bit DRAM chips Each DRAM chip has 1K rows of cells with 1K cells in each row The time taken for a single refresh operation is 100 nanoseconds The time required to perform one refresh operation on all the cells in the memory unit is 100 nanoseconds 100 imes 2 10 nanoseconds 100 imes 2 20 nanoseconds 3200 imes 2 20 nanosesonds ,Ram,150 A dynamic RAM has a memory cycle time of 64 nsec It has to be refreshed 100 times per msec and each refresh takes 100 nsec What percentage of the memory cycle time is used for refreshing 10 6 4 1 0 64 ,Ram,150 A dynamic RAM has a memory cycle time of 64 nsec It has to be refreshed 100 times per msec and each refresh takes 100 nsec What percentage of the memory cycle time is used for refreshing 10 6 4 1 0 64 ,Ram,150 A dynamic RAM has a memory cycle time of 64 nsec It has to be refreshed 100 times per msec and each refresh takes 100 nsec What percentage of the memory cycle time is used for refreshing 10 6 4 1 0 64 ,Ram,150 A main memory unit with a capacity of 4 megabytes is built using 1M imes 1 bit DRAM chips Each DRAM chip has 1K rows of cells with 1K cells in each row The time taken for a single refresh operation is 100 nanoseconds The time required to perform one refresh operation on all the cells in the memory unit is 100 nanoseconds 100 imes 2 10 nanoseconds 100 imes 2 20 nanoseconds 3200 imes 2 20 nanosesonds ,Ram,150 A dynamic RAM has a memory cycle time of 64 nsec It has to be refreshed 100 times per msec and each refresh takes 100 nsec What percentage of the memory cycle time is used for refreshing 10 6 4 1 0 64 ,Ram,150 A dynamic RAM has a memory cycle time of 64 nsec It has to be refreshed 100 times per msec and each refresh takes 100 nsec What percentage of the memory cycle time is used for refreshing 10 6 4 1 0 64 ,Ram,150 A dynamic RAM has a memory cycle time of 64 nsec It has to be refreshed 100 times per msec and each refresh takes 100 nsec What percentage of the memory cycle time is used for refreshing 10 6 4 1 0 64 ,Ram,150 A main memory unit with a capacity of 4 megabytes is built using 1M imes 1 bit DRAM chips Each DRAM chip has 1K rows of cells with 1K cells in each row The time taken for a single refresh operation is 100 nanoseconds The time required to perform one refresh operation on all the cells in the memory unit is 100 nanoseconds 100 imes 2 10 nanoseconds 100 imes 2 20 nanoseconds 3200 imes 2 20 nanosesonds ,Ram,150 A dynamic RAM has a memory cycle time of 64 nsec It has to be refreshed 100 times per msec and each refresh takes 100 nsec What percentage of the memory cycle time is used for refreshing 10 6 4 1 0 64 ,Ram,150 A main memory unit with a capacity of 4 megabytes is built using 1M imes 1 bit DRAM chips Each DRAM chip has 1K rows of cells with 1K cells in each row The time taken for a single refresh operation is 100 nanoseconds The time required to perform one refresh operation on all the cells in the memory unit is 100 nanoseconds 100 imes 2 10 nanoseconds 100 imes 2 20 nanoseconds 3200 imes 2 20 nanosesonds ,Ram,150 A dynamic RAM has a memory cycle time of 64 nsec It has to be refreshed 100 times per msec and each refresh takes 100 nsec What percentage of the memory cycle time is used for refreshing 10 6 4 1 0 64 ,Ram,150 A dynamic RAM has a memory cycle time of 64 nsec It has to be refreshed 100 times per msec and each refresh takes 100 nsec What percentage of the memory cycle time is used for refreshing 10 6 4 1 0 64 ,Ram,150 Consider a finite sequence of random values X x_1 x_2 dots x_n Let mu_x be the mean and sigma_x be he standard deviation of X Let another finite sequence Y of equal length be derived from this as y_i a x_i b where a and b are positive constants Let mu_y be the mean and sigma_y be the standard deviation of this sequence Which one of the following statements is INCORRECT A Index position of mode of X in X is the same as the index position of mode of Y in Y B Index position of median of X in X is the same as the index position of median of Y in Y C mu_y a mu_x b D sigma_y a sigma_x b ,Random Variable,151 Let f x be the continuous probability density function of a random variable x the probability that a lt x leq b is f b a f b f a int limits_a b f x dx int limits_a b xf x dx ,Random Variable,151 If the difference between the expectation of the square of a random variable left E left X 2 right right and he square of the expectation of the random variable left E left X right right 2 is denoted by R then A R 0 B R lt 0 C R geq 0 D R gt 0 ,Random Variable,151 For any discrete random variable X with probability mass function P X j p_j p_j geq 0 j in 0 dots N and Sigma_ j 0 N p_j 1 define the polynomial function g_x z Sigma_ j 0 N p_j z j For a certain discrete random variable Y there exists a scalar beta in 0 1 such that g_y z 1 beta beta z N The expectation of Y is N beta 1 beta N beta N 1 beta Not expressible in terms of N and beta alone ,Random Variable,151 For any discrete random variable X with probability mass function P X j p_j p_j geq 0 j in 0 dots N and Sigma_ j 0 N p_j 1 define the polynomial function g_x z Sigma_ j 0 N p_j z j For a certain discrete random variable Y there exists a scalar beta in 0 1 such that g_y z 1 beta beta z N The expectation of Y is N beta 1 beta N beta N 1 beta Not expressible in terms of N and beta alone ,Random Variable,151 Consider a finite sequence of random values X x_1 x_2 dots x_n Let mu_x be the mean and sigma_x be he standard deviation of X Let another finite sequence Y of equal length be derived from this as y_i a x_i b where a and b are positive constants Let mu_y be the mean and sigma_y be the standard deviation of this sequence Which one of the following statements is INCORRECT A Index position of mode of X in X is the same as the index position of mode of Y in Y B Index position of median of X in X is the same as the index position of median of Y in Y C mu_y a mu_x b D sigma_y a sigma_x b ,Random Variable,151 Let f x be the continuous probability density function of a random variable x the probability that a lt x leq b is f b a f b f a int limits_a b f x dx int limits_a b xf x dx ,Random Variable,151 Consider a random variable X that takes values 1 and u22121 with probability 0 5 each The values of the cumulative distribution function F x at x u22121 and 1 are A 0 and 0 5 B 0 and 1 C 0 5 and 1 D 0 25 and 0 75,Random Variable,151 Nobody knows yet if P NP Consider the language L defined as follows L begin cases 0 1 amp ext if P NP phi amp otherwise end cases Which of the following statements is true L is recursive L is recursively enumerable but not recursive L is not recursively enumerable Whether L is recursively enumerable or not will be known after we find out if P NP ,Recursive And Recursively Enumerable Languages,152 Choose the correct alternatives More than one may be correct Recursive languages are A proper superset of context free languages Always recognizable by pushdown automata Also called type emptyset languages Recognizable by Turing machines ,Recursive And Recursively Enumerable Languages,152 If L and bar L are recursively enumerable then L is regular context free context sensitive recursive ,Recursive And Recursively Enumerable Languages,152 Let A leq_m B denotes that language A is mapping reducible also known as many to one reducible to language B Which one of the following is FALSE If A leq_m B and B is recursive then A is recursive If A leq_m B and A is undecidable then B is undecidable If A leq_m B and B is recursively enumerable then A is recursively enumerable If A leq_m B and B is not recursively enumerable then A is not recursively enumerable ,Recursive And Recursively Enumerable Languages,152 Choose the correct alternatives More than one may be correct Recursive languages are A proper superset of context free languages Always recognizable by pushdown automata Also called type emptyset languages Recognizable by Turing machines ,Recursive And Recursively Enumerable Languages,152 Let R a b c and S d e f be two relations in which d is the foreign key of S that refers to the primary key of R Consider the following four operations R and S Insert into R Insert into S Delete from R Delete from S Which of the following can cause violation of the referential integrity constraint above Both I and IV Both II and III All of these None of these ,Referential Integrity,153 Consider the following tables T1 and T2 T1 P Q 2 2 3 8 7 3 5 8 6 9 8 5 9 8 T2 R S 2 2 8 3 3 2 9 7 5 7 7 2 In table T1 P is the primary key and Q is the foreign key referencing R in table T2 with on delete cascade and on update cascade In table T2 R is the primary key and S is the foreign key referencing P in table T1 with on delete set NULL and on update cascade In order to delete record langle 3 8 rangle from the table T1 the number of additional records that need to be deleted from table T1 is _______ ,Referential Integrity,153 Consider the following tables T1 and T2 T1 P Q 2 2 3 8 7 3 5 8 6 9 8 5 9 8 T2 R S 2 2 8 3 3 2 9 7 5 7 7 2 In table T1 P is the primary key and Q is the foreign key referencing R in table T2 with on delete cascade and on update cascade In table T2 R is the primary key and S is the foreign key referencing P in table T1 with on delete set NULL and on update cascade In order to delete record langle 3 8 rangle from the table T1 the number of additional records that need to be deleted from table T1 is _______ ,Referential Integrity,153 Let R a b c and S d e f be two relations in which d is the foreign key of S that refers to the primary key of R Consider the following four operations R and S Insert into R Insert into S Delete from R Delete from S Which of the following can cause violation of the referential integrity constraint above Both I and IV Both II and III All of these None of these ,Referential Integrity,153 The following table has two attributes A and C where A is the primary key and C is the foreign key referencing A with on delete cascade A C 2 4 3 4 4 3 5 2 7 2 9 5 6 4 The set of all tuples that must be additionally deleted to preserve referential integrity when the tuple 2 4 is deleted is 3 4 and 6 4 5 2 and 7 2 5 2 7 2 and 9 5 3 4 4 3 and 6 4 ,Referential Integrity,153 Consider the following tables T1 and T2 T1 P Q 2 2 3 8 7 3 5 8 6 9 8 5 9 8 T2 R S 2 2 8 3 3 2 9 7 5 7 7 2 In table T1 P is the primary key and Q is the foreign key referencing R in table T2 with on delete cascade and on update cascade In table T2 R is the primary key and S is the foreign key referencing P in table T1 with on delete set NULL and on update cascade In order to delete record langle 3 8 rangle from the table T1 the number of additional records that need to be deleted from table T1 is _______ ,Referential Integrity,153 Let R a b c and S d e f be two relations in which d is the foreign key of S that refers to the primary key of R Consider the following four operations R and S Insert into R Insert into S Delete from R Delete from S Which of the following can cause violation of the referential integrity constraint above Both I and IV Both II and III All of these None of these ,Referential Integrity,153 Consider the following tables T1 and T2 T1 P Q 2 2 3 8 7 3 5 8 6 9 8 5 9 8 T2 R S 2 2 8 3 3 2 9 7 5 7 7 2 In table T1 P is the primary key and Q is the foreign key referencing R in table T2 with on delete cascade and on update cascade In table T2 R is the primary key and S is the foreign key referencing P in table T1 with on delete set NULL and on update cascade In order to delete record langle 3 8 rangle from the table T1 the number of additional records that need to be deleted from table T1 is _______ ,Referential Integrity,153 Let R a b c and S d e f be two relations in which d is the foreign key of S that refers to the primary key of R Consider the following four operations R and S Insert into R Insert into S Delete from R Delete from S Which of the following can cause violation of the referential integrity constraint above Both I and IV Both II and III All of these None of these ,Referential Integrity,153 The following table has two attributes A and C where A is the primary key and C is the foreign key referencing A with on delete cascade A C 2 4 3 4 4 3 5 2 7 2 9 5 6 4 The set of all tuples that must be additionally deleted to preserve referential integrity when the tuple 2 4 is deleted is 3 4 and 6 4 5 2 and 7 2 5 2 7 2 and 9 5 3 4 4 3 and 6 4 ,Referential Integrity,153 Consider the following tables T1 and T2 T1 P Q 2 2 3 8 7 3 5 8 6 9 8 5 9 8 T2 R S 2 2 8 3 3 2 9 7 5 7 7 2 In table T1 P is the primary key and Q is the foreign key referencing R in table T2 with on delete cascade and on update cascade In table T2 R is the primary key and S is the foreign key referencing P in table T1 with on delete set NULL and on update cascade In order to delete record langle 3 8 rangle from the table T1 the number of additional records that need to be deleted from table T1 is _______ ,Referential Integrity,153 Consider the following tables T1 and T2 T1 P Q 2 2 3 8 7 3 5 8 6 9 8 5 9 8 T2 R S 2 2 8 3 3 2 9 7 5 7 7 2 In table T1 P is the primary key and Q is the foreign key referencing R in table T2 with on delete cascade and on update cascade In table T2 R is the primary key and S is the foreign key referencing P in table T1 with on delete set NULL and on update cascade In order to delete record langle 3 8 rangle from the table T1 the number of additional records that need to be deleted from table T1 is _______ ,Referential Integrity,153 If the regular set A is represented by A 01 1 and the regular set B is represented by B left left 01 right 1 right which of the following is true a A subset B b B subset A c A and B are incomparable d A B ,Regular Expressions,154 Give a regular expression for the set of binary strings where every 0 is immediately followed by exactly k 1 s and preceded by at least k 1 u2019s k is a fixed integer ,Regular Expressions,154 The string 1101 does not belong to the set represented by a 110 0 1 b 1 0 1 101 c 10 01 00 11 d 00 11 0 ,Regular Expressions,154 Consider the alphabet Sigma 0 1 the null empty string lambda and the set of strings X_0 X_1 ext and X_2 generated by the corresponding non terminals of a regular grammar X_0 X_1 ext and X_2 are related as follows X_0 1 X_1 X_1 0 X_1 1 X_2 X_2 0 X_1 lambda Which one of the following choices precisely represents the strings in X_0 10 0 10 1 10 0 10 1 1 0 10 1 10 0 10 1 110 0 10 1 ,Regular Grammar,155 Consider the alphabet Sigma 0 1 the null empty string lambda and the set of strings X_0 X_1 ext and X_2 generated by the corresponding non terminals of a regular grammar X_0 X_1 ext and X_2 are related as follows X_0 1 X_1 X_1 0 X_1 1 X_2 X_2 0 X_1 lambda Which one of the following choices precisely represents the strings in X_0 10 0 10 1 10 0 10 1 1 0 10 1 10 0 10 1 110 0 10 1 ,Regular Grammar,155 Consider the alphabet Sigma 0 1 the null empty string lambda and the set of strings X_0 X_1 ext and X_2 generated by the corresponding non terminals of a regular grammar X_0 X_1 ext and X_2 are related as follows X_0 1 X_1 X_1 0 X_1 1 X_2 X_2 0 X_1 lambda Which one of the following choices precisely represents the strings in X_0 10 0 10 1 10 0 10 1 1 0 10 1 10 0 10 1 110 0 10 1 ,Regular Grammar,155 Consider the regular grammar below S u2192 bS aA u03f5 A u2192 aS bA The Myhill Nerode equivalence classes for the language generated by the grammar are w u220a a b a w is even and w u220a a b a w is odd w u220a a b a w is even and w u220a a b b w is odd w u220a a b a w b w and w u220a a b a w u2260 b w u03f5 wa w u220a a b and wb w u220a a b ,Regular Grammar,155 Consider the alphabet Sigma 0 1 the null empty string lambda and the set of strings X_0 X_1 ext and X_2 generated by the corresponding non terminals of a regular grammar X_0 X_1 ext and X_2 are related as follows X_0 1 X_1 X_1 0 X_1 1 X_2 X_2 0 X_1 lambda Which one of the following choices precisely represents the strings in X_0 10 0 10 1 10 0 10 1 1 0 10 1 10 0 10 1 110 0 10 1 ,Regular Grammar,155 Is the language generated by the grammer G regular If so give a regular expression for it else prove otherwise G S rightarrow aB B rightarrow bC C rightarrow xB C rightarrow c ,Regular Grammar,155 Is the language generated by the grammer G regular If so give a regular expression for it else prove otherwise G S rightarrow aB B rightarrow bC C rightarrow xB C rightarrow c ,Regular Grammar,155 Consider the alphabet Sigma 0 1 the null empty string lambda and the set of strings X_0 X_1 ext and X_2 generated by the corresponding non terminals of a regular grammar X_0 X_1 ext and X_2 are related as follows X_0 1 X_1 X_1 0 X_1 1 X_2 X_2 0 X_1 lambda Which one of the following choices precisely represents the strings in X_0 10 0 10 1 10 0 10 1 1 0 10 1 10 0 10 1 110 0 10 1 ,Regular Grammar,155 Consider the alphabet Sigma 0 1 the null empty string lambda and the set of strings X_0 X_1 ext and X_2 generated by the corresponding non terminals of a regular grammar X_0 X_1 ext and X_2 are related as follows X_0 1 X_1 X_1 0 X_1 1 X_2 X_2 0 X_1 lambda Which one of the following choices precisely represents the strings in X_0 10 0 10 1 10 0 10 1 1 0 10 1 10 0 10 1 110 0 10 1 ,Regular Grammar,155 Consider the regular grammar below S u2192 bS aA u03f5 A u2192 aS bA The Myhill Nerode equivalence classes for the language generated by the grammar are w u220a a b a w is even and w u220a a b a w is odd w u220a a b a w is even and w u220a a b b w is odd w u220a a b a w b w and w u220a a b a w u2260 b w u03f5 wa w u220a a b and wb w u220a a b ,Regular Grammar,155 Is the language generated by the grammer G regular If so give a regular expression for it else prove otherwise G S rightarrow aB B rightarrow bC C rightarrow xB C rightarrow c ,Regular Grammar,155 Is the language generated by the grammer G regular If so give a regular expression for it else prove otherwise G S rightarrow aB B rightarrow bC C rightarrow xB C rightarrow c ,Regular Grammar,155 The number of edges in a regular graph of degree d and n vertices is ____________,Regular Graph,156 The number of edges in a regular graph of degree d and n vertices is ____________,Regular Graph,156 The number of edges in a regular graph of degree d and n vertices is ____________,Regular Graph,156 The number of edges in a regular graph of degree d and n vertices is ____________,Regular Graph,156 The number of edges in a regular graph of degree d and n vertices is ____________,Regular Graph,156 The number of edges in a regular graph of degree d and n vertices is ____________,Regular Graph,156 The number of edges in a regular graph of degree d and n vertices is ____________,Regular Graph,156 The number of edges in a regular graph of degree d and n vertices is ____________,Regular Graph,156 The number of edges in a regular graph of degree d and n vertices is ____________,Regular Graph,156 The number of edges in a regular graph of degree d and n vertices is ____________,Regular Graph,156 The number of edges in a regular graph of degree d and n vertices is ____________,Regular Graph,156 The number of edges in a regular graph of degree d and n vertices is ____________,Regular Graph,156 The number of edges in a regular graph of degree d and n vertices is ____________,Regular Graph,156 The number of edges in a regular graph of degree d and n vertices is ____________,Regular Graph,156 Consider the following two statements S_1 left 0 2n mid n geq 1 right is a regular language S_2 left 0 m1 n0 m n mid m geq 1 ext and n geq 1 right is a regular language Which of the following statement is correct Only S_1 is correct Only S_2 is correct Both S_1 and S_2 are correct None of S_1 and S_2 is correct ,Regular Languages,157 Let L subseteq Sigma where Sigma left a b right Which of the following is true a L left x mid x ext has an equal number of a ext s and b ext s right is regular b L left a nb n mid n geq 1 right is regular c L left x mid x ext has more number of a ext s than b ext s right is regular d L left a mb n mid m geq 1 n geq 1 right is regular,Regular Languages,157 Let L be a regular language Consider the constructions on L below ext repeat L ww mid w in L ext prefix L u mid exists v uv in L ext suffix L v mid exists u uv in L ext half L u mid exists v v u ext and uv in L Which of the constructions could lead to a non regular language Both I and IV Only 1 Only IV Both II and III Which choice of L is best suited to support your answer above a b u03f5 a ab bab ab a nb n mid n geq 0 ,Regular Languages,157 Let L subseteq Sigma where Sigma left a b right Which of the following is true a L left x mid x ext has an equal number of a ext s and b ext s right is regular b L left a nb n mid n geq 1 right is regular c L left x mid x ext has more number of a ext s than b ext s right is regular d L left a mb n mid m geq 1 n geq 1 right is regular,Regular Languages,157 Student school id sch roll no sname saddress School school id sch name sch address sch phone Enrolment school id sch roll no erollno examname ExamResult erollno examname marks Consider the following tuple relational calculus query t u2203 E u220a Enrolment t E school id x x u220a Enrolment x school id t u2203 B u220a ExamResult B erollno x erollno B examname x examname B marks gt 35 x x u220a Enrolment x school id t 100 gt 35 If a student needs to score more than 35 marks to pass an exam what does the query return The empty set schools with more than 35 of its students enrolled in some exam or the other schools with a pass percentage above 35 over all exams taken together schools with a pass percentage above 35 over each exam ,Relational Calculus,159 The relational algebra expression equivalent to the following tuple calculus expression left t mid t in r land left t A 10 land t B 20 right right is sigma_ A 10 lor B 20 r sigma_ A 10 r cup sigma_ B 20 r sigma_ A 10 r cap sigma_ B 20 r sigma_ A 10 r sigma_ B 20 r ,Relational Calculus,159 The following relations are used to store data about students courses enrollment of students in courses and teachers of courses Attributes for primary key in each relation are marked by u2018 u2019 Students rollno sname saddr courses cno cname enroll rollno cno grade each tno tname cao cno is course number cname is course name tno is teacher number tname is teacher name sname is student name etc Write a SQL query for retrieving roll number and name of students who got A grade in at least one course taught by teacher names Ramesh for the above relational database ,Relational Calculus,159 Let R and S be relational schemes such that R a b c and S c Now consider the following queries on the database pi_ R S r pi_ R S left pi_ R S r imes s pi_ R S S r right left t mid t in pi_ R S r wedge forall u in s left exists v in r left u v S wedge t v left R S right right right right left t mid t in pi_ R S r wedge forall v in r left exists u in s left u v S wedge t v left R S right right right right Select R a R b From R S Where R c S c Which of the above queries are equivalent 1 and 2 1 and 3 2 and 4 3 and 4 ,Relational Calculus,159 Consider the relation employee name sex supervisorName with name as the key supervisorName gives the name of the supervisor of the employee under consideration What does the following Tuple Relational Calculus query produce left e name mid employee e wedge left forall x right left eg employee left x right vee x supervisorName eq e name vee x sex male right right Names of employees with a male supervisor Names of employees with no immediate male subordinates Names of employees with no immediate female subordinates Names of employees with a female supervisor ,Relational Calculus,159 Let R_1 left underline A B C right and R_2 left underline D E right be two relation schema where the primary keys are shown underlined and let C be a foreign key in R_1 referring to R_2 Suppose there is no violation of the above referential integrity constraint in the corresponding relation instances r_1 and r_2 Which of the following relational algebra expressions would necessarily produce an empty relation Pi_D r_2 Pi_C r_1 Pi_C r_1 Pi_D r_2 Pi_D left r_1 bowtie_ C eq D r_2 right Pi_C left r_1 bowtie_ C D r_2 right ,Relational Calculus,159 Let R_1 left underline A B C right and R_2 left underline D E right be two relation schema where the primary keys are shown underlined and let C be a foreign key in R_1 referring to R_2 Suppose there is no violation of the above referential integrity constraint in the corresponding relation instances r_1 and r_2 Which of the following relational algebra expressions would necessarily produce an empty relation Pi_D r_2 Pi_C r_1 Pi_C r_1 Pi_D r_2 Pi_D left r_1 bowtie_ C eq D r_2 right Pi_C left r_1 bowtie_ C D r_2 right ,Relational Calculus,159 Consider the relation employee name sex supervisorName with name as the key supervisorName gives the name of the supervisor of the employee under consideration What does the following Tuple Relational Calculus query produce left e name mid employee e wedge left forall x right left eg employee left x right vee x supervisorName eq e name vee x sex male right right Names of employees with a male supervisor Names of employees with no immediate male subordinates Names of employees with no immediate female subordinates Names of employees with a female supervisor ,Relational Calculus,159 In a certain operating system deadlock prevention is attemped using the following scheme Each process is assigned a unique timestamp and is restarted with the same timestamp if killed Let Ph be the process holding a resource R Pr be a process requesting for the same resource R and T Ph and T Pr be their timestamps respectively The decision to wait or preempt one of the processes is based on the following algorithm if T Pr lt T Ph then kill Pr else wait Which one of the following is TRUE The scheme is deadlock free but not starvation free The scheme is not deadlock free but starvation free The scheme is neither deadlock free nor starvation free The scheme is both deadlock free and starvation free ,Resource Allocation,161 The amount of ROM needed to implement a 4 bit multiplier is 64 bits 128 bits 1 Kbits 2 Kbits ,Rom,162 The amount of ROM needed to implement a 4 bit multiplier is 64 bits 128 bits 1 Kbits 2 Kbits ,Rom,162 What is the minimum size of ROM required to store the complete truth table of an 8 bit imes 8 bit multiplier 32 K imes 16 bits 64 K imes 16 bits 16 K imes 32 bits 64 K x imes 32 bits ,Rom,162 The amount of ROM needed to implement a 4 bit multiplier is 64 bits 128 bits 1 Kbits 2 Kbits ,Rom,162 A ROM is used to store the table for multiplication of two 8 bit unsigned integers The size of ROM required is 256 u2a2f 16 64 K u2a2f 8 4 K u2a2f 16 64 K u2a2f 16 ,Rom,162 What is the minimum size of ROM required to store the complete truth table of an 8 bit imes 8 bit multiplier 32 K imes 16 bits 64 K imes 16 bits 16 K imes 32 bits 64 K x imes 32 bits ,Rom,162 The amount of ROM needed to implement a 4 bit multiplier is 64 bits 128 bits 1 Kbits 2 Kbits ,Rom,162 What is the minimum size of ROM required to store the complete truth table of an 8 bit imes 8 bit multiplier 32 K imes 16 bits 64 K imes 16 bits 16 K imes 32 bits 64 K x imes 32 bits ,Rom,162 The amount of ROM needed to implement a 4 bit multiplier is 64 bits 128 bits 1 Kbits 2 Kbits ,Rom,162 The amount of ROM needed to implement a 4 bit multiplier is 64 bits 128 bits 1 Kbits 2 Kbits ,Rom,162 The amount of ROM needed to implement a 4 bit multiplier is 64 bits 128 bits 1 Kbits 2 Kbits ,Rom,162 The amount of ROM needed to implement a 4 bit multiplier is 64 bits 128 bits 1 Kbits 2 Kbits ,Rom,162 In a network of LANs connected by bridges packets are sent from one LAN to another through intermediate bridges Since more than one path may exist between two LANs packets may have to be routed through multiple bridges Why is the spanning tree algorithm used for bridge routing For shortest path routing between LANs For avoiding loops in the routing paths For fault tolerance For minimizing collisions ,Routing,163 In a network of LANs connected by bridges packets are sent from one LAN to another through intermediate bridges Since more than one path may exist between two LANs packets may have to be routed through multiple bridges Why is the spanning tree algorithm used for bridge routing For shortest path routing between LANs For avoiding loops in the routing paths For fault tolerance For minimizing collisions ,Routing,163 Consider a simple graph with unit edge costs Each node in the graph represents a router Each node maintains a routing table indicating the next hop router to be used to relay a packet to its destination and the cost of the path to the destination through that router Initially the routing table is empty The routing table is synchronously updated as follows In each updation interval three tasks are performed A node determines whether its neighbours in the graph are accessible If so it sets the tentative cost to each accessible neighbour as 1 Otherwise the cost is set to u221e From each accessible neighbour it gets the costs to relay to other nodes via that neighbour as the next hop Each node updates its routing table based on the information received in the previous two steps by choosing the minimum cost For the graph given above possible routing tables for various nodes after they have stabilized are shown in the following options Identify the correct table Table for node A A B B 1 C C 1 D B 3 E C 3 F C 4 Table for node C A A 1 B B 1 C D D 1 E E 1 F E 3 Table for node B A A 1 B C C 1 D D 1 E C 2 F D 2 Table for node D A B 3 B B 1 C C 1 D E E 1 F F 1 ,Routing,163 Consider the following statements about the routing protocols Routing Information Protocol RIP and Oprn Shortest Path First OSPF in an IPv4 network RIP uses distance vector routing RIP packets are sent using UDP OSPF packets are sent using TCP OSPF operation is based on link state routing Which of the above statements are CORRECT I and IV only I II and III only I II and IV only II III and IV only ,Routing,163 Consider a simple graph with unit edge costs Each node in the graph represents a router Each node maintains a routing table indicating the next hop router to be used to relay a packet to its destination and the cost of the path to the destination through that router Initially the routing table is empty The routing table is synchronously updated as follows In each updation interval three tasks are performed A node determines whether its neighbours in the graph are accessible If so it sets the tentative cost to each accessible neighbour as 1 Otherwise the cost is set to u221e From each accessible neighbour it gets the costs to relay to other nodes via that neighbour as the next hop Each node updates its routing table based on the information received in the previous two steps by choosing the minimum cost Continuing from the earlier problem suppose at some time t when the costs have stabilized node A goes down The cost from node F to node A at time t 100 is gt 100 but finite infty 3 gt 3 and leq 100 ,Routing,163 A group of 15 routers are interconnected in a centralized complete binary tree with a router at each tree node Router i communicates with router j by sending a message to the root of the tree The root then sends the message back down to router j The mean number of hops per message assuming all possible router pairs are equally likely is 3 4 26 4 53 5 26 ,Routing,163 Consider the following statements about the routing protocols Routing Information Protocol RIP and Oprn Shortest Path First OSPF in an IPv4 network RIP uses distance vector routing RIP packets are sent using UDP OSPF packets are sent using TCP OSPF operation is based on link state routing Which of the above statements are CORRECT I and IV only I II and III only I II and IV only II III and IV only ,Routing,163 Consider the following statements about the routing protocols Routing Information Protocol RIP and Oprn Shortest Path First OSPF in an IPv4 network RIP uses distance vector routing RIP packets are sent using UDP OSPF packets are sent using TCP OSPF operation is based on link state routing Which of the above statements are CORRECT I and IV only I II and III only I II and IV only II III and IV only ,Routing,163 In a RSA cryptosystem a participant A uses two prime numbers p 13 and q 17 to generate here public and private keys If the public key of A is 35 then the private key of A is __________ ,Rsa Security Networks,164 In a RSA cryptosystem a participant A uses two prime numbers p 13 and q 17 to generate here public and private keys If the public key of A is 35 then the private key of A is __________ ,Rsa Security Networks,164 In a RSA cryptosystem a participant A uses two prime numbers p 13 and q 17 to generate here public and private keys If the public key of A is 35 then the private key of A is __________ ,Rsa Security Networks,164 In a RSA cryptosystem a participant A uses two prime numbers p 13 and q 17 to generate here public and private keys If the public key of A is 35 then the private key of A is __________ ,Rsa Security Networks,164 In a RSA cryptosystem a participant A uses two prime numbers p 13 and q 17 to generate here public and private keys If the public key of A is 35 then the private key of A is __________ ,Rsa Security Networks,164 In a RSA cryptosystem a participant A uses two prime numbers p 13 and q 17 to generate here public and private keys If the public key of A is 35 then the private key of A is __________ ,Rsa Security Networks,164 In a RSA cryptosystem a participant A uses two prime numbers p 13 and q 17 to generate here public and private keys If the public key of A is 35 then the private key of A is __________ ,Rsa Security Networks,164 In a RSA cryptosystem a participant A uses two prime numbers p 13 and q 17 to generate here public and private keys If the public key of A is 35 then the private key of A is __________ ,Rsa Security Networks,164 In a RSA cryptosystem a participant A uses two prime numbers p 13 and q 17 to generate here public and private keys If the public key of A is 35 then the private key of A is __________ ,Rsa Security Networks,164 In a RSA cryptosystem a participant A uses two prime numbers p 13 and q 17 to generate here public and private keys If the public key of A is 35 then the private key of A is __________ ,Rsa Security Networks,164 In a RSA cryptosystem a participant A uses two prime numbers p 13 and q 17 to generate here public and private keys If the public key of A is 35 then the private key of A is __________ ,Rsa Security Networks,164 In a RSA cryptosystem a participant A uses two prime numbers p 13 and q 17 to generate here public and private keys If the public key of A is 35 then the private key of A is __________ ,Rsa Security Networks,164 In a RSA cryptosystem a participant A uses two prime numbers p 13 and q 17 to generate here public and private keys If the public key of A is 35 then the private key of A is __________ ,Rsa Security Networks,164 In a RSA cryptosystem a participant A uses two prime numbers p 13 and q 17 to generate here public and private keys If the public key of A is 35 then the private key of A is __________ ,Rsa Security Networks,164 Consider a database that has the relation schemas EMP EmpId EmpName DeptId and DEPT DeptName DeptId Note that the DeptId can be permitted to be NULL in the relation EMP Consider the following queries on the database expressed in tuple relational calculus t exists u in EMP t EmpName u EmpName wedge forall v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId v DeptId Which of the above queries are safe I and II only I and III only II and III only I II and III ,Safe Query,165 Consider a database that has the relation schemas EMP EmpId EmpName DeptId and DEPT DeptName DeptId Note that the DeptId can be permitted to be NULL in the relation EMP Consider the following queries on the database expressed in tuple relational calculus t exists u in EMP t EmpName u EmpName wedge forall v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId v DeptId Which of the above queries are safe I and II only I and III only II and III only I II and III ,Safe Query,165 Consider a database that has the relation schemas EMP EmpId EmpName DeptId and DEPT DeptName DeptId Note that the DeptId can be permitted to be NULL in the relation EMP Consider the following queries on the database expressed in tuple relational calculus t exists u in EMP t EmpName u EmpName wedge forall v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId v DeptId Which of the above queries are safe I and II only I and III only II and III only I II and III ,Safe Query,165 Consider a database that has the relation schemas EMP EmpId EmpName DeptId and DEPT DeptName DeptId Note that the DeptId can be permitted to be NULL in the relation EMP Consider the following queries on the database expressed in tuple relational calculus t exists u in EMP t EmpName u EmpName wedge forall v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId v DeptId Which of the above queries are safe I and II only I and III only II and III only I II and III ,Safe Query,165 Consider a database that has the relation schemas EMP EmpId EmpName DeptId and DEPT DeptName DeptId Note that the DeptId can be permitted to be NULL in the relation EMP Consider the following queries on the database expressed in tuple relational calculus t exists u in EMP t EmpName u EmpName wedge forall v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId v DeptId Which of the above queries are safe I and II only I and III only II and III only I II and III ,Safe Query,165 Consider a database that has the relation schemas EMP EmpId EmpName DeptId and DEPT DeptName DeptId Note that the DeptId can be permitted to be NULL in the relation EMP Consider the following queries on the database expressed in tuple relational calculus t exists u in EMP t EmpName u EmpName wedge forall v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId v DeptId Which of the above queries are safe I and II only I and III only II and III only I II and III ,Safe Query,165 Consider a database that has the relation schemas EMP EmpId EmpName DeptId and DEPT DeptName DeptId Note that the DeptId can be permitted to be NULL in the relation EMP Consider the following queries on the database expressed in tuple relational calculus t exists u in EMP t EmpName u EmpName wedge forall v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId v DeptId Which of the above queries are safe I and II only I and III only II and III only I II and III ,Safe Query,165 Consider a database that has the relation schemas EMP EmpId EmpName DeptId and DEPT DeptName DeptId Note that the DeptId can be permitted to be NULL in the relation EMP Consider the following queries on the database expressed in tuple relational calculus t exists u in EMP t EmpName u EmpName wedge forall v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId v DeptId Which of the above queries are safe I and II only I and III only II and III only I II and III ,Safe Query,165 Consider a database that has the relation schemas EMP EmpId EmpName DeptId and DEPT DeptName DeptId Note that the DeptId can be permitted to be NULL in the relation EMP Consider the following queries on the database expressed in tuple relational calculus t exists u in EMP t EmpName u EmpName wedge forall v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId v DeptId Which of the above queries are safe I and II only I and III only II and III only I II and III ,Safe Query,165 Consider a database that has the relation schemas EMP EmpId EmpName DeptId and DEPT DeptName DeptId Note that the DeptId can be permitted to be NULL in the relation EMP Consider the following queries on the database expressed in tuple relational calculus t exists u in EMP t EmpName u EmpName wedge forall v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId v DeptId Which of the above queries are safe I and II only I and III only II and III only I II and III ,Safe Query,165 Consider a database that has the relation schemas EMP EmpId EmpName DeptId and DEPT DeptName DeptId Note that the DeptId can be permitted to be NULL in the relation EMP Consider the following queries on the database expressed in tuple relational calculus t exists u in EMP t EmpName u EmpName wedge forall v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId v DeptId Which of the above queries are safe I and II only I and III only II and III only I II and III ,Safe Query,165 Consider a database that has the relation schemas EMP EmpId EmpName DeptId and DEPT DeptName DeptId Note that the DeptId can be permitted to be NULL in the relation EMP Consider the following queries on the database expressed in tuple relational calculus t exists u in EMP t EmpName u EmpName wedge forall v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId v DeptId Which of the above queries are safe I and II only I and III only II and III only I II and III ,Safe Query,165 Consider a database that has the relation schemas EMP EmpId EmpName DeptId and DEPT DeptName DeptId Note that the DeptId can be permitted to be NULL in the relation EMP Consider the following queries on the database expressed in tuple relational calculus t exists u in EMP t EmpName u EmpName wedge forall v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId v DeptId Which of the above queries are safe I and II only I and III only II and III only I II and III ,Safe Query,165 Consider a database that has the relation schemas EMP EmpId EmpName DeptId and DEPT DeptName DeptId Note that the DeptId can be permitted to be NULL in the relation EMP Consider the following queries on the database expressed in tuple relational calculus t exists u in EMP t EmpName u EmpName wedge forall v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId eq v DeptId t exists u in EMP t EmpName u EmpName wedge exists v in DEPT t DeptId v DeptId Which of the above queries are safe I and II only I and III only II and III only I II and III ,Safe Query,165 Consider a 128 imes 10 3 bits second satellite communication link with one way propagation delay of 150 milliseconds Selective retransmission repeat protocol is used on this link to send data with a frame size of 1 kilobyte Neglect the transmission time of acknowledgement The minimum number of bits required for the sequence number field to achieve 100 utilization is ________ ,Selective Repeat,166 Consider a 128 imes 10 3 bits second satellite communication link with one way propagation delay of 150 milliseconds Selective retransmission repeat protocol is used on this link to send data with a frame size of 1 kilobyte Neglect the transmission time of acknowledgement The minimum number of bits required for the sequence number field to achieve 100 utilization is ________ ,Selective Repeat,166 Consider a 128 imes 10 3 bits second satellite communication link with one way propagation delay of 150 milliseconds Selective retransmission repeat protocol is used on this link to send data with a frame size of 1 kilobyte Neglect the transmission time of acknowledgement The minimum number of bits required for the sequence number field to achieve 100 utilization is ________ ,Selective Repeat,166 Consider a 128 imes 10 3 bits second satellite communication link with one way propagation delay of 150 milliseconds Selective retransmission repeat protocol is used on this link to send data with a frame size of 1 kilobyte Neglect the transmission time of acknowledgement The minimum number of bits required for the sequence number field to achieve 100 utilization is ________ ,Selective Repeat,166 Consider a 128 imes 10 3 bits second satellite communication link with one way propagation delay of 150 milliseconds Selective retransmission repeat protocol is used on this link to send data with a frame size of 1 kilobyte Neglect the transmission time of acknowledgement The minimum number of bits required for the sequence number field to achieve 100 utilization is ________ ,Selective Repeat,166 Consider a 128 imes 10 3 bits second satellite communication link with one way propagation delay of 150 milliseconds Selective retransmission repeat protocol is used on this link to send data with a frame size of 1 kilobyte Neglect the transmission time of acknowledgement The minimum number of bits required for the sequence number field to achieve 100 utilization is ________ ,Selective Repeat,166 Consider a 128 imes 10 3 bits second satellite communication link with one way propagation delay of 150 milliseconds Selective retransmission repeat protocol is used on this link to send data with a frame size of 1 kilobyte Neglect the transmission time of acknowledgement The minimum number of bits required for the sequence number field to achieve 100 utilization is ________ ,Selective Repeat,166 Consider a 128 imes 10 3 bits second satellite communication link with one way propagation delay of 150 milliseconds Selective retransmission repeat protocol is used on this link to send data with a frame size of 1 kilobyte Neglect the transmission time of acknowledgement The minimum number of bits required for the sequence number field to achieve 100 utilization is ________ ,Selective Repeat,166 Consider a 128 imes 10 3 bits second satellite communication link with one way propagation delay of 150 milliseconds Selective retransmission repeat protocol is used on this link to send data with a frame size of 1 kilobyte Neglect the transmission time of acknowledgement The minimum number of bits required for the sequence number field to achieve 100 utilization is ________ ,Selective Repeat,166 Consider a 128 imes 10 3 bits second satellite communication link with one way propagation delay of 150 milliseconds Selective retransmission repeat protocol is used on this link to send data with a frame size of 1 kilobyte Neglect the transmission time of acknowledgement The minimum number of bits required for the sequence number field to achieve 100 utilization is ________ ,Selective Repeat,166 Consider a 128 imes 10 3 bits second satellite communication link with one way propagation delay of 150 milliseconds Selective retransmission repeat protocol is used on this link to send data with a frame size of 1 kilobyte Neglect the transmission time of acknowledgement The minimum number of bits required for the sequence number field to achieve 100 utilization is ________ ,Selective Repeat,166 Consider a 128 imes 10 3 bits second satellite communication link with one way propagation delay of 150 milliseconds Selective retransmission repeat protocol is used on this link to send data with a frame size of 1 kilobyte Neglect the transmission time of acknowledgement The minimum number of bits required for the sequence number field to achieve 100 utilization is ________ ,Selective Repeat,166 Consider a 128 imes 10 3 bits second satellite communication link with one way propagation delay of 150 milliseconds Selective retransmission repeat protocol is used on this link to send data with a frame size of 1 kilobyte Neglect the transmission time of acknowledgement The minimum number of bits required for the sequence number field to achieve 100 utilization is ________ ,Selective Repeat,166 Consider a 128 imes 10 3 bits second satellite communication link with one way propagation delay of 150 milliseconds Selective retransmission repeat protocol is used on this link to send data with a frame size of 1 kilobyte Neglect the transmission time of acknowledgement The minimum number of bits required for the sequence number field to achieve 100 utilization is ________ ,Selective Repeat,166 Consider the blocked set semaphore where the signaling process awakens any one of the suspended process i e Wait S If S gt 0 then S leftarrow S 1 else suspend the execution of this process Signal S If there are processes that have been suspended on semaphore S then wake any one of them else S leftarrow S 1 Consider the following solution of mutual exclusion problem using blocked set semaphores s 1 cobegin P 1 P 2 P N coend Where the task body P i is begin while true do begin lt non critical section gt Wait S lt critical section gt Signal S end end Here N is the number of concurrent processors Which of the following is true The program fails to achieve mutual exclusion of critical regions The program achieves mutual exclusion but starvation freedom is ensured only for N leq 2 The program does not ensure mutual exclusion if N geq 3 The program achieves mutual exclusion but allows starvation for any N geq 2 The program achieves mutual exclusion and starvation freedom for any N geq 1 ,Semaphore,167 The P and V operations on counting semaphores where s is a counting semaphore are defined as follows P s s s 1 If s lt 0 then wait V s s s 1 If s lt 0 then wake up process waiting on s Assume that P_b and V_b the wait and signal operations on binary semaphores are provided Two binary semaphores x_b and y_b are used to implement the semaphore operations P s and V s as follows P s P_b x_b ext s s 1 ext if s lt 0 ext V_b x_b ext P_b y_b ext else V_b x_b V s P_b x_b ext s s 1 ext if s lt 0 V_b y_b ext V_b x_b The initial values of x_b and y_b are respectively 0 and 0 0 and 1 1 and 0 1 and 1 ,Semaphore,167 Consider a non negative counting semaphore S The operation P S decrements S and V S increments S During an execution 20 P S operations and 12 V S operations are issued in some order The largest initial value of S for which at least one P S operation will remain blocked is _______,Semaphore,167 Fill in the blanks Semaphore operations are atomic because they are implemented within the OS _________ ,Semaphore,167 Choose the correct alternatives more than one may be correct and write the corresponding letters only At a particular time of computation the value of a counting semaphore is 7 Then 20 P operations and 15 V operations were completed on this semaphore The resulting value of the semaphore is 42 2 7 12 ,Semaphore,167 The wait and signal operations of a monitor are implemented using semaphores as follows In the following x is a condition variable mutex is a semaphore initialized to 1 x_sem is a semaphore initialized to 0 x_count is the number of processes waiting on semaphore x_sem initially 0 next is a semaphore initialized to 0 next_count is the number of processes waiting on semaphore next initially 0 The body of each procedure that is visible outside the monitor is replaced with the following P mutex body of procedure if next_count gt 0 V next else V mutex Each occurrence of x wait is replaced with the following x_count x_count 1 if next_count gt 0 V next else V mutex E1 x_count x_count 1 Each occurrence of x signal is replaced with the following if x_count gt 0 next_count next_count 1 E2 P next next_count next_count 1 For correct implementation of the monitor statements E1 and E2 are respectively P x_sem V next V next P x_sem P next V x_sem P x_sem V x_sem ,Semaphore,167 The P and V operations on counting semaphores where s is a counting semaphore are defined as follows P s s s 1 If s lt 0 then wait V s s s 1 If s lt 0 then wake up process waiting on s Assume that P_b and V_b the wait and signal operations on binary semaphores are provided Two binary semaphores x_b and y_b are used to implement the semaphore operations P s and V s as follows P s P_b x_b ext s s 1 ext if s lt 0 ext V_b x_b ext P_b y_b ext else V_b x_b V s P_b x_b ext s s 1 ext if s lt 0 V_b y_b ext V_b x_b The initial values of x_b and y_b are respectively 0 and 0 0 and 1 1 and 0 1 and 1 ,Semaphore,167 The P and V operations on counting semaphores where s is a counting semaphore are defined as follows P s s s 1 If s lt 0 then wait V s s s 1 If s lt 0 then wake up process waiting on s Assume that P_b and V_b the wait and signal operations on binary semaphores are provided Two binary semaphores x_b and y_b are used to implement the semaphore operations P s and V s as follows P s P_b x_b ext s s 1 ext if s lt 0 ext V_b x_b ext P_b y_b ext else V_b x_b V s P_b x_b ext s s 1 ext if s lt 0 V_b y_b ext V_b x_b The initial values of x_b and y_b are respectively 0 and 0 0 and 1 1 and 0 1 and 1 ,Semaphore,167 Consider a non negative counting semaphore S The operation P S decrements S and V S increments S During an execution 20 P S operations and 12 V S operations are issued in some order The largest initial value of S for which at least one P S operation will remain blocked is _______,Semaphore,167 In serial communication employing 8 data bits a parity bit and 2 stop bits the minimum band rate required to sustain a transfer rate of 300 characters per second is 2400 band 19200 band 4800 band 1200 band ,Serial Communication,168 How many bytes of data can be sent in 15 seconds over a serial link with baud rate of 9600 in asynchronous mode with odd parity and two stop bits in the frame 10 000 bytes 12 000 bytes 15 000 bytes 27 000 bytes ,Serial Communication,168 How many bytes of data can be sent in 15 seconds over a serial link with baud rate of 9600 in asynchronous mode with odd parity and two stop bits in the frame 10 000 bytes 12 000 bytes 15 000 bytes 27 000 bytes ,Serial Communication,168 How many bytes of data can be sent in 15 seconds over a serial link with baud rate of 9600 in asynchronous mode with odd parity and two stop bits in the frame 10 000 bytes 12 000 bytes 15 000 bytes 27 000 bytes ,Serial Communication,168 In serial communication employing 8 data bits a parity bit and 2 stop bits the minimum band rate required to sustain a transfer rate of 300 characters per second is 2400 band 19200 band 4800 band 1200 band ,Serial Communication,168 How many bytes of data can be sent in 15 seconds over a serial link with baud rate of 9600 in asynchronous mode with odd parity and two stop bits in the frame 10 000 bytes 12 000 bytes 15 000 bytes 27 000 bytes ,Serial Communication,168 How many bytes of data can be sent in 15 seconds over a serial link with baud rate of 9600 in asynchronous mode with odd parity and two stop bits in the frame 10 000 bytes 12 000 bytes 15 000 bytes 27 000 bytes ,Serial Communication,168 How many bytes of data can be sent in 15 seconds over a serial link with baud rate of 9600 in asynchronous mode with odd parity and two stop bits in the frame 10 000 bytes 12 000 bytes 15 000 bytes 27 000 bytes ,Serial Communication,168 In serial communication employing 8 data bits a parity bit and 2 stop bits the minimum band rate required to sustain a transfer rate of 300 characters per second is 2400 band 19200 band 4800 band 1200 band ,Serial Communication,168 How many bytes of data can be sent in 15 seconds over a serial link with baud rate of 9600 in asynchronous mode with odd parity and two stop bits in the frame 10 000 bytes 12 000 bytes 15 000 bytes 27 000 bytes ,Serial Communication,168 How many bytes of data can be sent in 15 seconds over a serial link with baud rate of 9600 in asynchronous mode with odd parity and two stop bits in the frame 10 000 bytes 12 000 bytes 15 000 bytes 27 000 bytes ,Serial Communication,168 How many bytes of data can be sent in 15 seconds over a serial link with baud rate of 9600 in asynchronous mode with odd parity and two stop bits in the frame 10 000 bytes 12 000 bytes 15 000 bytes 27 000 bytes ,Serial Communication,168 In serial communication employing 8 data bits a parity bit and 2 stop bits the minimum band rate required to sustain a transfer rate of 300 characters per second is 2400 band 19200 band 4800 band 1200 band ,Serial Communication,168 Let S be an infinite set and S_1 dots S_n be sets such that S_1 cup S_2 cup dots cup S_n S Then at least one of the set S_i is a finite set not more than one of the set S_i can be finite at least one of the sets S_i is an infinite not more than one of the sets S_i can be infinite None of the above ,Sets,169 The below figure shows four D type flip flops connnected as a shift register using an XOR gate The initial state and three subsequent states for three clock pulses are also given State Q_ A Q_ B Q_ C Q_ D Initial 1 1 1 1 After the first clock 0 1 1 1 After the second clock 0 0 1 1 After the third clock 0 0 0 1 The state Q_ A Q_ B Q_ C Q_ D after the fourth clock pulse is 0000 1111 1001 1000 ,Shift Registers,170 The below figure shows four D type flip flops connnected as a shift register using an XOR gate The initial state and three subsequent states for three clock pulses are also given State Q_ A Q_ B Q_ C Q_ D Initial 1 1 1 1 After the first clock 0 1 1 1 After the second clock 0 0 1 1 After the third clock 0 0 0 1 The state Q_ A Q_ B Q_ C Q_ D after the fourth clock pulse is 0000 1111 1001 1000 ,Shift Registers,170 The below figure shows four D type flip flops connnected as a shift register using an XOR gate The initial state and three subsequent states for three clock pulses are also given State Q_ A Q_ B Q_ C Q_ D Initial 1 1 1 1 After the first clock 0 1 1 1 After the second clock 0 0 1 1 After the third clock 0 0 0 1 The state Q_ A Q_ B Q_ C Q_ D after the fourth clock pulse is 0000 1111 1001 1000 ,Shift Registers,170 The below figure shows four D type flip flops connnected as a shift register using an XOR gate The initial state and three subsequent states for three clock pulses are also given State Q_ A Q_ B Q_ C Q_ D Initial 1 1 1 1 After the first clock 0 1 1 1 After the second clock 0 0 1 1 After the third clock 0 0 0 1 The state Q_ A Q_ B Q_ C Q_ D after the fourth clock pulse is 0000 1111 1001 1000 ,Shift Registers,170 The below figure shows four D type flip flops connnected as a shift register using an XOR gate The initial state and three subsequent states for three clock pulses are also given State Q_ A Q_ B Q_ C Q_ D Initial 1 1 1 1 After the first clock 0 1 1 1 After the second clock 0 0 1 1 After the third clock 0 0 0 1 The state Q_ A Q_ B Q_ C Q_ D after the fourth clock pulse is 0000 1111 1001 1000 ,Shift Registers,170 The below figure shows four D type flip flops connnected as a shift register using an XOR gate The initial state and three subsequent states for three clock pulses are also given State Q_ A Q_ B Q_ C Q_ D Initial 1 1 1 1 After the first clock 0 1 1 1 After the second clock 0 0 1 1 After the third clock 0 0 0 1 The state Q_ A Q_ B Q_ C Q_ D after the fourth clock pulse is 0000 1111 1001 1000 ,Shift Registers,170 The below figure shows four D type flip flops connnected as a shift register using an XOR gate The initial state and three subsequent states for three clock pulses are also given State Q_ A Q_ B Q_ C Q_ D Initial 1 1 1 1 After the first clock 0 1 1 1 After the second clock 0 0 1 1 After the third clock 0 0 0 1 The state Q_ A Q_ B Q_ C Q_ D after the fourth clock pulse is 0000 1111 1001 1000 ,Shift Registers,170 The below figure shows four D type flip flops connnected as a shift register using an XOR gate The initial state and three subsequent states for three clock pulses are also given State Q_ A Q_ B Q_ C Q_ D Initial 1 1 1 1 After the first clock 0 1 1 1 After the second clock 0 0 1 1 After the third clock 0 0 0 1 The state Q_ A Q_ B Q_ C Q_ D after the fourth clock pulse is 0000 1111 1001 1000 ,Shift Registers,170 The below figure shows four D type flip flops connnected as a shift register using an XOR gate The initial state and three subsequent states for three clock pulses are also given State Q_ A Q_ B Q_ C Q_ D Initial 1 1 1 1 After the first clock 0 1 1 1 After the second clock 0 0 1 1 After the third clock 0 0 0 1 The state Q_ A Q_ B Q_ C Q_ D after the fourth clock pulse is 0000 1111 1001 1000 ,Shift Registers,170 The below figure shows four D type flip flops connnected as a shift register using an XOR gate The initial state and three subsequent states for three clock pulses are also given State Q_ A Q_ B Q_ C Q_ D Initial 1 1 1 1 After the first clock 0 1 1 1 After the second clock 0 0 1 1 After the third clock 0 0 0 1 The state Q_ A Q_ B Q_ C Q_ D after the fourth clock pulse is 0000 1111 1001 1000 ,Shift Registers,170 The below figure shows four D type flip flops connnected as a shift register using an XOR gate The initial state and three subsequent states for three clock pulses are also given State Q_ A Q_ B Q_ C Q_ D Initial 1 1 1 1 After the first clock 0 1 1 1 After the second clock 0 0 1 1 After the third clock 0 0 0 1 The state Q_ A Q_ B Q_ C Q_ D after the fourth clock pulse is 0000 1111 1001 1000 ,Shift Registers,170 The below figure shows four D type flip flops connnected as a shift register using an XOR gate The initial state and three subsequent states for three clock pulses are also given State Q_ A Q_ B Q_ C Q_ D Initial 1 1 1 1 After the first clock 0 1 1 1 After the second clock 0 0 1 1 After the third clock 0 0 0 1 The state Q_ A Q_ B Q_ C Q_ D after the fourth clock pulse is 0000 1111 1001 1000 ,Shift Registers,170 The below figure shows four D type flip flops connnected as a shift register using an XOR gate The initial state and three subsequent states for three clock pulses are also given State Q_ A Q_ B Q_ C Q_ D Initial 1 1 1 1 After the first clock 0 1 1 1 After the second clock 0 0 1 1 After the third clock 0 0 0 1 The state Q_ A Q_ B Q_ C Q_ D after the fourth clock pulse is 0000 1111 1001 1000 ,Shift Registers,170 The below figure shows four D type flip flops connnected as a shift register using an XOR gate The initial state and three subsequent states for three clock pulses are also given State Q_ A Q_ B Q_ C Q_ D Initial 1 1 1 1 After the first clock 0 1 1 1 After the second clock 0 0 1 1 After the third clock 0 0 0 1 The state Q_ A Q_ B Q_ C Q_ D after the fourth clock pulse is 0000 1111 1001 1000 ,Shift Registers,170 The maximum window size for data transmission using the selective reject protocol with n ext bit frame sequence numbers is 2 n 2 n 1 2 n 1 2 n 2 ,Sliding Window,171 A client process P needs to make a TCP connection to a server process S Consider the following situation the server process S executes a ext socket a ext bind and a ext listen system call in that order following which it is preempted Subsequently the client process P executes a ext socket system call followed by ext connect system call to connect to the server process S The server process has not executed any ext accept system call Which one of the following events could take place ext connect system call returns successfully ext connect system call blocks ext connect system call returns an error ext connect system call results in a core dump ,Sockets,172 Identify the correct order in which a server process must invoke the function calls accept bind listen and recv according to UNIX socket API listen accept bind recv bind listen accept recv bind accept listen recv accept listen bind recv ,Sockets,172 Identify the correct order in which a server process must invoke the function calls accept bind listen and recv according to UNIX socket API listen accept bind recv bind listen accept recv bind accept listen recv accept listen bind recv ,Sockets,172 A client process P needs to make a TCP connection to a server process S Consider the following situation the server process S executes a ext socket a ext bind and a ext listen system call in that order following which it is preempted Subsequently the client process P executes a ext socket system call followed by ext connect system call to connect to the server process S The server process has not executed any ext accept system call Which one of the following events could take place ext connect system call returns successfully ext connect system call blocks ext connect system call returns an error ext connect system call results in a core dump ,Sockets,172 Identify the correct order in which a server process must invoke the function calls accept bind listen and recv according to UNIX socket API listen accept bind recv bind listen accept recv bind accept listen recv accept listen bind recv ,Sockets,172 Identify the correct order in which a server process must invoke the function calls accept bind listen and recv according to UNIX socket API listen accept bind recv bind listen accept recv bind accept listen recv accept listen bind recv ,Sockets,172 A client process P needs to make a TCP connection to a server process S Consider the following situation the server process S executes a ext socket a ext bind and a ext listen system call in that order following which it is preempted Subsequently the client process P executes a ext socket system call followed by ext connect system call to connect to the server process S The server process has not executed any ext accept system call Which one of the following events could take place ext connect system call returns successfully ext connect system call blocks ext connect system call returns an error ext connect system call results in a core dump ,Sockets,172 A client process P needs to make a TCP connection to a server process S Consider the following situation the server process S executes a ext socket a ext bind and a ext listen system call in that order following which it is preempted Subsequently the client process P executes a ext socket system call followed by ext connect system call to connect to the server process S The server process has not executed any ext accept system call Which one of the following events could take place ext connect system call returns successfully ext connect system call blocks ext connect system call returns an error ext connect system call results in a core dump ,Sockets,172 Identify the correct order in which a server process must invoke the function calls accept bind listen and recv according to UNIX socket API listen accept bind recv bind listen accept recv bind accept listen recv accept listen bind recv ,Sockets,172 Identify the correct order in which a server process must invoke the function calls accept bind listen and recv according to UNIX socket API listen accept bind recv bind listen accept recv bind accept listen recv accept listen bind recv ,Sockets,172 Identify the correct order in which a server process must invoke the function calls accept bind listen and recv according to UNIX socket API listen accept bind recv bind listen accept recv bind accept listen recv accept listen bind recv ,Sockets,172 A client process P needs to make a TCP connection to a server process S Consider the following situation the server process S executes a ext socket a ext bind and a ext listen system call in that order following which it is preempted Subsequently the client process P executes a ext socket system call followed by ext connect system call to connect to the server process S The server process has not executed any ext accept system call Which one of the following events could take place ext connect system call returns successfully ext connect system call blocks ext connect system call returns an error ext connect system call results in a core dump ,Sockets,172 Identify the correct order in which a server process must invoke the function calls accept bind listen and recv according to UNIX socket API listen accept bind recv bind listen accept recv bind accept listen recv accept listen bind recv ,Sockets,172 Given relations r w x and s y z the result of select distinct w x from r s is guaranteed to be same as r provided r has no duplicates and s is non empty r and s have no duplicates s has no duplicates and r is non empty r and s have the same number of tuples ,Sql,173 Suppose a stack implementation supports an instruction REVERSE which reverses the order of elements on the stack in addition to the PUSH and POP instructions Which one of the following statements is TRUE with respect to this modified stack A queue cannot be implemented using this stack A queue can be implemented where ENQUEUE takes a single instruction and DEQUEUE takes a sequence of two instructions A queue can be implemented where ENQUEUE takes a sequence of three instructions and DEQUEUE takes a single instruction A queue can be implemented where both ENQUEUE and DEQUEUE take a single instruction each ,Stack,174 Based on the given statements select the most appropriate option to solve the given question If two floors in a certain building are 9 feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building Statements I Each step is 3 4 foot high II Each step is 1 foot wide Statements I alone is sufficient but statement II alone is not sufficient Statements II alone is sufficient but statement I alone is not sufficient Both statements together are sufficient but neither statement alone is sufficient Statements I and II together are not sufficient ,Statement Sufficiency,175 Based on the given statements select the most appropriate option to solve the given question If two floors in a certain building are 9 feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building Statements I Each step is 3 4 foot high II Each step is 1 foot wide Statements I alone is sufficient but statement II alone is not sufficient Statements II alone is sufficient but statement I alone is not sufficient Both statements together are sufficient but neither statement alone is sufficient Statements I and II together are not sufficient ,Statement Sufficiency,175 Based on the given statements select the most appropriate option to solve the given question If two floors in a certain building are 9 feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building Statements I Each step is 3 4 foot high II Each step is 1 foot wide Statements I alone is sufficient but statement II alone is not sufficient Statements II alone is sufficient but statement I alone is not sufficient Both statements together are sufficient but neither statement alone is sufficient Statements I and II together are not sufficient ,Statement Sufficiency,175 Based on the given statements select the most appropriate option to solve the given question If two floors in a certain building are 9 feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building Statements I Each step is 3 4 foot high II Each step is 1 foot wide Statements I alone is sufficient but statement II alone is not sufficient Statements II alone is sufficient but statement I alone is not sufficient Both statements together are sufficient but neither statement alone is sufficient Statements I and II together are not sufficient ,Statement Sufficiency,175 Based on the given statements select the most appropriate option to solve the given question If two floors in a certain building are 9 feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building Statements I Each step is 3 4 foot high II Each step is 1 foot wide Statements I alone is sufficient but statement II alone is not sufficient Statements II alone is sufficient but statement I alone is not sufficient Both statements together are sufficient but neither statement alone is sufficient Statements I and II together are not sufficient ,Statement Sufficiency,175 Based on the given statements select the most appropriate option to solve the given question If two floors in a certain building are 9 feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building Statements I Each step is 3 4 foot high II Each step is 1 foot wide Statements I alone is sufficient but statement II alone is not sufficient Statements II alone is sufficient but statement I alone is not sufficient Both statements together are sufficient but neither statement alone is sufficient Statements I and II together are not sufficient ,Statement Sufficiency,175 Based on the given statements select the most appropriate option to solve the given question If two floors in a certain building are 9 feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building Statements I Each step is 3 4 foot high II Each step is 1 foot wide Statements I alone is sufficient but statement II alone is not sufficient Statements II alone is sufficient but statement I alone is not sufficient Both statements together are sufficient but neither statement alone is sufficient Statements I and II together are not sufficient ,Statement Sufficiency,175 Based on the given statements select the most appropriate option to solve the given question If two floors in a certain building are 9 feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building Statements I Each step is 3 4 foot high II Each step is 1 foot wide Statements I alone is sufficient but statement II alone is not sufficient Statements II alone is sufficient but statement I alone is not sufficient Both statements together are sufficient but neither statement alone is sufficient Statements I and II together are not sufficient ,Statement Sufficiency,175 Based on the given statements select the most appropriate option to solve the given question If two floors in a certain building are 9 feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building Statements I Each step is 3 4 foot high II Each step is 1 foot wide Statements I alone is sufficient but statement II alone is not sufficient Statements II alone is sufficient but statement I alone is not sufficient Both statements together are sufficient but neither statement alone is sufficient Statements I and II together are not sufficient ,Statement Sufficiency,175 Based on the given statements select the most appropriate option to solve the given question If two floors in a certain building are 9 feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building Statements I Each step is 3 4 foot high II Each step is 1 foot wide Statements I alone is sufficient but statement II alone is not sufficient Statements II alone is sufficient but statement I alone is not sufficient Both statements together are sufficient but neither statement alone is sufficient Statements I and II together are not sufficient ,Statement Sufficiency,175 Based on the given statements select the most appropriate option to solve the given question If two floors in a certain building are 9 feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building Statements I Each step is 3 4 foot high II Each step is 1 foot wide Statements I alone is sufficient but statement II alone is not sufficient Statements II alone is sufficient but statement I alone is not sufficient Both statements together are sufficient but neither statement alone is sufficient Statements I and II together are not sufficient ,Statement Sufficiency,175 Based on the given statements select the most appropriate option to solve the given question If two floors in a certain building are 9 feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building Statements I Each step is 3 4 foot high II Each step is 1 foot wide Statements I alone is sufficient but statement II alone is not sufficient Statements II alone is sufficient but statement I alone is not sufficient Both statements together are sufficient but neither statement alone is sufficient Statements I and II together are not sufficient ,Statement Sufficiency,175 Based on the given statements select the most appropriate option to solve the given question If two floors in a certain building are 9 feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building Statements I Each step is 3 4 foot high II Each step is 1 foot wide Statements I alone is sufficient but statement II alone is not sufficient Statements II alone is sufficient but statement I alone is not sufficient Both statements together are sufficient but neither statement alone is sufficient Statements I and II together are not sufficient ,Statement Sufficiency,175 Based on the given statements select the most appropriate option to solve the given question If two floors in a certain building are 9 feet apart how many steps are there in a set of stairs that extends from the first floor to the second floor of the building Statements I Each step is 3 4 foot high II Each step is 1 foot wide Statements I alone is sufficient but statement II alone is not sufficient Statements II alone is sufficient but statement I alone is not sufficient Both statements together are sufficient but neither statement alone is sufficient Statements I and II together are not sufficient ,Statement Sufficiency,175 Consider a Boolean function f w x y z Suppose that exactly one of its inputs is allowed to change at a time If the function happens to be true for two input vectors i_ 1 left langle w_ 1 x_ 1 y_ 1 z_ 1 right rangle and i_ 2 left langle w_ 2 x_ 2 y_ 2 z_ 2 right rangle we would like the function to remain true as the input changes from i_ 1 to i_ 2 i_ 1 and i_ 2 differ in exactly one bit position without becoming false momentarily Let f w x y z sum 5 7 11 12 13 15 Which of the following cube covers of f will ensure that the required property is satisfied overline w xz wx overline y x overline y z xyz wyz wxy overline w xz wyz wx overline y overline z xz w overline x yz wx overline y wyz wxz overline w xz x overline y z xyz ,Static Hazard,176 Consider a Boolean function f w x y z Suppose that exactly one of its inputs is allowed to change at a time If the function happens to be true for two input vectors i_ 1 left langle w_ 1 x_ 1 y_ 1 z_ 1 right rangle and i_ 2 left langle w_ 2 x_ 2 y_ 2 z_ 2 right rangle we would like the function to remain true as the input changes from i_ 1 to i_ 2 i_ 1 and i_ 2 differ in exactly one bit position without becoming false momentarily Let f w x y z sum 5 7 11 12 13 15 Which of the following cube covers of f will ensure that the required property is satisfied overline w xz wx overline y x overline y z xyz wyz wxy overline w xz wyz wx overline y overline z xz w overline x yz wx overline y wyz wxz overline w xz x overline y z xyz ,Static Hazard,176 Consider a Boolean function f w x y z Suppose that exactly one of its inputs is allowed to change at a time If the function happens to be true for two input vectors i_ 1 left langle w_ 1 x_ 1 y_ 1 z_ 1 right rangle and i_ 2 left langle w_ 2 x_ 2 y_ 2 z_ 2 right rangle we would like the function to remain true as the input changes from i_ 1 to i_ 2 i_ 1 and i_ 2 differ in exactly one bit position without becoming false momentarily Let f w x y z sum 5 7 11 12 13 15 Which of the following cube covers of f will ensure that the required property is satisfied overline w xz wx overline y x overline y z xyz wyz wxy overline w xz wyz wx overline y overline z xz w overline x yz wx overline y wyz wxz overline w xz x overline y z xyz ,Static Hazard,176 Consider a Boolean function f w x y z Suppose that exactly one of its inputs is allowed to change at a time If the function happens to be true for two input vectors i_ 1 left langle w_ 1 x_ 1 y_ 1 z_ 1 right rangle and i_ 2 left langle w_ 2 x_ 2 y_ 2 z_ 2 right rangle we would like the function to remain true as the input changes from i_ 1 to i_ 2 i_ 1 and i_ 2 differ in exactly one bit position without becoming false momentarily Let f w x y z sum 5 7 11 12 13 15 Which of the following cube covers of f will ensure that the required property is satisfied overline w xz wx overline y x overline y z xyz wyz wxy overline w xz wyz wx overline y overline z xz w overline x yz wx overline y wyz wxz overline w xz x overline y z xyz ,Static Hazard,176 Consider a Boolean function f w x y z Suppose that exactly one of its inputs is allowed to change at a time If the function happens to be true for two input vectors i_ 1 left langle w_ 1 x_ 1 y_ 1 z_ 1 right rangle and i_ 2 left langle w_ 2 x_ 2 y_ 2 z_ 2 right rangle we would like the function to remain true as the input changes from i_ 1 to i_ 2 i_ 1 and i_ 2 differ in exactly one bit position without becoming false momentarily Let f w x y z sum 5 7 11 12 13 15 Which of the following cube covers of f will ensure that the required property is satisfied overline w xz wx overline y x overline y z xyz wyz wxy overline w xz wyz wx overline y overline z xz w overline x yz wx overline y wyz wxz overline w xz x overline y z xyz ,Static Hazard,176 Consider a Boolean function f w x y z Suppose that exactly one of its inputs is allowed to change at a time If the function happens to be true for two input vectors i_ 1 left langle w_ 1 x_ 1 y_ 1 z_ 1 right rangle and i_ 2 left langle w_ 2 x_ 2 y_ 2 z_ 2 right rangle we would like the function to remain true as the input changes from i_ 1 to i_ 2 i_ 1 and i_ 2 differ in exactly one bit position without becoming false momentarily Let f w x y z sum 5 7 11 12 13 15 Which of the following cube covers of f will ensure that the required property is satisfied overline w xz wx overline y x overline y z xyz wyz wxy overline w xz wyz wx overline y overline z xz w overline x yz wx overline y wyz wxz overline w xz x overline y z xyz ,Static Hazard,176 Consider a Boolean function f w x y z Suppose that exactly one of its inputs is allowed to change at a time If the function happens to be true for two input vectors i_ 1 left langle w_ 1 x_ 1 y_ 1 z_ 1 right rangle and i_ 2 left langle w_ 2 x_ 2 y_ 2 z_ 2 right rangle we would like the function to remain true as the input changes from i_ 1 to i_ 2 i_ 1 and i_ 2 differ in exactly one bit position without becoming false momentarily Let f w x y z sum 5 7 11 12 13 15 Which of the following cube covers of f will ensure that the required property is satisfied overline w xz wx overline y x overline y z xyz wyz wxy overline w xz wyz wx overline y overline z xz w overline x yz wx overline y wyz wxz overline w xz x overline y z xyz ,Static Hazard,176 Consider a Boolean function f w x y z Suppose that exactly one of its inputs is allowed to change at a time If the function happens to be true for two input vectors i_ 1 left langle w_ 1 x_ 1 y_ 1 z_ 1 right rangle and i_ 2 left langle w_ 2 x_ 2 y_ 2 z_ 2 right rangle we would like the function to remain true as the input changes from i_ 1 to i_ 2 i_ 1 and i_ 2 differ in exactly one bit position without becoming false momentarily Let f w x y z sum 5 7 11 12 13 15 Which of the following cube covers of f will ensure that the required property is satisfied overline w xz wx overline y x overline y z xyz wyz wxy overline w xz wyz wx overline y overline z xz w overline x yz wx overline y wyz wxz overline w xz x overline y z xyz ,Static Hazard,176 Consider a Boolean function f w x y z Suppose that exactly one of its inputs is allowed to change at a time If the function happens to be true for two input vectors i_ 1 left langle w_ 1 x_ 1 y_ 1 z_ 1 right rangle and i_ 2 left langle w_ 2 x_ 2 y_ 2 z_ 2 right rangle we would like the function to remain true as the input changes from i_ 1 to i_ 2 i_ 1 and i_ 2 differ in exactly one bit position without becoming false momentarily Let f w x y z sum 5 7 11 12 13 15 Which of the following cube covers of f will ensure that the required property is satisfied overline w xz wx overline y x overline y z xyz wyz wxy overline w xz wyz wx overline y overline z xz w overline x yz wx overline y wyz wxz overline w xz x overline y z xyz ,Static Hazard,176 Consider a Boolean function f w x y z Suppose that exactly one of its inputs is allowed to change at a time If the function happens to be true for two input vectors i_ 1 left langle w_ 1 x_ 1 y_ 1 z_ 1 right rangle and i_ 2 left langle w_ 2 x_ 2 y_ 2 z_ 2 right rangle we would like the function to remain true as the input changes from i_ 1 to i_ 2 i_ 1 and i_ 2 differ in exactly one bit position without becoming false momentarily Let f w x y z sum 5 7 11 12 13 15 Which of the following cube covers of f will ensure that the required property is satisfied overline w xz wx overline y x overline y z xyz wyz wxy overline w xz wyz wx overline y overline z xz w overline x yz wx overline y wyz wxz overline w xz x overline y z xyz ,Static Hazard,176 Consider a Boolean function f w x y z Suppose that exactly one of its inputs is allowed to change at a time If the function happens to be true for two input vectors i_ 1 left langle w_ 1 x_ 1 y_ 1 z_ 1 right rangle and i_ 2 left langle w_ 2 x_ 2 y_ 2 z_ 2 right rangle we would like the function to remain true as the input changes from i_ 1 to i_ 2 i_ 1 and i_ 2 differ in exactly one bit position without becoming false momentarily Let f w x y z sum 5 7 11 12 13 15 Which of the following cube covers of f will ensure that the required property is satisfied overline w xz wx overline y x overline y z xyz wyz wxy overline w xz wyz wx overline y overline z xz w overline x yz wx overline y wyz wxz overline w xz x overline y z xyz ,Static Hazard,176 Consider a Boolean function f w x y z Suppose that exactly one of its inputs is allowed to change at a time If the function happens to be true for two input vectors i_ 1 left langle w_ 1 x_ 1 y_ 1 z_ 1 right rangle and i_ 2 left langle w_ 2 x_ 2 y_ 2 z_ 2 right rangle we would like the function to remain true as the input changes from i_ 1 to i_ 2 i_ 1 and i_ 2 differ in exactly one bit position without becoming false momentarily Let f w x y z sum 5 7 11 12 13 15 Which of the following cube covers of f will ensure that the required property is satisfied overline w xz wx overline y x overline y z xyz wyz wxy overline w xz wyz wx overline y overline z xz w overline x yz wx overline y wyz wxz overline w xz x overline y z xyz ,Static Hazard,176 Consider a Boolean function f w x y z Suppose that exactly one of its inputs is allowed to change at a time If the function happens to be true for two input vectors i_ 1 left langle w_ 1 x_ 1 y_ 1 z_ 1 right rangle and i_ 2 left langle w_ 2 x_ 2 y_ 2 z_ 2 right rangle we would like the function to remain true as the input changes from i_ 1 to i_ 2 i_ 1 and i_ 2 differ in exactly one bit position without becoming false momentarily Let f w x y z sum 5 7 11 12 13 15 Which of the following cube covers of f will ensure that the required property is satisfied overline w xz wx overline y x overline y z xyz wyz wxy overline w xz wyz wx overline y overline z xz w overline x yz wx overline y wyz wxz overline w xz x overline y z xyz ,Static Hazard,176 Consider a Boolean function f w x y z Suppose that exactly one of its inputs is allowed to change at a time If the function happens to be true for two input vectors i_ 1 left langle w_ 1 x_ 1 y_ 1 z_ 1 right rangle and i_ 2 left langle w_ 2 x_ 2 y_ 2 z_ 2 right rangle we would like the function to remain true as the input changes from i_ 1 to i_ 2 i_ 1 and i_ 2 differ in exactly one bit position without becoming false momentarily Let f w x y z sum 5 7 11 12 13 15 Which of the following cube covers of f will ensure that the required property is satisfied overline w xz wx overline y x overline y z xyz wyz wxy overline w xz wyz wx overline y overline z xz w overline x yz wx overline y wyz wxz overline w xz x overline y z xyz ,Static Hazard,176 On a wireless link the probability of packet error is 0 2 A stop and wait protocol is used to transfer data across the link The channel condition is assumed to be independent from transmission to transmission What is the average number of transmission attempts required to transfer 100 packets 100 125 150 200 ,Stop And Wait,177 Suppose that the stop and wait protocol is used on a link with a bit rate of 64 kilobits per second and 20 milliseconds propagation delay Assume that the transmission time for the acknowledgement and the processing time at nodes are negligible Then the minimum frame size in bytes to achieve a link utilization of at least 50 is_________________ ,Stop And Wait,177 Suppose that the stop and wait protocol is used on a link with a bit rate of 64 kilobits per second and 20 milliseconds propagation delay Assume that the transmission time for the acknowledgement and the processing time at nodes are negligible Then the minimum frame size in bytes to achieve a link utilization of at least 50 is_________________ ,Stop And Wait,177 On a wireless link the probability of packet error is 0 2 A stop and wait protocol is used to transfer data across the link The channel condition is assumed to be independent from transmission to transmission What is the average number of transmission attempts required to transfer 100 packets 100 125 150 200 ,Stop And Wait,177 The values of parameters for the Stop and Wait ARQ protocol are as given below Bit rate of the transmission channel 1 Mbps Propagation delay from sender to receiver 0 75 ms Time to process a frame 0 25 ms Number of bytes in the information frame 1980 Number of bytes in the acknowledge frame 20 Number of overhead bytes in the information frame 20 Assume there are no transmission errors Then the transmission efficiency expressed in percentage of the Stop and Wait ARQ protocol for the above parameters is _____________ correct to 2 decimal places ,Stop And Wait,177 The values of parameters for the Stop and Wait ARQ protocol are as given below Bit rate of the transmission channel 1 Mbps Propagation delay from sender to receiver 0 75 ms Time to process a frame 0 25 ms Number of bytes in the information frame 1980 Number of bytes in the acknowledge frame 20 Number of overhead bytes in the information frame 20 Assume there are no transmission errors Then the transmission efficiency expressed in percentage of the Stop and Wait ARQ protocol for the above parameters is _____________ correct to 2 decimal places ,Stop And Wait,177 The values of parameters for the Stop and Wait ARQ protocol are as given below Bit rate of the transmission channel 1 Mbps Propagation delay from sender to receiver 0 75 ms Time to process a frame 0 25 ms Number of bytes in the information frame 1980 Number of bytes in the acknowledge frame 20 Number of overhead bytes in the information frame 20 Assume there are no transmission errors Then the transmission efficiency expressed in percentage of the Stop and Wait ARQ protocol for the above parameters is _____________ correct to 2 decimal places ,Stop And Wait,177 On a wireless link the probability of packet error is 0 2 A stop and wait protocol is used to transfer data across the link The channel condition is assumed to be independent from transmission to transmission What is the average number of transmission attempts required to transfer 100 packets 100 125 150 200 ,Stop And Wait,177 Suppose that the stop and wait protocol is used on a link with a bit rate of 64 kilobits per second and 20 milliseconds propagation delay Assume that the transmission time for the acknowledgement and the processing time at nodes are negligible Then the minimum frame size in bytes to achieve a link utilization of at least 50 is_________________ ,Stop And Wait,177 Suppose that the stop and wait protocol is used on a link with a bit rate of 64 kilobits per second and 20 milliseconds propagation delay Assume that the transmission time for the acknowledgement and the processing time at nodes are negligible Then the minimum frame size in bytes to achieve a link utilization of at least 50 is_________________ ,Stop And Wait,177 A sender uses the Stop and Wait ARQ protocol for reliable transmission of frames Frames are of size 1000 bytes and the transmission rate at the sender is 80 Kbps 1 Kbps 1000 bits second Size of an acknowledgement is 100 bytes and the transmission rate at the receiver is 8 Kbps The one way propagation delay is 100 milliseconds Assuming no frame is lost the sender throughout is ________ bytes second ,Stop And Wait,177 Consider the following relational schema ext Suppliers underline ext sid integer ext sname string city string street string ext Parts underline ext pid integer ext pname string color string ext Catalog underline ext sid integer pid integer ext cost real Consider the following relational query on the above database SELECT S sname FROM Suppliers S WHERE S sid NOT IN SELECT C sid FROM Catalog C WHERE C pid NOT IN SELECT P pid FROM Parts P WHERE P color lt gt blue Assume that relations corresponding to the above schema are not empty Which one of the following is the correct interpretation of the above query Find the names of all suppliers who have supplied a non blue part Find the names of all suppliers who have not supplied a non blue part Find the names of all suppliers who have supplied only non blue part Find the names of all suppliers who have not supplied only blue parts ,Sub Queries,178 Consider the following relational schema ext Suppliers underline ext sid integer ext sname string city string street string ext Parts underline ext pid integer ext pname string color string ext Catalog underline ext sid integer pid integer ext cost real Consider the following relational query on the above database SELECT S sname FROM Suppliers S WHERE S sid NOT IN SELECT C sid FROM Catalog C WHERE C pid NOT IN SELECT P pid FROM Parts P WHERE P color lt gt blue Assume that relations corresponding to the above schema are not empty Which one of the following is the correct interpretation of the above query Find the names of all suppliers who have supplied a non blue part Find the names of all suppliers who have not supplied a non blue part Find the names of all suppliers who have supplied only non blue part Find the names of all suppliers who have not supplied only blue parts ,Sub Queries,178 Consider the following relational schema ext Suppliers underline ext sid integer ext sname string city string street string ext Parts underline ext pid integer ext pname string color string ext Catalog underline ext sid integer pid integer ext cost real Consider the following relational query on the above database SELECT S sname FROM Suppliers S WHERE S sid NOT IN SELECT C sid FROM Catalog C WHERE C pid NOT IN SELECT P pid FROM Parts P WHERE P color lt gt blue Assume that relations corresponding to the above schema are not empty Which one of the following is the correct interpretation of the above query Find the names of all suppliers who have supplied a non blue part Find the names of all suppliers who have not supplied a non blue part Find the names of all suppliers who have supplied only non blue part Find the names of all suppliers who have not supplied only blue parts ,Sub Queries,178 Consider the following relational schema ext Suppliers underline ext sid integer ext sname string city string street string ext Parts underline ext pid integer ext pname string color string ext Catalog underline ext sid integer pid integer ext cost real Consider the following relational query on the above database SELECT S sname FROM Suppliers S WHERE S sid NOT IN SELECT C sid FROM Catalog C WHERE C pid NOT IN SELECT P pid FROM Parts P WHERE P color lt gt blue Assume that relations corresponding to the above schema are not empty Which one of the following is the correct interpretation of the above query Find the names of all suppliers who have supplied a non blue part Find the names of all suppliers who have not supplied a non blue part Find the names of all suppliers who have supplied only non blue part Find the names of all suppliers who have not supplied only blue parts ,Sub Queries,178 Consider the following relational schema ext Suppliers underline ext sid integer ext sname string city string street string ext Parts underline ext pid integer ext pname string color string ext Catalog underline ext sid integer pid integer ext cost real Consider the following relational query on the above database SELECT S sname FROM Suppliers S WHERE S sid NOT IN SELECT C sid FROM Catalog C WHERE C pid NOT IN SELECT P pid FROM Parts P WHERE P color lt gt blue Assume that relations corresponding to the above schema are not empty Which one of the following is the correct interpretation of the above query Find the names of all suppliers who have supplied a non blue part Find the names of all suppliers who have not supplied a non blue part Find the names of all suppliers who have supplied only non blue part Find the names of all suppliers who have not supplied only blue parts ,Sub Queries,178 Consider the following relations A B and C A Id Name Age 12 Arun 60 15 Shreya 24 99 Rohit 11 B Id Name Age 15 Shreya 24 25 Hari 40 98 Rohit 20 99 Rohit 11 C Id Phone Area 10 2200 02 99 2100 01 How many tuples does the result of the following SQL query contain SELECT A Id FROM A WHERE A Age gt ALL SELECT B Age FROM B WHERE B Name lsquo Arun rsquo 4 3 0 1 ,Sub Queries,178 Consider the following relations A B and C A Id Name Age 12 Arun 60 15 Shreya 24 99 Rohit 11 B Id Name Age 15 Shreya 24 25 Hari 40 98 Rohit 20 99 Rohit 11 C Id Phone Area 10 2200 02 99 2100 01 How many tuples does the result of the following SQL query contain SELECT A Id FROM A WHERE A Age gt ALL SELECT B Age FROM B WHERE B Name lsquo Arun rsquo 4 3 0 1 ,Sub Queries,178 Consider the following relations A B and C A Id Name Age 12 Arun 60 15 Shreya 24 99 Rohit 11 B Id Name Age 15 Shreya 24 25 Hari 40 98 Rohit 20 99 Rohit 11 C Id Phone Area 10 2200 02 99 2100 01 How many tuples does the result of the following SQL query contain SELECT A Id FROM A WHERE A Age gt ALL SELECT B Age FROM B WHERE B Name lsquo Arun rsquo 4 3 0 1 ,Sub Queries,178 Consider the following relations A B and C A Id Name Age 12 Arun 60 15 Shreya 24 99 Rohit 11 B Id Name Age 15 Shreya 24 25 Hari 40 98 Rohit 20 99 Rohit 11 C Id Phone Area 10 2200 02 99 2100 01 How many tuples does the result of the following SQL query contain SELECT A Id FROM A WHERE A Age gt ALL SELECT B Age FROM B WHERE B Name lsquo Arun rsquo 4 3 0 1 ,Sub Queries,178 Consider the following relations A B and C A Id Name Age 12 Arun 60 15 Shreya 24 99 Rohit 11 B Id Name Age 15 Shreya 24 25 Hari 40 98 Rohit 20 99 Rohit 11 C Id Phone Area 10 2200 02 99 2100 01 How many tuples does the result of the following SQL query contain SELECT A Id FROM A WHERE A Age gt ALL SELECT B Age FROM B WHERE B Name lsquo Arun rsquo 4 3 0 1 ,Sub Queries,178 Consider the following relations A B and C A Id Name Age 12 Arun 60 15 Shreya 24 99 Rohit 11 B Id Name Age 15 Shreya 24 25 Hari 40 98 Rohit 20 99 Rohit 11 C Id Phone Area 10 2200 02 99 2100 01 How many tuples does the result of the following SQL query contain SELECT A Id FROM A WHERE A Age gt ALL SELECT B Age FROM B WHERE B Name lsquo Arun rsquo 4 3 0 1 ,Sub Queries,178 Consider the following relational schema ext Suppliers underline ext sid integer ext sname string city string street string ext Parts underline ext pid integer ext pname string color string ext Catalog underline ext sid integer pid integer ext cost real Consider the following relational query on the above database SELECT S sname FROM Suppliers S WHERE S sid NOT IN SELECT C sid FROM Catalog C WHERE C pid NOT IN SELECT P pid FROM Parts P WHERE P color lt gt blue Assume that relations corresponding to the above schema are not empty Which one of the following is the correct interpretation of the above query Find the names of all suppliers who have supplied a non blue part Find the names of all suppliers who have not supplied a non blue part Find the names of all suppliers who have supplied only non blue part Find the names of all suppliers who have not supplied only blue parts ,Sub Queries,178 Consider the following relations A B and C A Id Name Age 12 Arun 60 15 Shreya 24 99 Rohit 11 B Id Name Age 15 Shreya 24 25 Hari 40 98 Rohit 20 99 Rohit 11 C Id Phone Area 10 2200 02 99 2100 01 How many tuples does the result of the following SQL query contain SELECT A Id FROM A WHERE A Age gt ALL SELECT B Age FROM B WHERE B Name lsquo Arun rsquo 4 3 0 1 ,Sub Queries,178 Use the patterns given to prove that sum limits_ i 0 n 1 2i 1 n 2 You are not permitted to employ induction Use the result obtained in a to prove that sum limits_ i 1 n i frac n n 1 2 ,Summation,180 Let P sum_ substack 1 le i le 2k i odd i and Q sum_ substack 1 le i le 2k i even i where k is a positive integer Then P Q k P Q k P Q P Q 2k ,Summation,180 sum limits_ x 1 99 frac 1 x x 1 __________________ ,Summation,180 Use the patterns given to prove that sum limits_ i 0 n 1 2i 1 n 2 You are not permitted to employ induction Use the result obtained in a to prove that sum limits_ i 1 n i frac n n 1 2 ,Summation,180 Let P sum_ substack 1 le i le 2k i odd i and Q sum_ substack 1 le i le 2k i even i where k is a positive integer Then P Q k P Q k P Q P Q 2k ,Summation,180 Let P sum_ substack 1 le i le 2k i odd i and Q sum_ substack 1 le i le 2k i even i where k is a positive integer Then P Q k P Q k P Q P Q 2k ,Summation,180 Use the patterns given to prove that sum limits_ i 0 n 1 2i 1 n 2 You are not permitted to employ induction Use the result obtained in a to prove that sum limits_ i 1 n i frac n n 1 2 ,Summation,180 sum limits_ x 1 99 frac 1 x x 1 __________________ ,Summation,180 sum limits_ x 1 99 frac 1 x x 1 __________________ ,Summation,180 Let P sum_ substack 1 le i le 2k i odd i and Q sum_ substack 1 le i le 2k i even i where k is a positive integer Then P Q k P Q k P Q P Q 2k ,Summation,180 sum limits_ x 1 99 frac 1 x x 1 __________________ ,Summation,180 Let P sum_ substack 1 le i le 2k i odd i and Q sum_ substack 1 le i le 2k i even i where k is a positive integer Then P Q k P Q k P Q P Q 2k ,Summation,180 Choose the correct alternatives more than one may be correct and write the corresponding letters only Advantage of synchronous sequential circuits over asynchronous ones is faster operation ease of avoiding problems due to hazards lower hardware requirement better noise immunity none of the above ,Synchronous Asynchronous Circuits,181 Choose the correct alternatives more than one may be correct and write the corresponding letters only Advantage of synchronous sequential circuits over asynchronous ones is faster operation ease of avoiding problems due to hazards lower hardware requirement better noise immunity none of the above ,Synchronous Asynchronous Circuits,181 Choose the correct alternatives more than one may be correct and write the corresponding letters only Advantage of synchronous sequential circuits over asynchronous ones is faster operation ease of avoiding problems due to hazards lower hardware requirement better noise immunity none of the above ,Synchronous Asynchronous Circuits,181 Choose the correct alternatives more than one may be correct and write the corresponding letters only Advantage of synchronous sequential circuits over asynchronous ones is faster operation ease of avoiding problems due to hazards lower hardware requirement better noise immunity none of the above ,Synchronous Asynchronous Circuits,181 Choose the correct alternatives more than one may be correct and write the corresponding letters only Advantage of synchronous sequential circuits over asynchronous ones is faster operation ease of avoiding problems due to hazards lower hardware requirement better noise immunity none of the above ,Synchronous Asynchronous Circuits,181 Choose the correct alternatives more than one may be correct and write the corresponding letters only Advantage of synchronous sequential circuits over asynchronous ones is faster operation ease of avoiding problems due to hazards lower hardware requirement better noise immunity none of the above ,Synchronous Asynchronous Circuits,181 Choose the correct alternatives more than one may be correct and write the corresponding letters only Advantage of synchronous sequential circuits over asynchronous ones is faster operation ease of avoiding problems due to hazards lower hardware requirement better noise immunity none of the above ,Synchronous Asynchronous Circuits,181 Choose the correct alternatives more than one may be correct and write the corresponding letters only Advantage of synchronous sequential circuits over asynchronous ones is faster operation ease of avoiding problems due to hazards lower hardware requirement better noise immunity none of the above ,Synchronous Asynchronous Circuits,181 Choose the correct alternatives more than one may be correct and write the corresponding letters only Advantage of synchronous sequential circuits over asynchronous ones is faster operation ease of avoiding problems due to hazards lower hardware requirement better noise immunity none of the above ,Synchronous Asynchronous Circuits,181 Choose the correct alternatives more than one may be correct and write the corresponding letters only Advantage of synchronous sequential circuits over asynchronous ones is faster operation ease of avoiding problems due to hazards lower hardware requirement better noise immunity none of the above ,Synchronous Asynchronous Circuits,181 Choose the correct alternatives more than one may be correct and write the corresponding letters only Advantage of synchronous sequential circuits over asynchronous ones is faster operation ease of avoiding problems due to hazards lower hardware requirement better noise immunity none of the above ,Synchronous Asynchronous Circuits,181 Choose the correct alternatives more than one may be correct and write the corresponding letters only Advantage of synchronous sequential circuits over asynchronous ones is faster operation ease of avoiding problems due to hazards lower hardware requirement better noise immunity none of the above ,Synchronous Asynchronous Circuits,181 Choose the correct alternatives more than one may be correct and write the corresponding letters only Advantage of synchronous sequential circuits over asynchronous ones is faster operation ease of avoiding problems due to hazards lower hardware requirement better noise immunity none of the above ,Synchronous Asynchronous Circuits,181 Choose the correct alternatives more than one may be correct and write the corresponding letters only Advantage of synchronous sequential circuits over asynchronous ones is faster operation ease of avoiding problems due to hazards lower hardware requirement better noise immunity none of the above ,Synchronous Asynchronous Circuits,181 Consider the circuit given below with initial state Q_0 1 Q_1 Q_2 0 The state of the circuit is given by the value 4Q_2 2Q_1 Q_0 Which one of the following is correct state sequence of the circuit 1 3 4 6 7 5 2 1 2 5 3 7 6 4 1 2 7 3 5 6 4 1 6 5 7 2 3 4 ,Synchronous Circuit,182 Consider the circuit given below with initial state Q_0 1 Q_1 Q_2 0 The state of the circuit is given by the value 4Q_2 2Q_1 Q_0 Which one of the following is correct state sequence of the circuit 1 3 4 6 7 5 2 1 2 5 3 7 6 4 1 2 7 3 5 6 4 1 6 5 7 2 3 4 ,Synchronous Circuit,182 Consider the circuit given below with initial state Q_0 1 Q_1 Q_2 0 The state of the circuit is given by the value 4Q_2 2Q_1 Q_0 Which one of the following is correct state sequence of the circuit 1 3 4 6 7 5 2 1 2 5 3 7 6 4 1 2 7 3 5 6 4 1 6 5 7 2 3 4 ,Synchronous Circuit,182 Consider the circuit given below with initial state Q_0 1 Q_1 Q_2 0 The state of the circuit is given by the value 4Q_2 2Q_1 Q_0 Which one of the following is correct state sequence of the circuit 1 3 4 6 7 5 2 1 2 5 3 7 6 4 1 2 7 3 5 6 4 1 6 5 7 2 3 4 ,Synchronous Circuit,182 Consider the circuit given below with initial state Q_0 1 Q_1 Q_2 0 The state of the circuit is given by the value 4Q_2 2Q_1 Q_0 Which one of the following is correct state sequence of the circuit 1 3 4 6 7 5 2 1 2 5 3 7 6 4 1 2 7 3 5 6 4 1 6 5 7 2 3 4 ,Synchronous Circuit,182 Consider the circuit given below with initial state Q_0 1 Q_1 Q_2 0 The state of the circuit is given by the value 4Q_2 2Q_1 Q_0 Which one of the following is correct state sequence of the circuit 1 3 4 6 7 5 2 1 2 5 3 7 6 4 1 2 7 3 5 6 4 1 6 5 7 2 3 4 ,Synchronous Circuit,182 Consider the circuit given below with initial state Q_0 1 Q_1 Q_2 0 The state of the circuit is given by the value 4Q_2 2Q_1 Q_0 Which one of the following is correct state sequence of the circuit 1 3 4 6 7 5 2 1 2 5 3 7 6 4 1 2 7 3 5 6 4 1 6 5 7 2 3 4 ,Synchronous Circuit,182 Consider the circuit given below with initial state Q_0 1 Q_1 Q_2 0 The state of the circuit is given by the value 4Q_2 2Q_1 Q_0 Which one of the following is correct state sequence of the circuit 1 3 4 6 7 5 2 1 2 5 3 7 6 4 1 2 7 3 5 6 4 1 6 5 7 2 3 4 ,Synchronous Circuit,182 Consider the circuit given below with initial state Q_0 1 Q_1 Q_2 0 The state of the circuit is given by the value 4Q_2 2Q_1 Q_0 Which one of the following is correct state sequence of the circuit 1 3 4 6 7 5 2 1 2 5 3 7 6 4 1 2 7 3 5 6 4 1 6 5 7 2 3 4 ,Synchronous Circuit,182 Consider the circuit given below with initial state Q_0 1 Q_1 Q_2 0 The state of the circuit is given by the value 4Q_2 2Q_1 Q_0 Which one of the following is correct state sequence of the circuit 1 3 4 6 7 5 2 1 2 5 3 7 6 4 1 2 7 3 5 6 4 1 6 5 7 2 3 4 ,Synchronous Circuit,182 Consider the circuit given below with initial state Q_0 1 Q_1 Q_2 0 The state of the circuit is given by the value 4Q_2 2Q_1 Q_0 Which one of the following is correct state sequence of the circuit 1 3 4 6 7 5 2 1 2 5 3 7 6 4 1 2 7 3 5 6 4 1 6 5 7 2 3 4 ,Synchronous Circuit,182 Consider the circuit given below with initial state Q_0 1 Q_1 Q_2 0 The state of the circuit is given by the value 4Q_2 2Q_1 Q_0 Which one of the following is correct state sequence of the circuit 1 3 4 6 7 5 2 1 2 5 3 7 6 4 1 2 7 3 5 6 4 1 6 5 7 2 3 4 ,Synchronous Circuit,182 Consider the circuit given below with initial state Q_0 1 Q_1 Q_2 0 The state of the circuit is given by the value 4Q_2 2Q_1 Q_0 Which one of the following is correct state sequence of the circuit 1 3 4 6 7 5 2 1 2 5 3 7 6 4 1 2 7 3 5 6 4 1 6 5 7 2 3 4 ,Synchronous Circuit,182 Consider the circuit given below with initial state Q_0 1 Q_1 Q_2 0 The state of the circuit is given by the value 4Q_2 2Q_1 Q_0 Which one of the following is correct state sequence of the circuit 1 3 4 6 7 5 2 1 2 5 3 7 6 4 1 2 7 3 5 6 4 1 6 5 7 2 3 4 ,Synchronous Circuit,182 Design a synchronous counter to go through the following states 1 4 2 3 1 4 2 3 1 4 dots ,Synchronous Counter,183 Design a synchronous counter to go through the following states 1 4 2 3 1 4 2 3 1 4 dots ,Synchronous Counter,183 Design a synchronous counter to go through the following states 1 4 2 3 1 4 2 3 1 4 dots ,Synchronous Counter,183 Design a synchronous counter to go through the following states 1 4 2 3 1 4 2 3 1 4 dots ,Synchronous Counter,183 Design a synchronous counter to go through the following states 1 4 2 3 1 4 2 3 1 4 dots ,Synchronous Counter,183 Design a synchronous counter to go through the following states 1 4 2 3 1 4 2 3 1 4 dots ,Synchronous Counter,183 Design a synchronous counter to go through the following states 1 4 2 3 1 4 2 3 1 4 dots ,Synchronous Counter,183 Design a synchronous counter to go through the following states 1 4 2 3 1 4 2 3 1 4 dots ,Synchronous Counter,183 Design a synchronous counter to go through the following states 1 4 2 3 1 4 2 3 1 4 dots ,Synchronous Counter,183 Design a synchronous counter to go through the following states 1 4 2 3 1 4 2 3 1 4 dots ,Synchronous Counter,183 Design a synchronous counter to go through the following states 1 4 2 3 1 4 2 3 1 4 dots ,Synchronous Counter,183 Design a synchronous counter to go through the following states 1 4 2 3 1 4 2 3 1 4 dots ,Synchronous Counter,183 Design a synchronous counter to go through the following states 1 4 2 3 1 4 2 3 1 4 dots ,Synchronous Counter,183 Design a synchronous counter to go through the following states 1 4 2 3 1 4 2 3 1 4 dots ,Synchronous Counter,183 System calls are usually invoked by using a software interrupt polling an indirect jump a privileged instruction ,System Calls,184 System calls are usually invoked by using a software interrupt polling an indirect jump a privileged instruction ,System Calls,184 System calls are usually invoked by using a software interrupt polling an indirect jump a privileged instruction ,System Calls,184 System calls are usually invoked by using a software interrupt polling an indirect jump a privileged instruction ,System Calls,184 System calls are usually invoked by using a software interrupt polling an indirect jump a privileged instruction ,System Calls,184 System calls are usually invoked by using a software interrupt polling an indirect jump a privileged instruction ,System Calls,184 System calls are usually invoked by using a software interrupt polling an indirect jump a privileged instruction ,System Calls,184 System calls are usually invoked by using a software interrupt polling an indirect jump a privileged instruction ,System Calls,184 System calls are usually invoked by using a software interrupt polling an indirect jump a privileged instruction ,System Calls,184 System calls are usually invoked by using a software interrupt polling an indirect jump a privileged instruction ,System Calls,184 System calls are usually invoked by using a software interrupt polling an indirect jump a privileged instruction ,System Calls,184 System calls are usually invoked by using a software interrupt polling an indirect jump a privileged instruction ,System Calls,184 System calls are usually invoked by using a software interrupt polling an indirect jump a privileged instruction ,System Calls,184 System calls are usually invoked by using a software interrupt polling an indirect jump a privileged instruction ,System Calls,184 Consider the following set of equations x 2y 5 4x 8y 12 3x 6y 3z 15 This set has unique solution has no solution has finite number of solutions has infinite number of solutions ,System Of Equations,185 What values of x y and z satisfy the following system of linear equations begin bmatrix 1 amp 2 amp 3 1 amp 3 amp 4 2 amp 2 amp 3 end bmatrix begin bmatrix x y z end bmatrix begin bmatrix 6 8 12 end bmatrix x 6 y 3 z 2 x 12 y 3 z 4 x 6 y 6 z 4 x 12 y 3 z 0 ,System Of Equations,185 If the following system has non trivial solution u00a0 px qy rz 0 qx ry pz 0 rx py qz 0 then which one of the following options is TRUE u00a0 p q r 0 ext or p q r p q r 0 ext or p q r p q r 0 ext or p q r p q r 0 ext or p q r ,System Of Equations,185 Consider the following system of linear equations left begin array ccc 2 amp 1 amp 4 4 amp 3 amp 12 1 amp 2 amp 8 end array right left begin array ccc x y z end array right left begin array ccc alpha 5 7 end array right Notice that the second and the third columns of the coefficient matrix are linearly dependent For how many values of alpha does this system of equations have infinitely many solutions 0 1 2 3 ,System Of Equations,185 The three way handshake for TCP connection establishment is shown below Which of the following statements are TRUE S1 Loss of SYN ACK from the server will not establish a connection S2 Loss of ACK from the client cannot establish the connection S3 The server moves LISTEN u2192 SYN_RCVD u2192 SYN_SENT u2192 ESTABLISHED in the state machine on no packet loss S4 The server moves LISTEN u2192 SYN_RCVD u2192 ESTABLISHED in the state machine on no packet loss S 2 and S 3 only S 1 and S 4 only S 1 and S 3 only S 2 and S 4 only ,Tcp,186 Consider the following statements TCP connections are full duplex TCP has no option for selective acknowledgement TCP connections are message streams Only I is correct Only I and III are correct Only II and III are correct All of I II and III are correct ,Tcp,186 Assume that the bandwidth for a TCP connection is 1048560 bits sec Let alpha be the value of RTT in milliseconds rounded off to the nearest integer after which the TCP window scale option is needed Let beta be the maximum possible window size with window scale option Then the values of alpha and beta are 63 milliseconds 65535 imes 2 14 63 milliseconds 65535 imes 2 16 500 milliseconds 65535 imes 2 14 500 milliseconds 65535 imes 2 16 ,Tcp,186 Consider the following statements about the timeout value used in TCP The timeout value is set to the RTT Round Trip Time measured during TCP connection establishment for the entire duration of the connection Appropriate RTT estimation algorithm is used to set the timeout value of a TCP connection Timeout value is set to twice the propagation delay from the sender to the receiver Which of the following choices hold i is false but ii and iii are true i and iii are false but ii is title i and ii are false but iii is true i ii and iii are false ,Tcp,186 Consider a TCP client and a TCP server running on two different machines After completing data transfer the TCP client calls close to terminate the connection and a FIN segment is sent to the TCP server Server side TCP responds by sending an ACK which is received by the client side TCP As per the TCP connection state diagram RFC 793 in which state does the client side TCP connection wait for the FIN from the server side TCP LAST ACK TIME WAIT FIN WAIT 1 FIN WAIT 2 ,Tcp,186 Assume that the bandwidth for a TCP connection is 1048560 bits sec Let alpha be the value of RTT in milliseconds rounded off to the nearest integer after which the TCP window scale option is needed Let beta be the maximum possible window size with window scale option Then the values of alpha and beta are 63 milliseconds 65535 imes 2 14 63 milliseconds 65535 imes 2 16 500 milliseconds 65535 imes 2 14 500 milliseconds 65535 imes 2 16 ,Tcp,186 After Rajendra Chola returned from his voyage to Indonesia he ________ to visit the temple in Thanjavur was wishing is wishing wished had wished ,Tenses,187 After Rajendra Chola returned from his voyage to Indonesia he ________ to visit the temple in Thanjavur was wishing is wishing wished had wished ,Tenses,187 After Rajendra Chola returned from his voyage to Indonesia he ________ to visit the temple in Thanjavur was wishing is wishing wished had wished ,Tenses,187 After Rajendra Chola returned from his voyage to Indonesia he ________ to visit the temple in Thanjavur was wishing is wishing wished had wished ,Tenses,187 After Rajendra Chola returned from his voyage to Indonesia he ________ to visit the temple in Thanjavur was wishing is wishing wished had wished ,Tenses,187 After Rajendra Chola returned from his voyage to Indonesia he ________ to visit the temple in Thanjavur was wishing is wishing wished had wished ,Tenses,187 After Rajendra Chola returned from his voyage to Indonesia he ________ to visit the temple in Thanjavur was wishing is wishing wished had wished ,Tenses,187 After Rajendra Chola returned from his voyage to Indonesia he ________ to visit the temple in Thanjavur was wishing is wishing wished had wished ,Tenses,187 After Rajendra Chola returned from his voyage to Indonesia he ________ to visit the temple in Thanjavur was wishing is wishing wished had wished ,Tenses,187 After Rajendra Chola returned from his voyage to Indonesia he ________ to visit the temple in Thanjavur was wishing is wishing wished had wished ,Tenses,187 After Rajendra Chola returned from his voyage to Indonesia he ________ to visit the temple in Thanjavur was wishing is wishing wished had wished ,Tenses,187 After Rajendra Chola returned from his voyage to Indonesia he ________ to visit the temple in Thanjavur was wishing is wishing wished had wished ,Tenses,187 After Rajendra Chola returned from his voyage to Indonesia he ________ to visit the temple in Thanjavur was wishing is wishing wished had wished ,Tenses,187 After Rajendra Chola returned from his voyage to Indonesia he ________ to visit the temple in Thanjavur was wishing is wishing wished had wished ,Tenses,187 Threads of a process share global variables but not heap heap but not global variables neither global variables nor heap both heap and global variables ,Threads,188 A thread is usually defined as a light weight process because an Operating System OS maintains smaller data structure for a thread than for a process In relation to this which of the following statement is correct OS maintains only scheduling and accounting information for each thread OS maintains only CPU registers for each thread OS does not maintain virtual memory state for each thread OS does not maintain a separate stack for each thread ,Threads,188 A thread is usually defined as a light weight process because an Operating System OS maintains smaller data structure for a thread than for a process In relation to this which of the following statement is correct OS maintains only scheduling and accounting information for each thread OS maintains only CPU registers for each thread OS does not maintain virtual memory state for each thread OS does not maintain a separate stack for each thread ,Threads,188 Consider the following statements with respect to user level threads and kernel supported threads context switch is faster with kernel supported threads for user level threads a system call can block the entire process Kernel supported threads can be scheduled independently User level threads are transparent to the kernel Which of the above statements are true II III and IV only II and III only I and III only I and II only ,Threads,188 Consider the following statements with respect to user level threads and kernel supported threads context switch is faster with kernel supported threads for user level threads a system call can block the entire process Kernel supported threads can be scheduled independently User level threads are transparent to the kernel Which of the above statements are true II III and IV only II and III only I and III only I and II only ,Threads,188 Consider the following statements with respect to user level threads and kernel supported threads context switch is faster with kernel supported threads for user level threads a system call can block the entire process Kernel supported threads can be scheduled independently User level threads are transparent to the kernel Which of the above statements are true II III and IV only II and III only I and III only I and II only ,Threads,188 Consider the following statements with respect to user level threads and kernel supported threads context switch is faster with kernel supported threads for user level threads a system call can block the entire process Kernel supported threads can be scheduled independently User level threads are transparent to the kernel Which of the above statements are true II III and IV only II and III only I and III only I and II only ,Threads,188 Consider the following statements about user level threads and kernel level threads Which one of the following statements is FALSE Context switch time is longer for kernel level threads than for user level threads User level threads do not need any hardware support Related kernel level threads can be scheduled on different processors in a multi processor system Blocking one kernel level thread blocks all related threads ,Threads,188 A thread is usually defined as a light weight process because an Operating System OS maintains smaller data structure for a thread than for a process In relation to this which of the following statement is correct OS maintains only scheduling and accounting information for each thread OS maintains only CPU registers for each thread OS does not maintain virtual memory state for each thread OS does not maintain a separate stack for each thread ,Threads,188 A thread is usually defined as a light weight process because an Operating System OS maintains smaller data structure for a thread than for a process In relation to this which of the following statement is correct OS maintains only scheduling and accounting information for each thread OS maintains only CPU registers for each thread OS does not maintain virtual memory state for each thread OS does not maintain a separate stack for each thread ,Threads,188 Consider the following statements with respect to user level threads and kernel supported threads context switch is faster with kernel supported threads for user level threads a system call can block the entire process Kernel supported threads can be scheduled independently User level threads are transparent to the kernel Which of the above statements are true II III and IV only II and III only I and III only I and II only ,Threads,188 In a database system unique timestamps are assigned to each transaction using Lamport s logical clock Let TS T_ 1 and TS T_ 2 be the timestamps of transactions T_ 1 and T_ 2 respectively Besides T_ 1 holds a lock on the resource R and T_ 2 has requested a conflicting lock on the same resource R The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp if TS T_ 2 lt TS T_ 1 then T_ 1 is killed else T_ 2 waits Assume any transaction that is not killed terminates eventually Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks The database system is both deadlock free and starvation free The database system is deadlock free but not starvation free The database system is starvation free but not deadlock free The database system is neither deadlock free nor starvation free ,Timestamp Ordering,189 In a database system unique timestamps are assigned to each transaction using Lamport s logical clock Let TS T_ 1 and TS T_ 2 be the timestamps of transactions T_ 1 and T_ 2 respectively Besides T_ 1 holds a lock on the resource R and T_ 2 has requested a conflicting lock on the same resource R The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp if TS T_ 2 lt TS T_ 1 then T_ 1 is killed else T_ 2 waits Assume any transaction that is not killed terminates eventually Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks The database system is both deadlock free and starvation free The database system is deadlock free but not starvation free The database system is starvation free but not deadlock free The database system is neither deadlock free nor starvation free ,Timestamp Ordering,189 In a database system unique timestamps are assigned to each transaction using Lamport s logical clock Let TS T_ 1 and TS T_ 2 be the timestamps of transactions T_ 1 and T_ 2 respectively Besides T_ 1 holds a lock on the resource R and T_ 2 has requested a conflicting lock on the same resource R The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp if TS T_ 2 lt TS T_ 1 then T_ 1 is killed else T_ 2 waits Assume any transaction that is not killed terminates eventually Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks The database system is both deadlock free and starvation free The database system is deadlock free but not starvation free The database system is starvation free but not deadlock free The database system is neither deadlock free nor starvation free ,Timestamp Ordering,189 In a database system unique timestamps are assigned to each transaction using Lamport s logical clock Let TS T_ 1 and TS T_ 2 be the timestamps of transactions T_ 1 and T_ 2 respectively Besides T_ 1 holds a lock on the resource R and T_ 2 has requested a conflicting lock on the same resource R The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp if TS T_ 2 lt TS T_ 1 then T_ 1 is killed else T_ 2 waits Assume any transaction that is not killed terminates eventually Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks The database system is both deadlock free and starvation free The database system is deadlock free but not starvation free The database system is starvation free but not deadlock free The database system is neither deadlock free nor starvation free ,Timestamp Ordering,189 In a database system unique timestamps are assigned to each transaction using Lamport s logical clock Let TS T_ 1 and TS T_ 2 be the timestamps of transactions T_ 1 and T_ 2 respectively Besides T_ 1 holds a lock on the resource R and T_ 2 has requested a conflicting lock on the same resource R The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp if TS T_ 2 lt TS T_ 1 then T_ 1 is killed else T_ 2 waits Assume any transaction that is not killed terminates eventually Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks The database system is both deadlock free and starvation free The database system is deadlock free but not starvation free The database system is starvation free but not deadlock free The database system is neither deadlock free nor starvation free ,Timestamp Ordering,189 In a database system unique timestamps are assigned to each transaction using Lamport s logical clock Let TS T_ 1 and TS T_ 2 be the timestamps of transactions T_ 1 and T_ 2 respectively Besides T_ 1 holds a lock on the resource R and T_ 2 has requested a conflicting lock on the same resource R The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp if TS T_ 2 lt TS T_ 1 then T_ 1 is killed else T_ 2 waits Assume any transaction that is not killed terminates eventually Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks The database system is both deadlock free and starvation free The database system is deadlock free but not starvation free The database system is starvation free but not deadlock free The database system is neither deadlock free nor starvation free ,Timestamp Ordering,189 In a database system unique timestamps are assigned to each transaction using Lamport s logical clock Let TS T_ 1 and TS T_ 2 be the timestamps of transactions T_ 1 and T_ 2 respectively Besides T_ 1 holds a lock on the resource R and T_ 2 has requested a conflicting lock on the same resource R The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp if TS T_ 2 lt TS T_ 1 then T_ 1 is killed else T_ 2 waits Assume any transaction that is not killed terminates eventually Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks The database system is both deadlock free and starvation free The database system is deadlock free but not starvation free The database system is starvation free but not deadlock free The database system is neither deadlock free nor starvation free ,Timestamp Ordering,189 In a database system unique timestamps are assigned to each transaction using Lamport s logical clock Let TS T_ 1 and TS T_ 2 be the timestamps of transactions T_ 1 and T_ 2 respectively Besides T_ 1 holds a lock on the resource R and T_ 2 has requested a conflicting lock on the same resource R The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp if TS T_ 2 lt TS T_ 1 then T_ 1 is killed else T_ 2 waits Assume any transaction that is not killed terminates eventually Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks The database system is both deadlock free and starvation free The database system is deadlock free but not starvation free The database system is starvation free but not deadlock free The database system is neither deadlock free nor starvation free ,Timestamp Ordering,189 In a database system unique timestamps are assigned to each transaction using Lamport s logical clock Let TS T_ 1 and TS T_ 2 be the timestamps of transactions T_ 1 and T_ 2 respectively Besides T_ 1 holds a lock on the resource R and T_ 2 has requested a conflicting lock on the same resource R The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp if TS T_ 2 lt TS T_ 1 then T_ 1 is killed else T_ 2 waits Assume any transaction that is not killed terminates eventually Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks The database system is both deadlock free and starvation free The database system is deadlock free but not starvation free The database system is starvation free but not deadlock free The database system is neither deadlock free nor starvation free ,Timestamp Ordering,189 In a database system unique timestamps are assigned to each transaction using Lamport s logical clock Let TS T_ 1 and TS T_ 2 be the timestamps of transactions T_ 1 and T_ 2 respectively Besides T_ 1 holds a lock on the resource R and T_ 2 has requested a conflicting lock on the same resource R The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp if TS T_ 2 lt TS T_ 1 then T_ 1 is killed else T_ 2 waits Assume any transaction that is not killed terminates eventually Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks The database system is both deadlock free and starvation free The database system is deadlock free but not starvation free The database system is starvation free but not deadlock free The database system is neither deadlock free nor starvation free ,Timestamp Ordering,189 In a database system unique timestamps are assigned to each transaction using Lamport s logical clock Let TS T_ 1 and TS T_ 2 be the timestamps of transactions T_ 1 and T_ 2 respectively Besides T_ 1 holds a lock on the resource R and T_ 2 has requested a conflicting lock on the same resource R The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp if TS T_ 2 lt TS T_ 1 then T_ 1 is killed else T_ 2 waits Assume any transaction that is not killed terminates eventually Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks The database system is both deadlock free and starvation free The database system is deadlock free but not starvation free The database system is starvation free but not deadlock free The database system is neither deadlock free nor starvation free ,Timestamp Ordering,189 In a database system unique timestamps are assigned to each transaction using Lamport s logical clock Let TS T_ 1 and TS T_ 2 be the timestamps of transactions T_ 1 and T_ 2 respectively Besides T_ 1 holds a lock on the resource R and T_ 2 has requested a conflicting lock on the same resource R The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp if TS T_ 2 lt TS T_ 1 then T_ 1 is killed else T_ 2 waits Assume any transaction that is not killed terminates eventually Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks The database system is both deadlock free and starvation free The database system is deadlock free but not starvation free The database system is starvation free but not deadlock free The database system is neither deadlock free nor starvation free ,Timestamp Ordering,189 In a database system unique timestamps are assigned to each transaction using Lamport s logical clock Let TS T_ 1 and TS T_ 2 be the timestamps of transactions T_ 1 and T_ 2 respectively Besides T_ 1 holds a lock on the resource R and T_ 2 has requested a conflicting lock on the same resource R The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp if TS T_ 2 lt TS T_ 1 then T_ 1 is killed else T_ 2 waits Assume any transaction that is not killed terminates eventually Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks The database system is both deadlock free and starvation free The database system is deadlock free but not starvation free The database system is starvation free but not deadlock free The database system is neither deadlock free nor starvation free ,Timestamp Ordering,189 In a database system unique timestamps are assigned to each transaction using Lamport s logical clock Let TS T_ 1 and TS T_ 2 be the timestamps of transactions T_ 1 and T_ 2 respectively Besides T_ 1 holds a lock on the resource R and T_ 2 has requested a conflicting lock on the same resource R The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp if TS T_ 2 lt TS T_ 1 then T_ 1 is killed else T_ 2 waits Assume any transaction that is not killed terminates eventually Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks The database system is both deadlock free and starvation free The database system is deadlock free but not starvation free The database system is starvation free but not deadlock free The database system is neither deadlock free nor starvation free ,Timestamp Ordering,189 For a host machine that uses the token bucket algorithm for congestion control the token bucket has a capacity of 1 mega byte and the maximum output rate is 20 mega bytes per second Tokens arrive at a rate to sustain output at a rate of 10 mega bytes per second The token bucket is currently full and the machine needs to send 12 mega bytes of data The minimum time required to transmit the data is _____________ seconds ,Token Bucket,190 A computer on a 10 Mbps network is regulated by a token bucket The token bucket is filled at a rate of 2 Mbps It is initially filled to capacity with 16 Megabits What is the maximum duration for which the computer can transmit at the full 10 Mbps 1 6 seconds 2 seconds 5 seconds 8 seconds ,Token Bucket,190 A computer on a 10 Mbps network is regulated by a token bucket The token bucket is filled at a rate of 2 Mbps It is initially filled to capacity with 16 Megabits What is the maximum duration for which the computer can transmit at the full 10 Mbps 1 6 seconds 2 seconds 5 seconds 8 seconds ,Token Bucket,190 A computer on a 10 Mbps network is regulated by a token bucket The token bucket is filled at a rate of 2 Mbps It is initially filled to capacity with 16 Megabits What is the maximum duration for which the computer can transmit at the full 10 Mbps 1 6 seconds 2 seconds 5 seconds 8 seconds ,Token Bucket,190 For a host machine that uses the token bucket algorithm for congestion control the token bucket has a capacity of 1 mega byte and the maximum output rate is 20 mega bytes per second Tokens arrive at a rate to sustain output at a rate of 10 mega bytes per second The token bucket is currently full and the machine needs to send 12 mega bytes of data The minimum time required to transmit the data is _____________ seconds ,Token Bucket,190 A computer on a 10 Mbps network is regulated by a token bucket The token bucket is filled at a rate of 2 Mbps It is initially filled to capacity with 16 Megabits What is the maximum duration for which the computer can transmit at the full 10 Mbps 1 6 seconds 2 seconds 5 seconds 8 seconds ,Token Bucket,190 For a host machine that uses the token bucket algorithm for congestion control the token bucket has a capacity of 1 mega byte and the maximum output rate is 20 mega bytes per second Tokens arrive at a rate to sustain output at a rate of 10 mega bytes per second The token bucket is currently full and the machine needs to send 12 mega bytes of data The minimum time required to transmit the data is _____________ seconds ,Token Bucket,190 A computer on a 10 Mbps network is regulated by a token bucket The token bucket is filled at a rate of 2 Mbps It is initially filled to capacity with 16 Megabits What is the maximum duration for which the computer can transmit at the full 10 Mbps 1 6 seconds 2 seconds 5 seconds 8 seconds ,Token Bucket,190 A computer on a 10 Mbps network is regulated by a token bucket The token bucket is filled at a rate of 2 Mbps It is initially filled to capacity with 16 Megabits What is the maximum duration for which the computer can transmit at the full 10 Mbps 1 6 seconds 2 seconds 5 seconds 8 seconds ,Token Bucket,190 For a host machine that uses the token bucket algorithm for congestion control the token bucket has a capacity of 1 mega byte and the maximum output rate is 20 mega bytes per second Tokens arrive at a rate to sustain output at a rate of 10 mega bytes per second The token bucket is currently full and the machine needs to send 12 mega bytes of data The minimum time required to transmit the data is _____________ seconds ,Token Bucket,190 A computer on a 10 Mbps network is regulated by a token bucket The token bucket is filled at a rate of 2 Mbps It is initially filled to capacity with 16 Megabits What is the maximum duration for which the computer can transmit at the full 10 Mbps 1 6 seconds 2 seconds 5 seconds 8 seconds ,Token Bucket,190 For a host machine that uses the token bucket algorithm for congestion control the token bucket has a capacity of 1 mega byte and the maximum output rate is 20 mega bytes per second Tokens arrive at a rate to sustain output at a rate of 10 mega bytes per second The token bucket is currently full and the machine needs to send 12 mega bytes of data The minimum time required to transmit the data is _____________ seconds ,Token Bucket,190 For a host machine that uses the token bucket algorithm for congestion control the token bucket has a capacity of 1 mega byte and the maximum output rate is 20 mega bytes per second Tokens arrive at a rate to sustain output at a rate of 10 mega bytes per second The token bucket is currently full and the machine needs to send 12 mega bytes of data The minimum time required to transmit the data is _____________ seconds ,Token Bucket,190 Which level of locking provides the highest degree of concurrency in a relational database Page Table Row Page table and row level locking allow the same degree of concurrency ,Transaction And Concurrency,191 Which level of locking provides the highest degree of concurrency in a relational database Page Table Row Page table and row level locking allow the same degree of concurrency ,Transaction And Concurrency,191 Which level of locking provides the highest degree of concurrency in a relational database Page Table Row Page table and row level locking allow the same degree of concurrency ,Transaction And Concurrency,191 Which level of locking provides the highest degree of concurrency in a relational database Page Table Row Page table and row level locking allow the same degree of concurrency ,Transaction And Concurrency,191 Which level of locking provides the highest degree of concurrency in a relational database Page Table Row Page table and row level locking allow the same degree of concurrency ,Transaction And Concurrency,191 Which level of locking provides the highest degree of concurrency in a relational database Page Table Row Page table and row level locking allow the same degree of concurrency ,Transaction And Concurrency,191 Which level of locking provides the highest degree of concurrency in a relational database Page Table Row Page table and row level locking allow the same degree of concurrency ,Transaction And Concurrency,191 Which level of locking provides the highest degree of concurrency in a relational database Page Table Row Page table and row level locking allow the same degree of concurrency ,Transaction And Concurrency,191 Which level of locking provides the highest degree of concurrency in a relational database Page Table Row Page table and row level locking allow the same degree of concurrency ,Transaction And Concurrency,191 Which level of locking provides the highest degree of concurrency in a relational database Page Table Row Page table and row level locking allow the same degree of concurrency ,Transaction And Concurrency,191 Which level of locking provides the highest degree of concurrency in a relational database Page Table Row Page table and row level locking allow the same degree of concurrency ,Transaction And Concurrency,191 Which level of locking provides the highest degree of concurrency in a relational database Page Table Row Page table and row level locking allow the same degree of concurrency ,Transaction And Concurrency,191 Which level of locking provides the highest degree of concurrency in a relational database Page Table Row Page table and row level locking allow the same degree of concurrency ,Transaction And Concurrency,191 Which level of locking provides the highest degree of concurrency in a relational database Page Table Row Page table and row level locking allow the same degree of concurrency ,Transaction And Concurrency,191 Consider two transactions T_1 and T_2 and four schedules S_1 S_2 S_3 S_4 of T_1 and T_2 as given below T_1 R_1 x W_1 x W_1 y T_2 R_2 x R_2 y W_2 y S_1 R_1 x R_2 x R_2 y W_1 x W_1 y W_2 y S_2 R_1 x R_2 x R_2 y W_1 x W_2 y W_1 y S_3 R_1 x W_1 x R_2 x W_1 y R_2 y W_2 y S_4 R_2 x R_2 y R_1 x W_1 x W_1 y W_2 y Which of the above schedules are conflict serializable S_1 ext and S_2 S_2 ext and S_3 S_3 only S_4 only ,Transactions,192 Fig 7 shows a B tree where only key values are indicated in the records Each block can hold upto three records A record with a key value 34 is inserted into the B tree Obtain the modified B tree after insertion ,Tree,193 Fig 7 shows a B tree where only key values are indicated in the records Each block can hold upto three records A record with a key value 34 is inserted into the B tree Obtain the modified B tree after insertion ,Tree,193 Fig 7 shows a B tree where only key values are indicated in the records Each block can hold upto three records A record with a key value 34 is inserted into the B tree Obtain the modified B tree after insertion ,Tree,193 Fig 7 shows a B tree where only key values are indicated in the records Each block can hold upto three records A record with a key value 34 is inserted into the B tree Obtain the modified B tree after insertion ,Tree,193 Fig 7 shows a B tree where only key values are indicated in the records Each block can hold upto three records A record with a key value 34 is inserted into the B tree Obtain the modified B tree after insertion ,Tree,193 Fig 7 shows a B tree where only key values are indicated in the records Each block can hold upto three records A record with a key value 34 is inserted into the B tree Obtain the modified B tree after insertion ,Tree,193 Fig 7 shows a B tree where only key values are indicated in the records Each block can hold upto three records A record with a key value 34 is inserted into the B tree Obtain the modified B tree after insertion ,Tree,193 Fig 7 shows a B tree where only key values are indicated in the records Each block can hold upto three records A record with a key value 34 is inserted into the B tree Obtain the modified B tree after insertion ,Tree,193 Fig 7 shows a B tree where only key values are indicated in the records Each block can hold upto three records A record with a key value 34 is inserted into the B tree Obtain the modified B tree after insertion ,Tree,193 Fig 7 shows a B tree where only key values are indicated in the records Each block can hold upto three records A record with a key value 34 is inserted into the B tree Obtain the modified B tree after insertion ,Tree,193 Fig 7 shows a B tree where only key values are indicated in the records Each block can hold upto three records A record with a key value 34 is inserted into the B tree Obtain the modified B tree after insertion ,Tree,193 Fig 7 shows a B tree where only key values are indicated in the records Each block can hold upto three records A record with a key value 34 is inserted into the B tree Obtain the modified B tree after insertion ,Tree,193 Fig 7 shows a B tree where only key values are indicated in the records Each block can hold upto three records A record with a key value 34 is inserted into the B tree Obtain the modified B tree after insertion ,Tree,193 Fig 7 shows a B tree where only key values are indicated in the records Each block can hold upto three records A record with a key value 34 is inserted into the B tree Obtain the modified B tree after insertion ,Tree,193 Consider the following 2 3 4 tree i e B tree with a minimum degree of two in which each data item is a letter The usual alphabetical ordering of letters is used in constructing the tree What is the result of inserting G in the above tree None of the above ,Trees,194 Consider the pseudocode given below The function DoSomething takes as argument a pointer to the root of an arbitrary tree represented by the leftMostChild rightSibling representation Each node of the tree is of type treeNode ypedef struct treeNode treeptr struct treeNode treeptr leftMostChild rightSibling int DoSomething treeptr tree int value 0 if tree NULL if tree gt leftMostChild NULL value 1 else value DoSomething tree gt leftMostChild value value DoSomething tree gt rightSibling return value When the pointer to the root of a tree is passed as the argument to DoSomething the value returned by the function corresponds to the number of internal nodes in the tree height of the tree number of nodes without a right sibling in the tree number of leaf nodes in the tree ,Trees,194 The aim of the following question is to prove that the language M M is the code of the Turing Machine which irrespective of the input halts and outputs a 1 is undecidable This is to be done by reducing from the language M x M halts on x which is known to be undecidable In parts a and b describe the 2 main steps in the construction of M In part c describe the key property which relates the behaviour of M on its input w to the behaviour of M on x On input w what is the first step that M must make On input w based on the outcome of the first step what is the second step M must make What key property relates the behaviour of M on w to the behaviour of M on x ,Turing Machine,195 L_1 is a recursively enumerable language over Sigma An algorithm A effectively enumerates its words as omega_1 omega_2 omega_3 dots Define another language L_2 over Sigma cup left ext right as left w_i ext w_j mid w_i w_j in L_1 i lt j right Here is new symbol Consider the following assertions S_1 L_1 is recursive implies L_2 is recursive S_2 L_2 is recursive implies L_1 is recursive Which of the following statements is true Both S_1 and S_2 are true S_1 is true but S_2 is not necessarily true S_2 is true but S_1 is not necessarily true Neither is necessarily true ,Turing Machine,195 A single tape Turing Machine M has two states q0 and q1 of which q0 is the starting state The tape alphabet of M is 0 1 B and its input alphabet is 0 1 The symbol B is the blank symbol used to indicate end of an input string The transition function of M is described in the following table 0 1 B q0 q1 1 R q1 1 R Halt q1 q1 1 R q0 1 L q0 B L The table is interpreted as illustrated below The entry q1 1 R in row q0 and column 1 signifies that if M is in state q0 and reads 1 on the current page square then it writes 1 on the same tape square moves its tape head one position to the right and transitions to state q1 Which of the following statements is true about M M does not halt on any string in 0 1 M does not halt on any string in 00 1 M halts on all strings ending in a 0 M halts on all strings ending in a 1 ,Turing Machine,195 Let a decision problem X be defined as follows X Given a Turing machine M over Sigma and any word w in Sigma does M loop forever on w You may assume that the halting problem of Turing machine is undecidable but partially decidable Show that X is undecidable Show that X is not even partially decidable ,Turing Machine,195 Let langle M rangle be the encoding of a Turing machine as a string over Sigma left 0 1 right Let L left langle M rangle mid M ext is a Turing machine ext that accepts a string of length 2014 right Then L is decidable and recursively enumerable undecidable but recursively enumerable undecidable and not recursively enumerable decidable but not recursively enumerable ,Turing Machine,195 L_1 is a recursively enumerable language over Sigma An algorithm A effectively enumerates its words as omega_1 omega_2 omega_3 dots Define another language L_2 over Sigma cup left ext right as left w_i ext w_j mid w_i w_j in L_1 i lt j right Here is new symbol Consider the following assertions S_1 L_1 is recursive implies L_2 is recursive S_2 L_2 is recursive implies L_1 is recursive Which of the following statements is true Both S_1 and S_2 are true S_1 is true but S_2 is not necessarily true S_2 is true but S_1 is not necessarily true Neither is necessarily true ,Turing Machine,195 A single tape Turing Machine M has two states q0 and q1 of which q0 is the starting state The tape alphabet of M is 0 1 B and its input alphabet is 0 1 The symbol B is the blank symbol used to indicate end of an input string The transition function of M is described in the following table 0 1 B q0 q1 1 R q1 1 R Halt q1 q1 1 R q0 1 L q0 B L The table is interpreted as illustrated below The entry q1 1 R in row q0 and column 1 signifies that if M is in state q0 and reads 1 on the current page square then it writes 1 on the same tape square moves its tape head one position to the right and transitions to state q1 Which of the following statements is true about M M does not halt on any string in 0 1 M does not halt on any string in 00 1 M halts on all strings ending in a 0 M halts on all strings ending in a 1 ,Turing Machine,195 Consider the following languages L_ 1 left left langle M right rangle mid M ext takes at least 2016 steps on some input right L_ 2 left left langle M right rangle mid M ext takes at least 2016 steps on all inputs right and L_ 3 left left langle M right rangle mid M ext accepts epsilon right where for each Turing machine M left langle M right rangle denotes a specific encoding of M Which one of the following is TRUE L_ 1 is recursive and L_ 2 L_ 3 are not recursive L_ 2 is recursive and L_ 1 L_ 3 are not recursive L_ 1 L_ 2 are recursive and L_ 3 is not recursive L_ 1 L_ 2 L_ 3 are recursive ,Turing Machine,195 Consider socket API on a Linux machine that supports connected UDP sockets A connected UDP socket is a UDP socket on which connect function has already been called Which of the following statements is are CORRECT A connected UDP socket can be used to communicate with multiple peers simultaneously A process can successfully call connect function again for an already connected UDP socket I only II only Both I and II Neither I nor II ,Udp,196 A program on machine X attempts to open a UDP connection to port 5376 on a machine Y and a TCP connection to port 8632 on machine Z However there are no applications listening at the corresponding ports on Y and Z An ICMP Port Unreachable error will be generated by Y but not Z Z but not Y Neither Y nor Z Both Y and Z ,Udp,196 Consider socket API on a Linux machine that supports connected UDP sockets A connected UDP socket is a UDP socket on which connect function has already been called Which of the following statements is are CORRECT A connected UDP socket can be used to communicate with multiple peers simultaneously A process can successfully call connect function again for an already connected UDP socket I only II only Both I and II Neither I nor II ,Udp,196 Packets of the same session may be routed through different paths in TCP but not UDP TCP and UDP UDP but not TCP Neither TCP nor UDP ,Udp,196 Consider socket API on a Linux machine that supports connected UDP sockets A connected UDP socket is a UDP socket on which connect function has already been called Which of the following statements is are CORRECT A connected UDP socket can be used to communicate with multiple peers simultaneously A process can successfully call connect function again for an already connected UDP socket I only II only Both I and II Neither I nor II ,Udp,196 Consider socket API on a Linux machine that supports connected UDP sockets A connected UDP socket is a UDP socket on which connect function has already been called Which of the following statements is are CORRECT A connected UDP socket can be used to communicate with multiple peers simultaneously A process can successfully call connect function again for an already connected UDP socket I only II only Both I and II Neither I nor II ,Udp,196 The transport layer protocols used for real time multimedia file transfer DNS and email respectively are A TCP UDP UDP and TCP B UDP TCP TCP and UDP C UDP TCP UDP and TCP D TCP UDP TCP and UDP,Udp,196 A program on machine X attempts to open a UDP connection to port 5376 on a machine Y and a TCP connection to port 8632 on machine Z However there are no applications listening at the corresponding ports on Y and Z An ICMP Port Unreachable error will be generated by Y but not Z Z but not Y Neither Y nor Z Both Y and Z ,Udp,196 A program on machine X attempts to open a UDP connection to port 5376 on a machine Y and a TCP connection to port 8632 on machine Z However there are no applications listening at the corresponding ports on Y and Z An ICMP Port Unreachable error will be generated by Y but not Z Z but not Y Neither Y nor Z Both Y and Z ,Udp,196 A program on machine X attempts to open a UDP connection to port 5376 on a machine Y and a TCP connection to port 8632 on machine Z However there are no applications listening at the corresponding ports on Y and Z An ICMP Port Unreachable error will be generated by Y but not Z Z but not Y Neither Y nor Z Both Y and Z ,Udp,196 Consider socket API on a Linux machine that supports connected UDP sockets A connected UDP socket is a UDP socket on which connect function has already been called Which of the following statements is are CORRECT A connected UDP socket can be used to communicate with multiple peers simultaneously A process can successfully call connect function again for an already connected UDP socket I only II only Both I and II Neither I nor II ,Udp,196 Suppose you break a stick of unit length at a point chosen uniformly at random Then the expected length of the shorter stick is ________ ,Uniform Distribution,197 A point is randomly selected with uniform probability in the X Y plane within the rectangle with corners at 0 0 1 0 1 2 and 0 2 If p is the length of the position vector of the point the expected value of p 2 is left dfrac 2 3 right quad 1 left dfrac 4 3 right left dfrac 5 3 right ,Uniform Distribution,197 Suppose you break a stick of unit length at a point chosen uniformly at random Then the expected length of the shorter stick is ________ ,Uniform Distribution,197 A point is randomly selected with uniform probability in the X Y plane within the rectangle with corners at 0 0 1 0 1 2 and 0 2 If p is the length of the position vector of the point the expected value of p 2 is left dfrac 2 3 right quad 1 left dfrac 4 3 right left dfrac 5 3 right ,Uniform Distribution,197 A point is randomly selected with uniform probability in the X Y plane within the rectangle with corners at 0 0 1 0 1 2 and 0 2 If p is the length of the position vector of the point the expected value of p 2 is left dfrac 2 3 right quad 1 left dfrac 4 3 right left dfrac 5 3 right ,Uniform Distribution,197 Consider a selection of the form sigma_ A leq 100 r where r is a relation with 1000 tuples Assume that the attribute values for A among the tuples are uniformly distributed in the interval 0 500 Which one of the following options is the best estimate of the number of tuples returned by the given selection query 50 100 150 200 ,Uniform Distribution,197 Suppose you break a stick of unit length at a point chosen uniformly at random Then the expected length of the shorter stick is ________ ,Uniform Distribution,197 A point is randomly selected with uniform probability in the X Y plane within the rectangle with corners at 0 0 1 0 1 2 and 0 2 If p is the length of the position vector of the point the expected value of p 2 is left dfrac 2 3 right quad 1 left dfrac 4 3 right left dfrac 5 3 right ,Uniform Distribution,197 Consider a selection of the form sigma_ A leq 100 r where r is a relation with 1000 tuples Assume that the attribute values for A among the tuples are uniformly distributed in the interval 0 500 Which one of the following options is the best estimate of the number of tuples returned by the given selection query 50 100 150 200 ,Uniform Distribution,197 Consider a selection of the form sigma_ A leq 100 r where r is a relation with 1000 tuples Assume that the attribute values for A among the tuples are uniformly distributed in the interval 0 500 Which one of the following options is the best estimate of the number of tuples returned by the given selection query 50 100 150 200 ,Uniform Distribution,197 A point is randomly selected with uniform probability in the X Y plane within the rectangle with corners at 0 0 1 0 1 2 and 0 2 If p is the length of the position vector of the point the expected value of p 2 is left dfrac 2 3 right quad 1 left dfrac 4 3 right left dfrac 5 3 right ,Uniform Distribution,197 A point is randomly selected with uniform probability in the X Y plane within the rectangle with corners at 0 0 1 0 1 2 and 0 2 If p is the length of the position vector of the point the expected value of p 2 is left dfrac 2 3 right quad 1 left dfrac 4 3 right left dfrac 5 3 right ,Uniform Distribution,197 A user level process in Unix traps the signal sent on a Ctrl C input and has a signal handling routine that saves appropriate files before terminating the process When a Ctrl C input is given to this process what is the mode in which the signal handling routine executes User mode Kernel mode Superuser mode Privileged mode ,User Modes,198 A user level process in Unix traps the signal sent on a Ctrl C input and has a signal handling routine that saves appropriate files before terminating the process When a Ctrl C input is given to this process what is the mode in which the signal handling routine executes User mode Kernel mode Superuser mode Privileged mode ,User Modes,198 A user level process in Unix traps the signal sent on a Ctrl C input and has a signal handling routine that saves appropriate files before terminating the process When a Ctrl C input is given to this process what is the mode in which the signal handling routine executes User mode Kernel mode Superuser mode Privileged mode ,User Modes,198 A user level process in Unix traps the signal sent on a Ctrl C input and has a signal handling routine that saves appropriate files before terminating the process When a Ctrl C input is given to this process what is the mode in which the signal handling routine executes User mode Kernel mode Superuser mode Privileged mode ,User Modes,198 A user level process in Unix traps the signal sent on a Ctrl C input and has a signal handling routine that saves appropriate files before terminating the process When a Ctrl C input is given to this process what is the mode in which the signal handling routine executes User mode Kernel mode Superuser mode Privileged mode ,User Modes,198 A user level process in Unix traps the signal sent on a Ctrl C input and has a signal handling routine that saves appropriate files before terminating the process When a Ctrl C input is given to this process what is the mode in which the signal handling routine executes User mode Kernel mode Superuser mode Privileged mode ,User Modes,198 A user level process in Unix traps the signal sent on a Ctrl C input and has a signal handling routine that saves appropriate files before terminating the process When a Ctrl C input is given to this process what is the mode in which the signal handling routine executes User mode Kernel mode Superuser mode Privileged mode ,User Modes,198 A user level process in Unix traps the signal sent on a Ctrl C input and has a signal handling routine that saves appropriate files before terminating the process When a Ctrl C input is given to this process what is the mode in which the signal handling routine executes User mode Kernel mode Superuser mode Privileged mode ,User Modes,198 A user level process in Unix traps the signal sent on a Ctrl C input and has a signal handling routine that saves appropriate files before terminating the process When a Ctrl C input is given to this process what is the mode in which the signal handling routine executes User mode Kernel mode Superuser mode Privileged mode ,User Modes,198 A user level process in Unix traps the signal sent on a Ctrl C input and has a signal handling routine that saves appropriate files before terminating the process When a Ctrl C input is given to this process what is the mode in which the signal handling routine executes User mode Kernel mode Superuser mode Privileged mode ,User Modes,198 A user level process in Unix traps the signal sent on a Ctrl C input and has a signal handling routine that saves appropriate files before terminating the process When a Ctrl C input is given to this process what is the mode in which the signal handling routine executes User mode Kernel mode Superuser mode Privileged mode ,User Modes,198 A user level process in Unix traps the signal sent on a Ctrl C input and has a signal handling routine that saves appropriate files before terminating the process When a Ctrl C input is given to this process what is the mode in which the signal handling routine executes User mode Kernel mode Superuser mode Privileged mode ,User Modes,198 A user level process in Unix traps the signal sent on a Ctrl C input and has a signal handling routine that saves appropriate files before terminating the process When a Ctrl C input is given to this process what is the mode in which the signal handling routine executes User mode Kernel mode Superuser mode Privileged mode ,User Modes,198 A user level process in Unix traps the signal sent on a Ctrl C input and has a signal handling routine that saves appropriate files before terminating the process When a Ctrl C input is given to this process what is the mode in which the signal handling routine executes User mode Kernel mode Superuser mode Privileged mode ,User Modes,198 If V_1 and V_2 are 4 dimensional subspaces of a 6 dimensional vector space V then the smallest possible dimension of V_1 cap V_2 is _____ ,Vector Space,199 If V_1 and V_2 are 4 dimensional subspaces of a 6 dimensional vector space V then the smallest possible dimension of V_1 cap V_2 is _____ ,Vector Space,199 Consider the set of column vectors defined by X left x in R 3 mid x_1 x_2 x_3 0 ext where x T left x_1 x_2 x_3 right T right Which of the following is TRUE left left 1 1 0 right T left 1 0 1 right T right is a basis for the subspace X left left 1 1 0 right T left 1 0 1 right T right is a linearly independent set but it does not span X and therefore is not a basis of X X is not a subspace of R 3 None of the above ,Vector Space,199 Consider the set of column vectors defined by X left x in R 3 mid x_1 x_2 x_3 0 ext where x T left x_1 x_2 x_3 right T right Which of the following is TRUE left left 1 1 0 right T left 1 0 1 right T right is a basis for the subspace X left left 1 1 0 right T left 1 0 1 right T right is a linearly independent set but it does not span X and therefore is not a basis of X X is not a subspace of R 3 None of the above ,Vector Space,199 Consider the set of column vectors defined by X left x in R 3 mid x_1 x_2 x_3 0 ext where x T left x_1 x_2 x_3 right T right Which of the following is TRUE left left 1 1 0 right T left 1 0 1 right T right is a basis for the subspace X left left 1 1 0 right T left 1 0 1 right T right is a linearly independent set but it does not span X and therefore is not a basis of X X is not a subspace of R 3 None of the above ,Vector Space,199 If V_1 and V_2 are 4 dimensional subspaces of a 6 dimensional vector space V then the smallest possible dimension of V_1 cap V_2 is _____ ,Vector Space,199 Consider the set of column vectors defined by X left x in R 3 mid x_1 x_2 x_3 0 ext where x T left x_1 x_2 x_3 right T right Which of the following is TRUE left left 1 1 0 right T left 1 0 1 right T right is a basis for the subspace X left left 1 1 0 right T left 1 0 1 right T right is a linearly independent set but it does not span X and therefore is not a basis of X X is not a subspace of R 3 None of the above ,Vector Space,199 If V_1 and V_2 are 4 dimensional subspaces of a 6 dimensional vector space V then the smallest possible dimension of V_1 cap V_2 is _____ ,Vector Space,199 Let u and v be two vectors in R2 whose Euclidean norms satisfy left u right 2 left v right What is the value of alpha such that w u alpha v bisects the angle between u and v 2 frac 1 2 1 frac 1 2 ,Vector Space,199 Consider the set of column vectors defined by X left x in R 3 mid x_1 x_2 x_3 0 ext where x T left x_1 x_2 x_3 right T right Which of the following is TRUE left left 1 1 0 right T left 1 0 1 right T right is a basis for the subspace X left left 1 1 0 right T left 1 0 1 right T right is a linearly independent set but it does not span X and therefore is not a basis of X X is not a subspace of R 3 None of the above ,Vector Space,199 If V_1 and V_2 are 4 dimensional subspaces of a 6 dimensional vector space V then the smallest possible dimension of V_1 cap V_2 is _____ ,Vector Space,199 Let u and v be two vectors in R2 whose Euclidean norms satisfy left u right 2 left v right What is the value of alpha such that w u alpha v bisects the angle between u and v 2 frac 1 2 1 frac 1 2 ,Vector Space,199 Alexander turned his attention towards India since he had conquered Persia Which one of the statements below is logically valid and can be inferred from the above sentence Alexander would not have turned his attention towards India had he not conquered Persia Alexander was not ready to rest on his laurels and wanted to march to India Alexander was not completely in control of his army and could command it to move towards India Since Alexander s kingdom extended to Indian borders after the conquest of Persia he was keen to move further ,Verbal Reasoning,200 u201cWe lived in a culture that denied any merit to literary works considering them important only when they were handmaidens to something seemingly more urgent u2013 namely ideology This was a country where all gestures even the most private were interpreted in political terms u201d The author u2019s belief that ideology is not as important as literature is revealed by the word u2018culture u2019 u2018seemingly u2019 u2018urgent u2019 u2018political u2019 ,Verbal Reasoning,200 Alexander turned his attention towards India since he had conquered Persia Which one of the statements below is logically valid and can be inferred from the above sentence Alexander would not have turned his attention towards India had he not conquered Persia Alexander was not ready to rest on his laurels and wanted to march to India Alexander was not completely in control of his army and could command it to move towards India Since Alexander s kingdom extended to Indian borders after the conquest of Persia he was keen to move further ,Verbal Reasoning,200 Alexander turned his attention towards India since he had conquered Persia Which one of the statements below is logically valid and can be inferred from the above sentence Alexander would not have turned his attention towards India had he not conquered Persia Alexander was not ready to rest on his laurels and wanted to march to India Alexander was not completely in control of his army and could command it to move towards India Since Alexander s kingdom extended to Indian borders after the conquest of Persia he was keen to move further ,Verbal Reasoning,200 Alexander turned his attention towards India since he had conquered Persia Which one of the statements below is logically valid and can be inferred from the above sentence Alexander would not have turned his attention towards India had he not conquered Persia Alexander was not ready to rest on his laurels and wanted to march to India Alexander was not completely in control of his army and could command it to move towards India Since Alexander s kingdom extended to Indian borders after the conquest of Persia he was keen to move further ,Verbal Reasoning,200 u201cWe lived in a culture that denied any merit to literary works considering them important only when they were handmaidens to something seemingly more urgent u2013 namely ideology This was a country where all gestures even the most private were interpreted in political terms u201d The author u2019s belief that ideology is not as important as literature is revealed by the word u2018culture u2019 u2018seemingly u2019 u2018urgent u2019 u2018political u2019 ,Verbal Reasoning,200 Alexander turned his attention towards India since he had conquered Persia Which one of the statements below is logically valid and can be inferred from the above sentence Alexander would not have turned his attention towards India had he not conquered Persia Alexander was not ready to rest on his laurels and wanted to march to India Alexander was not completely in control of his army and could command it to move towards India Since Alexander s kingdom extended to Indian borders after the conquest of Persia he was keen to move further ,Verbal Reasoning,200 Alexander turned his attention towards India since he had conquered Persia Which one of the statements below is logically valid and can be inferred from the above sentence Alexander would not have turned his attention towards India had he not conquered Persia Alexander was not ready to rest on his laurels and wanted to march to India Alexander was not completely in control of his army and could command it to move towards India Since Alexander s kingdom extended to Indian borders after the conquest of Persia he was keen to move further ,Verbal Reasoning,200 Alexander turned his attention towards India since he had conquered Persia Which one of the statements below is logically valid and can be inferred from the above sentence Alexander would not have turned his attention towards India had he not conquered Persia Alexander was not ready to rest on his laurels and wanted to march to India Alexander was not completely in control of his army and could command it to move towards India Since Alexander s kingdom extended to Indian borders after the conquest of Persia he was keen to move further ,Verbal Reasoning,200 u201cWe lived in a culture that denied any merit to literary works considering them important only when they were handmaidens to something seemingly more urgent u2013 namely ideology This was a country where all gestures even the most private were interpreted in political terms u201d The author u2019s belief that ideology is not as important as literature is revealed by the word u2018culture u2019 u2018seemingly u2019 u2018urgent u2019 u2018political u2019 ,Verbal Reasoning,200 Alexander turned his attention towards India since he had conquered Persia Which one of the statements below is logically valid and can be inferred from the above sentence Alexander would not have turned his attention towards India had he not conquered Persia Alexander was not ready to rest on his laurels and wanted to march to India Alexander was not completely in control of his army and could command it to move towards India Since Alexander s kingdom extended to Indian borders after the conquest of Persia he was keen to move further ,Verbal Reasoning,200 Alexander turned his attention towards India since he had conquered Persia Which one of the statements below is logically valid and can be inferred from the above sentence Alexander would not have turned his attention towards India had he not conquered Persia Alexander was not ready to rest on his laurels and wanted to march to India Alexander was not completely in control of his army and could command it to move towards India Since Alexander s kingdom extended to Indian borders after the conquest of Persia he was keen to move further ,Verbal Reasoning,200 u201cWe lived in a culture that denied any merit to literary works considering them important only when they were handmaidens to something seemingly more urgent u2013 namely ideology This was a country where all gestures even the most private were interpreted in political terms u201d The author u2019s belief that ideology is not as important as literature is revealed by the word u2018culture u2019 u2018seemingly u2019 u2018urgent u2019 u2018political u2019 ,Verbal Reasoning,200 Let G be a simple graph with 20 vertices and 100 edges The size of the minimum vertex cover of G is 8 Then the size of the maximum independent set of G is 12 8 less than 8 more than 12 ,Vertex Cover,201 Let G be a simple graph with 20 vertices and 100 edges The size of the minimum vertex cover of G is 8 Then the size of the maximum independent set of G is 12 8 less than 8 more than 12 ,Vertex Cover,201 Let G be a simple graph with 20 vertices and 100 edges The size of the minimum vertex cover of G is 8 Then the size of the maximum independent set of G is 12 8 less than 8 more than 12 ,Vertex Cover,201 Let G be a simple graph with 20 vertices and 100 edges The size of the minimum vertex cover of G is 8 Then the size of the maximum independent set of G is 12 8 less than 8 more than 12 ,Vertex Cover,201 Let G be a simple graph with 20 vertices and 100 edges The size of the minimum vertex cover of G is 8 Then the size of the maximum independent set of G is 12 8 less than 8 more than 12 ,Vertex Cover,201 Let G be a simple graph with 20 vertices and 100 edges The size of the minimum vertex cover of G is 8 Then the size of the maximum independent set of G is 12 8 less than 8 more than 12 ,Vertex Cover,201 Let G be a simple graph with 20 vertices and 100 edges The size of the minimum vertex cover of G is 8 Then the size of the maximum independent set of G is 12 8 less than 8 more than 12 ,Vertex Cover,201 Let G be a simple graph with 20 vertices and 100 edges The size of the minimum vertex cover of G is 8 Then the size of the maximum independent set of G is 12 8 less than 8 more than 12 ,Vertex Cover,201 Let G be a simple graph with 20 vertices and 100 edges The size of the minimum vertex cover of G is 8 Then the size of the maximum independent set of G is 12 8 less than 8 more than 12 ,Vertex Cover,201 Let G be a simple graph with 20 vertices and 100 edges The size of the minimum vertex cover of G is 8 Then the size of the maximum independent set of G is 12 8 less than 8 more than 12 ,Vertex Cover,201 Let G be a simple graph with 20 vertices and 100 edges The size of the minimum vertex cover of G is 8 Then the size of the maximum independent set of G is 12 8 less than 8 more than 12 ,Vertex Cover,201 Let G be a simple graph with 20 vertices and 100 edges The size of the minimum vertex cover of G is 8 Then the size of the maximum independent set of G is 12 8 less than 8 more than 12 ,Vertex Cover,201 Let G be a simple graph with 20 vertices and 100 edges The size of the minimum vertex cover of G is 8 Then the size of the maximum independent set of G is 12 8 less than 8 more than 12 ,Vertex Cover,201 Let G be a simple graph with 20 vertices and 100 edges The size of the minimum vertex cover of G is 8 Then the size of the maximum independent set of G is 12 8 less than 8 more than 12 ,Vertex Cover,201 For the IEEE 802 11 MAC protocol for wireless communication which of the following statements is are TRUE I At least three non overlapping channels are available for transmissions II The RTS CTS mechanism is used for collision detection III Unicast frames are ACKed All I II and III I and III only II and III only II only ,Wifi,202 For the IEEE 802 11 MAC protocol for wireless communication which of the following statements is are TRUE I At least three non overlapping channels are available for transmissions II The RTS CTS mechanism is used for collision detection III Unicast frames are ACKed All I II and III I and III only II and III only II only ,Wifi,202 For the IEEE 802 11 MAC protocol for wireless communication which of the following statements is are TRUE I At least three non overlapping channels are available for transmissions II The RTS CTS mechanism is used for collision detection III Unicast frames are ACKed All I II and III I and III only II and III only II only ,Wifi,202 For the IEEE 802 11 MAC protocol for wireless communication which of the following statements is are TRUE I At least three non overlapping channels are available for transmissions II The RTS CTS mechanism is used for collision detection III Unicast frames are ACKed All I II and III I and III only II and III only II only ,Wifi,202 For the IEEE 802 11 MAC protocol for wireless communication which of the following statements is are TRUE I At least three non overlapping channels are available for transmissions II The RTS CTS mechanism is used for collision detection III Unicast frames are ACKed All I II and III I and III only II and III only II only ,Wifi,202 For the IEEE 802 11 MAC protocol for wireless communication which of the following statements is are TRUE I At least three non overlapping channels are available for transmissions II The RTS CTS mechanism is used for collision detection III Unicast frames are ACKed All I II and III I and III only II and III only II only ,Wifi,202 For the IEEE 802 11 MAC protocol for wireless communication which of the following statements is are TRUE I At least three non overlapping channels are available for transmissions II The RTS CTS mechanism is used for collision detection III Unicast frames are ACKed All I II and III I and III only II and III only II only ,Wifi,202 For the IEEE 802 11 MAC protocol for wireless communication which of the following statements is are TRUE I At least three non overlapping channels are available for transmissions II The RTS CTS mechanism is used for collision detection III Unicast frames are ACKed All I II and III I and III only II and III only II only ,Wifi,202 For the IEEE 802 11 MAC protocol for wireless communication which of the following statements is are TRUE I At least three non overlapping channels are available for transmissions II The RTS CTS mechanism is used for collision detection III Unicast frames are ACKed All I II and III I and III only II and III only II only ,Wifi,202 For the IEEE 802 11 MAC protocol for wireless communication which of the following statements is are TRUE I At least three non overlapping channels are available for transmissions II The RTS CTS mechanism is used for collision detection III Unicast frames are ACKed All I II and III I and III only II and III only II only ,Wifi,202 For the IEEE 802 11 MAC protocol for wireless communication which of the following statements is are TRUE I At least three non overlapping channels are available for transmissions II The RTS CTS mechanism is used for collision detection III Unicast frames are ACKed All I II and III I and III only II and III only II only ,Wifi,202 For the IEEE 802 11 MAC protocol for wireless communication which of the following statements is are TRUE I At least three non overlapping channels are available for transmissions II The RTS CTS mechanism is used for collision detection III Unicast frames are ACKed All I II and III I and III only II and III only II only ,Wifi,202 For the IEEE 802 11 MAC protocol for wireless communication which of the following statements is are TRUE I At least three non overlapping channels are available for transmissions II The RTS CTS mechanism is used for collision detection III Unicast frames are ACKed All I II and III I and III only II and III only II only ,Wifi,202 For the IEEE 802 11 MAC protocol for wireless communication which of the following statements is are TRUE I At least three non overlapping channels are available for transmissions II The RTS CTS mechanism is used for collision detection III Unicast frames are ACKed All I II and III I and III only II and III only II only ,Wifi,202 Select the pair of best expresses a relationship similar to that expressed in the pair Children Pediatrician Adult Orthopaedist Females Gynaecologist Kidney Nephrologist Skin Dermatologist ,Word Pairs,203 Select the pair of best expresses a relationship similar to that expressed in the pair Children Pediatrician Adult Orthopaedist Females Gynaecologist Kidney Nephrologist Skin Dermatologist ,Word Pairs,203 Select the pair of best expresses a relationship similar to that expressed in the pair Children Pediatrician Adult Orthopaedist Females Gynaecologist Kidney Nephrologist Skin Dermatologist ,Word Pairs,203 Select the pair of best expresses a relationship similar to that expressed in the pair Children Pediatrician Adult Orthopaedist Females Gynaecologist Kidney Nephrologist Skin Dermatologist ,Word Pairs,203 Select the pair of best expresses a relationship similar to that expressed in the pair Children Pediatrician Adult Orthopaedist Females Gynaecologist Kidney Nephrologist Skin Dermatologist ,Word Pairs,203 Select the pair of best expresses a relationship similar to that expressed in the pair Children Pediatrician Adult Orthopaedist Females Gynaecologist Kidney Nephrologist Skin Dermatologist ,Word Pairs,203 Select the pair of best expresses a relationship similar to that expressed in the pair Children Pediatrician Adult Orthopaedist Females Gynaecologist Kidney Nephrologist Skin Dermatologist ,Word Pairs,203 Select the pair of best expresses a relationship similar to that expressed in the pair Children Pediatrician Adult Orthopaedist Females Gynaecologist Kidney Nephrologist Skin Dermatologist ,Word Pairs,203 Select the pair of best expresses a relationship similar to that expressed in the pair Children Pediatrician Adult Orthopaedist Females Gynaecologist Kidney Nephrologist Skin Dermatologist ,Word Pairs,203 Select the pair of best expresses a relationship similar to that expressed in the pair Children Pediatrician Adult Orthopaedist Females Gynaecologist Kidney Nephrologist Skin Dermatologist ,Word Pairs,203 Select the pair of best expresses a relationship similar to that expressed in the pair Children Pediatrician Adult Orthopaedist Females Gynaecologist Kidney Nephrologist Skin Dermatologist ,Word Pairs,203 Select the pair of best expresses a relationship similar to that expressed in the pair Children Pediatrician Adult Orthopaedist Females Gynaecologist Kidney Nephrologist Skin Dermatologist ,Word Pairs,203 Select the pair of best expresses a relationship similar to that expressed in the pair Children Pediatrician Adult Orthopaedist Females Gynaecologist Kidney Nephrologist Skin Dermatologist ,Word Pairs,203 Select the pair of best expresses a relationship similar to that expressed in the pair Children Pediatrician Adult Orthopaedist Females Gynaecologist Kidney Nephrologist Skin Dermatologist ,Word Pairs,203 A transporter receives the same number of orders each day Currently he has some pending orders backlog to be shipped If he uses 7 trucks then at the end of the 4th day he can clear all the orders Alternatively if he uses only 3 trucks then all the orders are cleared at the end of the 10th day What is the minimum number of trucks required so that there will be no pending order at the end of 5th day A 4 B 5 C 6 D 7,Work Time,204 A transporter receives the same number of orders each day Currently he has some pending orders backlog to be shipped If he uses 7 trucks then at the end of the 4th day he can clear all the orders Alternatively if he uses only 3 trucks then all the orders are cleared at the end of the 10th day What is the minimum number of trucks required so that there will be no pending order at the end of 5th day A 4 B 5 C 6 D 7,Work Time,204 A transporter receives the same number of orders each day Currently he has some pending orders backlog to be shipped If he uses 7 trucks then at the end of the 4th day he can clear all the orders Alternatively if he uses only 3 trucks then all the orders are cleared at the end of the 10th day What is the minimum number of trucks required so that there will be no pending order at the end of 5th day A 4 B 5 C 6 D 7,Work Time,204 A transporter receives the same number of orders each day Currently he has some pending orders backlog to be shipped If he uses 7 trucks then at the end of the 4th day he can clear all the orders Alternatively if he uses only 3 trucks then all the orders are cleared at the end of the 10th day What is the minimum number of trucks required so that there will be no pending order at the end of 5th day A 4 B 5 C 6 D 7,Work Time,204 A transporter receives the same number of orders each day Currently he has some pending orders backlog to be shipped If he uses 7 trucks then at the end of the 4th day he can clear all the orders Alternatively if he uses only 3 trucks then all the orders are cleared at the end of the 10th day What is the minimum number of trucks required so that there will be no pending order at the end of 5th day A 4 B 5 C 6 D 7,Work Time,204 A transporter receives the same number of orders each day Currently he has some pending orders backlog to be shipped If he uses 7 trucks then at the end of the 4th day he can clear all the orders Alternatively if he uses only 3 trucks then all the orders are cleared at the end of the 10th day What is the minimum number of trucks required so that there will be no pending order at the end of 5th day A 4 B 5 C 6 D 7,Work Time,204 A transporter receives the same number of orders each day Currently he has some pending orders backlog to be shipped If he uses 7 trucks then at the end of the 4th day he can clear all the orders Alternatively if he uses only 3 trucks then all the orders are cleared at the end of the 10th day What is the minimum number of trucks required so that there will be no pending order at the end of 5th day A 4 B 5 C 6 D 7,Work Time,204 A transporter receives the same number of orders each day Currently he has some pending orders backlog to be shipped If he uses 7 trucks then at the end of the 4th day he can clear all the orders Alternatively if he uses only 3 trucks then all the orders are cleared at the end of the 10th day What is the minimum number of trucks required so that there will be no pending order at the end of 5th day A 4 B 5 C 6 D 7,Work Time,204 A transporter receives the same number of orders each day Currently he has some pending orders backlog to be shipped If he uses 7 trucks then at the end of the 4th day he can clear all the orders Alternatively if he uses only 3 trucks then all the orders are cleared at the end of the 10th day What is the minimum number of trucks required so that there will be no pending order at the end of 5th day A 4 B 5 C 6 D 7,Work Time,204 A transporter receives the same number of orders each day Currently he has some pending orders backlog to be shipped If he uses 7 trucks then at the end of the 4th day he can clear all the orders Alternatively if he uses only 3 trucks then all the orders are cleared at the end of the 10th day What is the minimum number of trucks required so that there will be no pending order at the end of 5th day A 4 B 5 C 6 D 7,Work Time,204 A transporter receives the same number of orders each day Currently he has some pending orders backlog to be shipped If he uses 7 trucks then at the end of the 4th day he can clear all the orders Alternatively if he uses only 3 trucks then all the orders are cleared at the end of the 10th day What is the minimum number of trucks required so that there will be no pending order at the end of 5th day A 4 B 5 C 6 D 7,Work Time,204 A transporter receives the same number of orders each day Currently he has some pending orders backlog to be shipped If he uses 7 trucks then at the end of the 4th day he can clear all the orders Alternatively if he uses only 3 trucks then all the orders are cleared at the end of the 10th day What is the minimum number of trucks required so that there will be no pending order at the end of 5th day A 4 B 5 C 6 D 7,Work Time,204 A transporter receives the same number of orders each day Currently he has some pending orders backlog to be shipped If he uses 7 trucks then at the end of the 4th day he can clear all the orders Alternatively if he uses only 3 trucks then all the orders are cleared at the end of the 10th day What is the minimum number of trucks required so that there will be no pending order at the end of 5th day A 4 B 5 C 6 D 7,Work Time,204 A transporter receives the same number of orders each day Currently he has some pending orders backlog to be shipped If he uses 7 trucks then at the end of the 4th day he can clear all the orders Alternatively if he uses only 3 trucks then all the orders are cleared at the end of the 10th day What is the minimum number of trucks required so that there will be no pending order at the end of 5th day A 4 B 5 C 6 D 7,Work Time,204 In the working set strategy which of the following is done by the operating system to prevent thrashing It initiates another process if there are enough extra frames It selects a process to suspend if the sum of the sizes of the working sets exceeds the total number of available frames I only II only Neither I nor II Both I and II ,Working Set,205 In the working set strategy which of the following is done by the operating system to prevent thrashing It initiates another process if there are enough extra frames It selects a process to suspend if the sum of the sizes of the working sets exceeds the total number of available frames I only II only Neither I nor II Both I and II ,Working Set,205 In the working set strategy which of the following is done by the operating system to prevent thrashing It initiates another process if there are enough extra frames It selects a process to suspend if the sum of the sizes of the working sets exceeds the total number of available frames I only II only Neither I nor II Both I and II ,Working Set,205 In the working set strategy which of the following is done by the operating system to prevent thrashing It initiates another process if there are enough extra frames It selects a process to suspend if the sum of the sizes of the working sets exceeds the total number of available frames I only II only Neither I nor II Both I and II ,Working Set,205 In the working set strategy which of the following is done by the operating system to prevent thrashing It initiates another process if there are enough extra frames It selects a process to suspend if the sum of the sizes of the working sets exceeds the total number of available frames I only II only Neither I nor II Both I and II ,Working Set,205 In the working set strategy which of the following is done by the operating system to prevent thrashing It initiates another process if there are enough extra frames It selects a process to suspend if the sum of the sizes of the working sets exceeds the total number of available frames I only II only Neither I nor II Both I and II ,Working Set,205 In the working set strategy which of the following is done by the operating system to prevent thrashing It initiates another process if there are enough extra frames It selects a process to suspend if the sum of the sizes of the working sets exceeds the total number of available frames I only II only Neither I nor II Both I and II ,Working Set,205 In the working set strategy which of the following is done by the operating system to prevent thrashing It initiates another process if there are enough extra frames It selects a process to suspend if the sum of the sizes of the working sets exceeds the total number of available frames I only II only Neither I nor II Both I and II ,Working Set,205 In the working set strategy which of the following is done by the operating system to prevent thrashing It initiates another process if there are enough extra frames It selects a process to suspend if the sum of the sizes of the working sets exceeds the total number of available frames I only II only Neither I nor II Both I and II ,Working Set,205 In the working set strategy which of the following is done by the operating system to prevent thrashing It initiates another process if there are enough extra frames It selects a process to suspend if the sum of the sizes of the working sets exceeds the total number of available frames I only II only Neither I nor II Both I and II ,Working Set,205 In the working set strategy which of the following is done by the operating system to prevent thrashing It initiates another process if there are enough extra frames It selects a process to suspend if the sum of the sizes of the working sets exceeds the total number of available frames I only II only Neither I nor II Both I and II ,Working Set,205 In the working set strategy which of the following is done by the operating system to prevent thrashing It initiates another process if there are enough extra frames It selects a process to suspend if the sum of the sizes of the working sets exceeds the total number of available frames I only II only Neither I nor II Both I and II ,Working Set,205 In the working set strategy which of the following is done by the operating system to prevent thrashing It initiates another process if there are enough extra frames It selects a process to suspend if the sum of the sizes of the working sets exceeds the total number of available frames I only II only Neither I nor II Both I and II ,Working Set,205 In the working set strategy which of the following is done by the operating system to prevent thrashing It initiates another process if there are enough extra frames It selects a process to suspend if the sum of the sizes of the working sets exceeds the total number of available frames I only II only Neither I nor II Both I and II ,Working Set,205 What happens when a bit string is XORed with itself n times as shown left B oplus B oplus B oplus B dots n ext times right complements when n is even complements when n is odd divides by 2 n always remains unchanged when n is even ,Xor,206 What happens when a bit string is XORed with itself n times as shown left B oplus B oplus B oplus B dots n ext times right complements when n is even complements when n is odd divides by 2 n always remains unchanged when n is even ,Xor,206 What happens when a bit string is XORed with itself n times as shown left B oplus B oplus B oplus B dots n ext times right complements when n is even complements when n is odd divides by 2 n always remains unchanged when n is even ,Xor,206 What happens when a bit string is XORed with itself n times as shown left B oplus B oplus B oplus B dots n ext times right complements when n is even complements when n is odd divides by 2 n always remains unchanged when n is even ,Xor,206 What happens when a bit string is XORed with itself n times as shown left B oplus B oplus B oplus B dots n ext times right complements when n is even complements when n is odd divides by 2 n always remains unchanged when n is even ,Xor,206 What happens when a bit string is XORed with itself n times as shown left B oplus B oplus B oplus B dots n ext times right complements when n is even complements when n is odd divides by 2 n always remains unchanged when n is even ,Xor,206 What happens when a bit string is XORed with itself n times as shown left B oplus B oplus B oplus B dots n ext times right complements when n is even complements when n is odd divides by 2 n always remains unchanged when n is even ,Xor,206 What happens when a bit string is XORed with itself n times as shown left B oplus B oplus B oplus B dots n ext times right complements when n is even complements when n is odd divides by 2 n always remains unchanged when n is even ,Xor,206 What happens when a bit string is XORed with itself n times as shown left B oplus B oplus B oplus B dots n ext times right complements when n is even complements when n is odd divides by 2 n always remains unchanged when n is even ,Xor,206 What happens when a bit string is XORed with itself n times as shown left B oplus B oplus B oplus B dots n ext times right complements when n is even complements when n is odd divides by 2 n always remains unchanged when n is even ,Xor,206 What happens when a bit string is XORed with itself n times as shown left B oplus B oplus B oplus B dots n ext times right complements when n is even complements when n is odd divides by 2 n always remains unchanged when n is even ,Xor,206 What happens when a bit string is XORed with itself n times as shown left B oplus B oplus B oplus B dots n ext times right complements when n is even complements when n is odd divides by 2 n always remains unchanged when n is even ,Xor,206 What happens when a bit string is XORed with itself n times as shown left B oplus B oplus B oplus B dots n ext times right complements when n is even complements when n is odd divides by 2 n always remains unchanged when n is even ,Xor,206 What happens when a bit string is XORed with itself n times as shown left B oplus B oplus B oplus B dots n ext times right complements when n is even complements when n is odd divides by 2 n always remains unchanged when n is even ,Xor,206