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| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| lim _ x rightarrow 4 frac sin x 4 x 4 ____ ,Limits,91 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 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 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 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| lim_ x rightarrow infty x frac 1 x is infty 0 1 Not defined ,Limits,91 | |
| 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 | |
| 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 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 | |
| Give a relational algebra expression using only the minimum number of operators from u222a u2212 which is equivalent to R u2229 S ,Sets,169 | |
| 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 | |
| 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 | |
| How many 4 digit even numbers have all 4 digits distinct 2240 2296 2620 4536 ,Permutations And Combinations,130 | |
| 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 | |
| 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 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 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 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 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 | |
| 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 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 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 | |
| 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 | |
| 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 | |
| On the set N of non negative integers the binary operation ______ is associative and non commutative ,Binary Operation,8 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| What is the size of the smallest MIS Maximal Independent Set of a chain of nine nodes 5 4 3 2 ,Graphs,76 | |
| 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 | |
| State whether the following statements are TRUE or FALSE The intersection of two CFL s is also a CFL ,Context Free Language,27 | |
| 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 | |
| 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 | |
| A Boolean function f is to be realized only by NOR gates Its K map is given below The realization is ,K Map,89 | |
| 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 | |
| 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 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 | |
| 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 | |
| The larger of the two eigenvalues of the matrix begin bmatrix 4 amp 5 2 amp 1 end bmatrix is _______ ,Eigen Value,50 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 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 | |
| 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 | |
| How many edges can there be in a forest with p components having n vertices in all ,Graphs,76 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 total number of Boolean functions which can be realised with four variables is 4 17 256 65 536 ,Boolean Algebra,12 | |
| 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 | |
| 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 | |
| If int limits_0 2 pi x sin x dx k pi then the value of k is equal to ______ ,Integration,86 | |
| 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 | |
| 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 | |
| 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 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 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 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 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 | |
| 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 | |
| A Boolean function x u2019y u2019 xy x u2019y is equivalent to x y x y x y x y ,Boolean Expressions,13 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 value of lim_ x rightarrow infty 1 x 2 e x is u00a0 0 frac 1 2 1 infty ,Limits,91 | |
| 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 | |
| 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 | |
| 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 | |
| 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 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 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 | |
| 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 | |
| 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 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 | |
| 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 | |
| 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 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| The number 43 in 2 s complement representation is 01010101 11010101 00101011 10101011 ,Number Representation,118 | |
| 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 | |
| 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 | |
| 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 | |
| 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 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 | |
| The number of distinct positive integral factors of 2014 is _____________,Number Theory,121 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 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 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 | |
| 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 | |
| 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 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 | |
| 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 | |
| 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 | |
| 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 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 | |
| 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 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 | |
| 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 | |
| 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 | |
| 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 | |