RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?
A.Friday
B.Saturday
C.Wednesday
D.Sunday
Answer: D.Sunday
Explanation: Explanation :
Number of days from 6th March, 2004 to 5th March 2005 = 365 days
(Though Feb 2004 has 29 days as it is a leap year, it will not come in the required period)
365 days = 1 odd day
Given that 6th March, 2005 is Monday
Hence 6th March, 2004 = (Monday - 1 odd day) = Sunday
Answer : Option D
Question: To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took.
A.375
B.475
C.575
D.675
Answer: D.675
Explanation: Let x be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made:
3⋅25+(x−3)⋅30=75+30(x−3)
Therefore: 25x=75+30(x−3)−100
25x=75+30x−90−100
190−75=30x−25
115=5x
x=23
So the company worked 23 days and they made 23⋅25+100=675 pieces.
correct answer D
Question: Number of ways in which the letters of word PARDENS can be arranged with vowels in alphabetical order, is
A.360
B.240
C.2520
D.480
Answer: C.2520
Explanation: Solution
Order of vowels of fixed
âˆ´ required number of ways are 7!/2!.
Answer C
Question: A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?
A.22
B.77
C.26
D.41
Answer: D.41
Explanation: (1 man + 1 woman)'s 1 day work = (1/3 + 1/4) = 7/12 Work done by 1 man and 1 woman in 1/4 day = (7/12 * 1/4) = 7/48
Remaining work = (1 - 7/48) = 41/48
Work done by 1 boy in 1/4 day = ( 1/12 * 1/4) = 1/48
Number of boys required = 41/48 * 41 = 41.
Answer: D
Question: A shopkeeper sold an article at $1200 and gained a 20% profit. What was the cost price?
A.$1000
B.$1020
C.$1040
D.$1060
Answer: A.$1000
Explanation: Let x be the cost price.
1.2x = 1200
x = 1200/1.2 = 1000
The answer is A.
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is ?
A.1/8
B.1/4
C.1/5
D.1/9
Answer: C.1/5
Explanation: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer:C
Question: A and B invests Rs.8000 and Rs.12000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
A.32:99
B.82:31
C.8:15
D.34:89
Answer: C.8:15
Explanation: A : B
(8000*4)+(4000*8) : (12000*6)+(9000*6)
64000 : 120000
8 : 15
Answer:C
Question: How many different possible arrangements S can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?
A.360
B.720
C.900
D.1800
Answer: C.900
Explanation: Total ways for arranging without restriction = 7!/ (2!2!) { 2! is becoz of two T's and other 2! for two I's)
Restriction : atleast one character between I's = Possible ways - both I's together i.e.o character between I's
_ _ _ _ _ (I I)
Both I's Together = 6! (Assuming 2 I's as one unit) /2!(for 2 T's) * 2! (No of arrangements of 2 I's)/2! (for 2 I's)
=6!/2!
Therefore ans S= 7!/ (2!2!) -6!/2! = 900
HENCE C.
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 48 years, was replaced by a new person. Find the age of the new person?
A.18
B.56
C.12
D.17
Answer: A.18
Explanation: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average
= (P-3) 10(P-3)
= 10P - 48 + Q
=> Q = 18
Answer:A
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
A.33/96
B.33/91
C.33/93
D.13/91
Answer: B.33/91
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91.Answer: B
Question: Find the invalid no.from the following series 15, 16, 33, 105, 424, 2124, 12756
A.16
B.33
C.105
D.424
Answer: B.33
Explanation: 2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16.
3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34
4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105
5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424
6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125
3th term should 34 instead of 33.
B
Question: A shopkeeper sold two radio sets for 792 each, gaining 10% on one, and losing 10% on the other. Then he
A.neither gains nor loses
B.gains 1%
C.loses 1%
D.gains 5%
Answer: C.loses 1%
Explanation: Sol.(c) When selling price of two articles is same and
% gain = % loss
then there will be always loss.
and overall % loss = (10)2⁄100% = 1%. Answer C
Question: If x and y are numbers such that (x+5)(y-5)=0, what is the smallest possible value of x^2 + y^2
A.0
B.4
C.9
D.25
Answer: D.25
Explanation: From (x+5)(y-5)=0 it follows that either x=-5 or y=5. Thus either x^2=25 or y^2=25.
Now, if x^2=8125, then the least value of y^2 is 0, so the least value of x^2 + y^2 = 25 + 0 = 25.
Similarly if y^2=25, then the least value of x^2 is 0, so the least value of x^2 + y^2 = 0 + 25 = 25.
Answer: D.
Question: In how many different ways can the letters of the word ‘GEOMETRY’ be arranged so that the vowels always come together?
A.4323
B.2797
C.4320
D.2997
Answer: C.4320
Explanation: Explanation:
There are in all 8 letters in the given word of which 3 are vowels. As the vowels should always be together, considering the 3 vowels as one letter, there are in all 6
letters which can be arranged in 6! ways = 720
Also the 3 vowels can be arranged in 3! ways = 6
Total number of arrangements = 720*6 = 4320
ANSWER:C
Question: if(x-10)(y-5)(z-2)=1000 then what is the least value of x+y+z? if x,y,z are all integer no.
A.7
B.8
C.9
D.10
Answer: A.7
Explanation: (x-10)(y-5)(z-2)=1000
put x=0
y=-5
z=12
then
(0-10)(-5-5)(12-2)=1000
(-10)(-10)(10)=1000
1000=1000
ANSWER:A
Question: In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many S different victory circles are possible?
A.24
B.52
C.96
D.144
Answer: B.52
Explanation: Possible scenarios are:
1. Gold/Silver/Bronze/No medal (no ties) - 4!=24;
2. Gold/Gold/Silver/No medal - 4!/2!=12;
3. Gold/Silver/Silver/No medal - 4!/2!=12;
4. Gold/Gold/Gold/No medal - 4!/3!=4.
Total: 24+12+12+4=52
Answer: B.
Question: In a cinema hall for the matinee show which started at 2.30 pm and ended at 5.30 pm the vehicle parking lot had only three wheelers (auto rickshaws) and four wheelers. Today the wheels of the vehicles parked was counted and found to be 240. What could be the number of three wheelers parked therein ?
A.10
B.48
C.37
D.97
Answer: B.48
Explanation: 3X + 4y = 240
by substitute through options 48 is correct
Answer: B
Question: How many cubes of 3cm edge can be cut out of a cube of 18cm edge
A.36
B.232
C.216
D.455
Answer: C.216
Explanation: number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216
Answer: C
Question: A = {2, 3, 5, 7, 11}
B = {2, 4, 6, 13}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?
A.15
B.16
C.19
D.20
Answer: C.19
Explanation: This would be the generic strategy:
Step 1: Find out the number of products you get.
5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4 = 20
Step 2: Remove the products that appear more than once.
Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.
2, 3
2, 4, 6
The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.
Answer = 20 - 1 = 19
ANSWER:C
Question: Bruce purchased 7kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
A.A)985
B.B)1050
C.C)1055
D.D)1065
Answer: A.A)985
Explanation: Cost of 7 kg grapes = 70 × 7 = 490.
Cost of 9 kg of mangoes = 55 × 9 = 495.
Total cost he has to pay = 490 + 495 = 985
A
Question: If the reciprocals of two consecutive positive integers are added together, what is the sum in terms of the greater integer p?
A.(2p-1)/(p^3- p)
B.(2p-1)/(p^4- p)
C.(2p-1)/(p^2- p)
D.(2p-1)/(p^2- 2p)
Answer: C.(2p-1)/(p^2- p)
Explanation: Let two consecutive positive integers be p and p-1 (Greater integer is p)
So,
(1/p) + [1/(p-1)]
= (2p-1)/p(p-1)
=(2p-1)/(p^2- p)
Answer : C
Question: Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 20 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?
A.3:5
B.9:25
C.5:2
D.25:9
Answer: C.5:2
Explanation: Same circumferential rate means that a point on both the gears would take same time to come back to the same position again.
Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B
Time A = 2*pi*25/Speed A
Time B = 2*pi*10/Speed B
Since the times are same,
50pi/Speed A = 20pi/Speed B
SpeedA/Speed B = 50pi/30pi = 5/2
Correct Option: C
Question: The ratio of the ages of Anil and his son at present is 7 : 3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2 : 1. Find the ratio of the present ages of Anil and his wife?
A.270
B.266
C.209
D.298
Answer: A.270
Explanation: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
Answer: A
Question: Income and expenditure of a person are in the ratio 9 : 8. If the income of the person is Rs. 36000, then find his savings?
A.2000
B.3000
C.4000
D.5000
Answer: C.4000
Explanation: Let the income and the expenditure of the person be Rs. 9x and Rs. 7x respectively.
Income, 9x = 36000
=> x = 4000
Savings = Income - expenditure
= 9x - 8x = x
So, savings =Rs.4000.
Answer: C
Question: A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
A.Rs. 7500
B.Rs. 9000
C.Rs. 9500
D.Rs. 10,000
Answer: A.Rs. 7500
Explanation: Solution: A : B : C = (20,000 * 24) : (15,000 * 24) : (20,000 * 18) = 4 : 3 : 3.
So B's share = Rs. (25000 * 3/10) = Rs. 7,500.
Answer: Option A
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 650, what is the least possible value of n?
A.10
B.11
C.12
D.13
Answer: D.13
Explanation: 650 = 2 * 5 * 5 * 13
so the least value forNcan be 13.
D
Question: Palindromes are words or phrases that read the same in both directions, e.g. EYE
Now consider the word LEVEL, such a word is known as palindromes.
Find the maximum possible number of five letter palindromes.
A.17515
B.17566
C.17576
D.None
Answer: C.17576
Explanation: Explanation :
The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways.
=> The first two letters can be chosen in 26*26=676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
=> All the three letters can be chosen in 676*26=17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
Answer : C
Question: -2, 5, 24, 61, ?
A.228
B.278
C.299
D.122
Answer: D.122
Explanation: ANSWER: D
Question: A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.675 in all. Find the share of B?
A.140
B.120
C.125
D.130
Answer: A.140
Explanation: A+B+C = 675
A = 3B
3B+B+B-25 = 675
5B = 700
B = 140
ANSWER A
Question: What is the are of an equilateral triangle of side 16 cm?
A.64√8 cm2
B.64√1 cm2
C.68√3 cm2
D.64√3 cm2
Answer: D.64√3 cm2
Explanation: Area of an equilateral triangle
= √3/4 S2
If S = 16, Area of triangle
= √3/4 * 16 * 16
= 64√3 cm2;
Answer: D
Question: A marketing company devised a methodology of spreading its message through one another. One person can tell it to 3 persons in 4 minutes and these three persons tell the other three persons each in further 4 minutes and the process continues so on. How many minutes will it take to spread the message to 2187 persons.
A.48 minutes
B.24 minutes
C.32 minutes
D.28 minutes
Answer: D.28 minutes
Explanation: according to the given condition 3^1 + 3^2 + 3^3 + ........ = 2187
or 3(3^x - 1)/(3-1) = 2187
or 3(3^x - 1)/2 = 2187
or 3^x - 1 = 2187*2/3 = 4374/3 = 1458
or 3^x = 1459 so x = 6 to 7
so total time taken = (6to7)*4 = 24 to 28 min
but if we take only the last step persons then 3^x = 2187 so x = 7
so time = 7*4 = 28 min
ANSWER:D
Question: Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 7000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?
A.100000
B.100500
C.147000
D.Data inadequate
Answer: C.147000
Explanation: Let the investment of X in 1995 be x.
∴ Profit = x⁄5
∴ Income = (x + x⁄5) = 6⁄5x
Investment of company X in 1996 would be (x – 7000) From the question,
(x - 7000) × 126⁄100 = 6⁄5x ⇒ x = 147000
Answer C
Question: Which of the following CANNOT be weighed using a balance scale and these unit weights: 1, 4, 7, and 10
A.13
B.15
C.17
D.19
Answer: A.13
Explanation: A. 13 (cannot be weighed)
B. 15 (can be weighed by keeping weights of 10,4 and 1 kg)
C. 17 (can be weighed by keeping weights of 10 and 7 kg)
D. 11(can be weighed by keeping weights of 10 and 1 kg)
E. 21 (can be weighed by keeping weights of 10, 7 and 4 kg)
A
Question: The average monthly salary of 10 employees in an organisation is Rs. 1600. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary?
A.Rs.3601
B.Rs.3618
C.Rs.2700
D.Rs.3619
Answer: C.Rs.2700
Explanation: Manager's monthly salary
= Rs. (1700 * 11 - 1600 * 10)
= Rs. 2700 Answer:C
Question: The angle between the minute hand and the hour hand of a clock when the time is 10.30, is
A.35°
B.65°
C.45°
D.135°
Answer: D.135°
Explanation: Angle between hands of a clock
When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock
=30(H−M/5)+M/2 degree
When the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H 'o clock
=30(M/5−H)−M/2 degree
Here H = 10, M = 30 and minute hand is behind the hour hand.
Hence the angle
=30(H−M/5)+M/2
=30(10−30/5)+30/2
=30(10−6)+15
=30×4+15 =135°
Answer is D.
Question: When x is multiplied by 3, the result is 26 more than the result of subtracting x from 26. What is the value of x?
A.-4
B.-2
C.11
D.13
Answer: D.13
Explanation: The equation that can be formed is:
3x-26=26-x
or, 4x=52
or, x=13.
D answer.
Question: The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
A.20,20
B.20,10
C.25,15
D.30,10
Answer: D.30,10
Explanation: Explanation:
Let their ages be x and (x + 20) years.
5 (x - 5) = (x + 20 - 5) or 4x = 40 or x = 10.
Their present ages are 30 years and 10 years
Option D
Question: The Brookfield girl scouts sold 90 boxes of cookies on their first day which averaged 30% more than the other local area teams. Increasing their effort, by the end of the second day their sales increased their average to be 50% more than the other teams. How many boxes of cookies must the girls have out sold by to have attained this average?
A.12
B.50
C.20
D.36
Answer: D.36
Explanation: Explanation: First, set the information into algebraic phrases, set that information into an equation, then solve.
Number of boxes sold the first day @ 30% more: 30% * 90=27
Increasing their effort on the second day average increased to 50%. (Let x represent the unknown amount of additional cookies sold to solve the equation.) Therefore, the total boxes sold by the girls is 90+x, and the total number of boxes increased in 27+x. This gives the equation as: 50%*(90+x)=27+x
Solve: Let's get rid of the percent sign
50/100*(90+x)=27+x
1/2 *(90+x)=27+x
Get rid of the fraction:
2[1/2 * (90+x)]=2(27+x)
1 * (90+x) =54+2x
90+x =54+2x
(90-54)+x = (54-54)+2x
36+x/x = 2x/x
36 = x
Answer: D
Question: If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 4 other contributions made before john's, what is the size of his donation?
A.$100
B.$175
C.$200
D.$250
Answer: B.$175
Explanation: Cavg = average contribution before John
Cavg*1.5 = 75, therefore the average cont is $50 before John.
If he needs to increase the average contribution by $25, he must put in $25 for each of the 4 people.
so $100.
But, he also has to put in the average for himself (the fiveth person), so add $75.
So $175 is your answer.
Answer B
Question: If the length of the longest chord of a certain circle is 14, what is the radius of that certain circle?
A.2.5
B.5
C.10
D.7
Answer: D.7
Explanation: Longest chord of a circle is the diameter of the circle
diameter = 2 * radius
If diameter of the circle is given as 14 = 2 * 7
so radius of the circle = 7
correct answer - D
Question: 1100 boys and 700 girls are examined in a test; 42% of the boys and 30% of the girls pass. The percentage of the total who failed is :
A.62 *2/0
B.62 *2/3
C.62 *2/6
D.62 *2/2
Answer: B.62 *2/3
Explanation: Explanation:
Total number of students = 1100 + 700 = 1800.
Number of students passed = (42% of 1100 + 30% of 700) - (462 + 210) = 672.
Number of failues = 1800-672 = 1128.
Percentage failure = (1128/1800 * 100 )% = 62 * 2/3 %.
Answer: B) 62 *2/3
Question: A clock is set at 5 am. If the clock loses 16 minutes in 24 hours, what will be the true time when the clock indicates 10 pm on 4th day?
A.7 pm
B.8 pm
C.12 pm
D.11 pm
Answer: D.11 pm
Explanation: Time from 5 am to 10 pm on the 4th day
= 3 days 17 hours
= 3 Ã— 24 + 17
= 89 hours.
Given that clock loses 16 minutes in 24 hours.
=> 23 hour 44 minutes of the given clock = 24 hours in a correct clock
23 44/60 hours of the given clock = 24 hours in a correct clock
=> 23 11/15 hours of the given clock = 24 hours in a correct clock
=> 356/15 hours of the given clock = 24 hours in a correct clock
89 hours of the given clock =24Ã—15/356Ã—89 hours in a correct clock
24Ã—15/4= 6Ã—15= 90 hours in a correct clock.
So the correct time is 90 hours after 5 am
= 3 days 18 hours after 5 am
= 11 pm on the 4th day.
Answer: D
Question: If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?
A.Rs.1529
B.Rs.1510
C.Rs.1500
D.Rs.1329
Answer: C.Rs.1500
Explanation: Let the cost price of an article be Rs. x.
(19% of x) - (12% of x) = 105
19x/100 - 12x/100 = 105 => 7x = 105 * 100
=> x = 1500
Cost price = Rs.1500
Answer:C
Question: The speed of a train is 90 kmph. What is the distance covered by it in 5 minutes?
A.7.5
B.66
C.77
D.52
Answer: A.7.5
Explanation: 90 * 5/60 = 7.5 kmph
Answer:A
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
A.50
B.88
C.77
D.55
Answer: A.50
Explanation: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer: A
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is?
A.2:3
B.4:3
C.6:7
D.9:16
Answer: B.4:3
Explanation: Answer: Option B
Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= âˆšb : âˆša = âˆš16 : âˆš9 = 4:3
Question: How many different pairs of numbers (s, t) such that s = 3t can be obtained if s and t are selected from the set of number {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: s = 3t.
So, s/3 = t
That means s is divisible by 3.
Only 0, 3, 6, 9 are divisible by 3.
Hence option (D).
Question: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/100 that a person who randomly guesses the answer to each question will be a winner?
A.5
B.10
C.50
D.100
Answer: C.50
Explanation: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be a winner?
A.5
B.10
C.50
D.100
E.1000
Soln: ans is B
Probability that one question is answered right is 1/2.
Now for minimum number of questions needed to take probability less than 1/1000 is
=> (1/2)^n < 1/100
n = 50 satisfies this.
C
Question: 5000 - 4500 ÷ 10.00 = ?
A.4550
B.5000
C.0.5
D.4000
Answer: A.4550
Explanation: Answer
Given expression =5000 - 4500 ÷ 10.00
= 5000 - 450
= 4550
Correct Option: A
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ?
A.5/6
B.5/9
C.5/3
D.5/0
Answer: B.5/9
Explanation: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer: B
Question: Find the no.of ways of arranging the boy and 6 guests at a circular table so that the boy always sits in a particular seat?
A.3!
B.6!
C.7!
D.9!
Answer: B.6!
Explanation: Ans.(B)
Sol. Total number of persons = 7 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 6 places in 6P6 = 6! Ways ... The number of required arrangements = 6! x 1= 6! = 6! ways
Question: one machine 10 hours to complete a production order and another machine 20 hours to complete the same order. How many hours would it take both machines working simultaneously at their respective rates to complete the order?
A.12/7hrs
B.20/3hrs
C.15/6hrs
D.8/9hrs
Answer: B.20/3hrs
Explanation: Machine A = 10 hours to complete an order
Machine B = 20hours to complete the same order
We're asked how long it would take the two machines, WORKING TOGETHER, to complete the order.
Using the Work Formula: (A)(B)/(A+B).....
(10)(20)/(10+20) = 20/3 hours to complete the job; Answer is B
Question: If f(x) = 2x^2 + y, and f(2) = 20, what is the value of f(5)?
A.104
B.60
C.62
D.50
Answer: C.62
Explanation: f(x) = 2x^2 + y
f(2) = 20
=> 2*(2)^2 + y = 20
=> 8 + y = 20
=> y = 12
f(5)= 2*(5)^2 + 12
= 62
Answer C