# BITS MCA Quantitative and Mathematical Ability Mock Paper 1

Objective MCQs Practice question Paper for BIT Ranchi MCA Entrance Exam

Ques. In a binomial distribution the probability of getting a success is 1/4 and standard deviation is 3, then its mean is
(a) 6
(b) 8
(c) 12
(d) 10
Ans: (a)

Ques. A sum of money doubles itself at compound interest in 15 years. It will become 8 times in
(a) 40 years
(b) 30 years
(c) 60 years
(d) 45 years
Ans: (d)

Ques. In a contingency table, row and column totals are often called
(a) simple tabulations
(b) cells
(c) marginals
Ans: (c)

Ques. Suppose X follows a binomial distribution with parameters n and p, where 0 < p < 1. If P(X = r)/P(X = n – r) is independent of n and r, then
(a) p = ½
(b) p = 1/3
(c) p = ¼
(d) None of these
Ans: (a)

Ques. The practical result of the central limit theorem is that
(a) researchers must take a large number of samples before inferences about the population can be made.
(b) the researcher must know the shape of the population distribution before inferences about the population can be made.
(c) small-sized samples should not be used in research.
(d) none of the above
Ans: (d)

Question: What should come in place of the question mark (?)
50, 26, 14, ?, 5, 3·5
(a) 6
(b) 8
(C) 10
(d) 12
Ans: (b)

Ques. What will be compound interest on Rs 15000 at 8% per annum for 1 year compounded half yearly.
(a) Rs 1224
(b) Rs 1300
(c) Rs 1200
(d) Rs 1000
Ans: (a)

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Ques. In an election there are 8 candidates, out of which 5 are to be choosen. If a voter may vote for any number of candidates but not greater than the number to be choosen, then in how many ways can a voter vote
(a) 216
(b) 114
(c) 218
(d) None of these
Ans: (c)

Ques. Two numbers within the bracket denote the ranks of 10 students of a class in two subject: (1, 10), (2, 9), (3, 8), (4, 7), (5, 6), (6, 5), (7, 4), (8, 3), (9, 2), (10, 1), then rank correlation coefficient is
(a) 0
(b) – 1
(c) 1
(d) 0.5
Ans: (b)

Ques. A pair of fair dice is rolled together till a sum of either 5 or 7 is obtained. Then the probability that 5 comes before 7 is
(a) 1/5
(b) 2/5
(c) 4/5
(d) None of these
Ans:
(d)

Ques. If the regression equations of the variables x and y be x = 19.13 – 0.83y  and y = 11.64 – 0.50x, then the correlation coefficient between x and y is
(a) 0.66
(b) – 0.64
(c) 0.001
(d) – 0.001
Ans: (b)

Ques. In a football championship, there were played 153 matches. Every team played one match with each other. The number of teams participating in the championship is
(a) 17
(b) 18
(c) 9
(d) 13
Ans: (b)

Ques. The third proportional to 0.36 and 0.48 is:
(a) 0.64
(b) 0.1728
(c) 0.44
(d) 0.82
Ans: (d)

Ques. A and B together can do a piece of work in 12 days which B and C together can do in 16 days. After A has been working at it for 5 days, and B for 7 days. C finishes. it in 13 days. In how many days could each do the work by himself?
(a) 16,48 and 26 days respectively
(b) 16,48 and 24 days respectively
(c) 26,48 and 24 days respectively
(d) 16,46 and 24 days respectively

Ans. (b)

Ques. If r = –0.97, then
(a) Correlation is negative and curved
(b) Correlation is linear and negative
(c) Correlation is in third and fourth quadrant
(d) None of these
Ans: (b)

Ques. 0.5737373 … =
(a) 284/497
(b) 284/495
(c) 568/990
(d) 567/990
Ans: (c)

Ques. A batsman scores runs in 10 innings 38, 70, 48, 34, 42, 55, 63, 46, 54, 44, then the mean deviation is
(a) 8.6
(b) 6.4
(c) 10.6
(d) 9.6
Ans: (a)

Ques. If two coins are tossed 5 times, then the probability of getting 5 heads and 5 tails is
(a) 63/256
(b) 1/1024
(c) 2/205
(d) 9/64
Ans: (d)

Ques. A frequency distribution (or probability distribution) of all possible values of sample means for a sample size of 200 is the
(a) population distribution
(b) sample distribution
(c) sampling distribution
(d) standard normal distribution.
Ans: (c)

Ques. There are 12 volleyball players in all in a college, out of which a team of 9 players is to be formed. If the captain always remains the same, then in how many ways can the team be formed
(a) 36
(b) 108
(c) 99
(d) 165
Ans: (d)

Ques. If the lines of regression coincide, then the value of correlation coefficient is
(a) 0
(b) 1
(c) 0.5
(d) 0.33
Ans: (b)

Ques. A man invested 1/3rd of the sum at 7%, 1/4th at 8% and the remaining at 10% for one year. If the annual interest is Rs. 408, then the investment is
(a) Rs. 8,400
(b) Rs. 4,800
(c) Rs. 5,000
(d) Rs. 7,200
Ans: (b)

Ques. The equation of the line joining the origin to the point (–4, 5) is
(a) 5x + 4y = 0
(b) 3x + 4y = 2
(c) 5x – 4y = 0
(d) 4x – 5y = 0
Ans: (a)

Ques. A can do a job in 3 days less time than B. A works at it alone for 4 days and then B takes over and completes it. If altogether 14 days were required to finish the job, how many days would each of them take alone to finish it?
(a) 13 days, 16 days
(b) 12 days, 15 days
(c) 15 days, 12 days
(d) 15 days, 18 days

Ans. (b)

Ques. Assuming that for a husband-wife couple the chances of their child being a boy or a girl are the same, the probability of their two children being a boy and a girl is
(a) ¼
(b) 1
(c) ½
(d) 1/8
Ans: (c)

Ques. The process of changing the original form of the data to a format suitable to perform a data analysis is
(a) cheating
(b) formatting
(c) data transformation
(d) normalization
Ans: (c)

Question: 2 rice varieties costing Rs 25 per kg and Rs 35 per kg were mixed as 2 : 3 and sold so as to gain 20%. What was the Selling Price of the mixture (Rs/kg)?
(a) 37.2
(b) 28.6
(c) 30
(d) 32
Ans: (a)

Ques. A tank contains 18,000 litres of water. If it decreases at the rate of 5% a day, what will be the quantity of water after 2 days
(a) 16,245 litres
(b) 15,234 litres
(c) 17,225 litres
(d) 18,200 litres
Ans: (a)

Ques. If you wish to estimate the mean of a particular population, doubling the range of acceptable error will reduce sample size to _____ its original size.
(a) one-half
(b) one-fourth
(c) twice
(d) It cannot be determined
Ans: (b)

Ques. Three number are in A.P. such that their sum is 18 and sum of their squares is 158. The greatest number among them is
(a) 10
(b) 11
(c) 12
(d) None of these
Ans: (b)

Ques. The mean deviation of the numbers 3, 4, 5, 6, 7 is
(a) 0
(b) 1.2
(c) 5
(d)  25
Ans: (b)

Question: The existence of the unique solution of system x y z = b, 2x × 3yz = 6, 5xy × az = 10 depends on
(a) b only
(b) a only
(c) a and b
(d) neither a nor b

Question: The sum of the two digits of a two digit number is 14. The difference between the first digit and the second digit of the two digit number is 2. What is the product of the two digits of the two digit number ?
(a) 56
(b) 48
(c) 45
(d) Cannot be determined
Ans: (b)

Question: Which of the following algebraic structures is not a field?
(a) (Q, +, *)
(b) (I, +, *)
(c) (R,+, *)
(d) (C, +, *)

Question: Which of the cones can be formed from a 252o sector of a circle of radius 10 by aligning the two straight sides?
(a) A cone with slant height of 10 and radius 6
(b) A cone with height of 10 and radius 6
(c) A cone with slant height of 10 and radius 7
(d) A cone with height of 10 and radius 7
Ans: (c)

Question: The largest term in the expansion of (3 + 2x)50 where x = 1/5 is
(a) 7th
(b) 51st
(c) 5th
(d) 6th

Question: A differentiable function f (x) has a relative minimum at x = 0, then the function y = f (x) + ax + b has a relative minimum at x = 0 for
(a) all b if a = 0
(b) all a and all b
(c) all b > 0
(d) all a > 0

Question: Consider all possible seven-digit binary numbers having four 1s and three 0s. What is the sum of all such numbers?
(a) 1470
(b) 1615
(c) 1740
(d) 1910
Ans. (d)

Question: The sum of a few (more than 2 and less than 100) consecutive integers is found to be 253. There can be 2 values of the total number of terms. The positive difference between these 2 values will be
(a) 15
(b) 20
(c) 25
(d) 35
Ans: (d)

Question: The workers in a factory produce widgets and whoosits. For each product, production time is constant and identical for all workers, but not necessarily equal for the two products. In one hour, 100 workers can produce 300 widgets and 200 whoosits. In two hours, 60 workers can produce 240 widgets and 300 whoosits. In three hours, 50 workers can produce 150 widgets and m whoosits. Then m equals
(a) 150
(b) 250
(c) 350
(d) 450
Ans: (d)

Question:  Let ABC be an acute angled triangle and CD be the altitude through C. If AB = 8 and CD = 6, what is the distance between the midpoints of AD and BC?
(a) 4.5
(b) 3
(c) 5
(d) 7.5
Ans: (c)

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Question: Given the nine-sided regular polygon A1 A2 A3 A4 A5 A6 A7 A8 A9, how many distinct equilateral triangles in the plane of the polygon have at least two vertices in the set {A1, A2, … A9}?
(a) 30
(b) 33
(c) 36
(d) 66
Ans: (d)

Ques. A and B working together can do a piece of work in 7 ½ days, B alone could do it in 12½ days. Supposing B works at it for 2½ days, in how many days A alone could finish the remaining work?
(a) 5 days
(b) 8 days
(c) 7 days
(d) 15 days

Ans. (d)