CA Foundation Quantitative Aptitude PYQ January 2025: Question Paper and Solutions

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Question directory and available solutions

100 indexed questions. Open a question to read its full statement and available answer.

1. If (4) 3 × (√2) n = 2 n , then n is
2. The standard deviation of the data 2, 4, 5, 6, 8, 17 is 23.33, then the standard deviation of the data 4, 8, 10, 12, 16, 34 is
3. The values of the first quartile and third quartile are 36.50 and 57.50. Then the semi-inter-quartile range is
4. Let A and B be two possible outcomes of a random experiment and P(A) = 1 / 3 , and P(B) = x. For what value of x are A and B mutually exclusive…
5. A random variable has the following probability distribution : X: 0, 1, 2, 3 P: 1 / 2 , 1 / 5 , 1 / 4 , 1 / 3 Find expected value of X.
6. What will be the mode of the Binomial distribution in which mean is 20 & Standard Deviation is √10?
7. If X is a Poisson variable such that P(X=1) = P(X=2) then the variance is
8. Which one of the following statement is wrong?
9. The AM & GM for two observations are 8 and 2. Find the values of two observations.
10. The mean deviation of normal distribution is approximately equal to
11. You are given the following data relating to a frequency distribution of 10 observations : ∑X = 50, ∑Y = 60, ∑X² = 300,…
12. If 3 percent of ceramic cup manufactured by a company are known to be defective. What is the probability that a sample of 100 cups are taken from…
13. A population comprises 7 members. The number of all possible samples of size 3 that can be drawn from it with replacement is
14. Let P(A) = 1 / 5 and P(B) = 3 / 5 . If A and B are mutually exclusive events then P(A∪B) is
15. If r = 0.8, b yx = 0.6, b xy = 0.5, x̄ = 5 and ȳ = 3, then the regression equation y on x is
16. Which one of the following index uses the method of average of base year and current year?
17. If r = 0.8 then coefficient of non determination is
18. The correlation coefficient between X and Y is 0.2 and Var(X) = 5Var(Y) then regression coefficient of X on Y is
19. Compute the rank correlation coefficient from the following data : n = 10, ∑d² = 5
20. When the cost of Beverages increased by 40%, the person said that the rise had increased his cost of living by 8%. Before the change in price, the…
21. If the prices of all the goods change in the same ratio, then
22. Given that ∑p 1 q n = 300, ∑p 0 q 0 = 125 and Paasche's index number is 200 then the value of ∑p 0 q n is
23. If Laspeyre's index number is 125 and Paasche's index number is 500 then Fisher's index number is
24. If x = √2 + 1 / √2 and y = √2 - 1 / √2 then x² + y² is
25. Suppose a father had a sum of ₹ 3,600 and he decided to divide this amount among his three sons Anil, Sunil and Nimal in such a way that 3 times…
26. L is wife of N, P is son of N, K is brother of N and father of O. What is the relationship of P and O?
27. C is sister of B. D is father of A. A is brother of B. D and E are married couple. How is C related to E?
28. Five people A, B, C, D, E are seated about a round table facing outside the center but not necessary in the same order. A sits at immediate right of…
29. Five friends A, B, C, D and E are sitting in a row facing east. A is sitting between C & D. B is second to the left of C. Who is sitting at the…
30. Five persons A, B, C, D & E sitting on a bench. A is immediate right of B. E is immediate left of C and immediate right of A. B is the right of D.…
31. Standard Error (SE) and square root of sample size are
32. The mean of three numbers is 135. Among the three numbers the biggest number is 180. The difference between the remaining two numbers is 25. Then…
33. B is daughter of A. C is brother of B. C is the only son of D. C and E are married couple. F is the only son of E. Then how is F related to A ?
34. Given that X is mother of Y. Z is son of X. A is brother of B. B is daughter of Y. Who is grandmother of A ?
35. U is father of W, X is son of V, Y is brother of U. If W is sister of X, how is X related to Y?
36. For the non-overlapping classes 25-34, 35-44, 45-54, 55-64 the class mark of the class 35-44 is
37. Non-probability Sampling is also known as :
38. Out of 1000 persons, 40% are female, others are male. In a marriage function, 300 persons enjoyed the song. 30% of the people who had not enjoyed…
39. In tabular presentation of data, stub is
40. Which sampling technique is most appropriate when a person wants to ensure that subgroups are proportionally represented ?
41. If x and y are related as 4x + 2y + 12 = 0 and mean deviation of x is 4.5, then the mean deviation of y is
42. For a distribution the mean is 30. The standard deviation is 2, then coefficient of variation is
43. Ogive is used to find
44. The algebraic sum of deviation of set of observations from their arithmetic mean is
45. Mean deviation is ________ when the deviations are taken from the median.
46. If the mode of the following data is 13, then the value of x in the data set is 13, 8, 6, 3, 8, 13, 2x + 3, 8, 13, 3, 5, 7
47. The best measure of central tendency is
48. A sample of 100 people is taken from a population of 1000. The sample mean height is 170 cm with a standard deviation of 10 cm. What is the standard…
49. In pie chart, if a category represents 25% of the total data, what will be the angle of corresponding sector?
50. Find the Harmonic Mean of 2, 4 & 6.
51. The ratio of age of two sisters is 5: 7. One is elder to the other by 8 years. Then the ratio of their age after 4 years between older to younger is
52. If x / y = a 2 +4 / a 2 -4 and x / y = (x/y) -5a , then the value of a is:
53. A firm manufactures two products A and B. Each product has to be processed on two machines. First machine can be used up to 15 hrs. and second can…
54. If α and β are roots of the equation 2x 2 - 4x + 6 = 0 then the quadratic equation with roots α 2 / β and β 2 / α is
55. A manufacturer produces two products A and B. The profit on product A is ₹ 8 on each unit and profit on product B is ₹ 13 on each unit. Then the…
56. What are the values of x & y from the given equations ? Given that x / 5 = y-x and x-5 / y-10 = 1
57. Anil deposited a certain amount in a bank at the rate of 10% per annum compounded semi-annually. At the end of one year Anil received a sum of ₹…
58. The simplified value of [5a 5 b 2 × 3(a b 3 ) 2 ]/(15a 2 b) is
59. Three Employees A, B and C of a firm receive variable incentive money in the ratio 3 : 4 : 5. Then the Management also gave a fixed incentive of ₹…
60. A certain amount at a rate of simple interest x, doubles in 5 years. At another rate of simple interest y, it becomes three times in 8 years. Then…
61. John borrows a loan of ₹ 10,000 from a bank and he agreed to pay back in 24 equal instalments at the rate of 10% compound interest per annum. Then…
62. What is the present value of ₹ 8,000 to be required after 10 years if the interest rate be 6%? (Given that (1.06) 10 = 1.7908)
63. The effective rate of interest corresponding to a nominal rate of 8% per annum payable quarterly is (Given that (1.02) 4 = 1.08243216)
64. Sunil plans to save for his higher studies. He wants to accumulate a sum of ₹ 5,00,000 at the end of 10 years. How much amount should he invest…
65. The future value of an annuity of ₹ 7,200 made annually for 5 years at the rate of 12% compounded annually is (Given that (1.12) 5 = 1.76234)
66. A certain amount is invested in a bank. What annual rate of interest compounded annually becomes 8 times of this investment in 5 years? (Given that…
67. If the compound interest on a certain sum for 2 years at 5% per annum is ₹ 246, then the simple interest on the same sum for double the time and…
68. Sam invested ₹ 12,000 for 10 years in a financial company. At the end of 10 th year his investment value is ₹ 18,000. Then the Compound Annual…
69. Mr. A invested ₹ 20,000 in a bank at the rate of 4.5% p.a. He received ₹ 27,500 after end of term. Find out the period ?
70. ₹ 1,500 is paid every years for 10 years to pay a loan. What is the loan amount, if rate of interest 5% p.a ? If (1.05) 10 = 1.6288
71. In how many ways can 5 Doctors, 4 Professors, and 6 Auditors be seated in a row so that all person of the same profession sit together?
72. The sum of the 4 th and 8 th term of an AP is 10. Then the sum of first eleven terms of the series is
73. Madhu deposits ₹ 100 in a Bank at the beginning of every year for 20 years at 10% interest rate compounded annually, how much would she earn after…
74. How much amount is required to be invested every year so as to accumulate ₹ 15,00,000 at the end of 20 years if interest is compounded annually at…
75. Assuming that the discount rate is 12% per annum, how much would you pay to receive ₹ 100, growing at 8% annually forever?
76. Find the 9 th term of the A.P. 8, 5, 2, -1, -4, -7.
77. The sum of series 1 + 2 + 3 + ....... is 55. The number of terms is :
78. A panel has total of 11 members including 5 males and 6 females. Find out the number of ways of picking 2 males and 3 females from the given panel…
79. The product of three numbers which are in GP is 512. Then the second number is
80. Let A = {a, b, c, d, e} then the number of proper subsets is
81. In how many ways can 13 balls be arranged, if 4 of them are black, 6 red & 5 are white?
82. The marginal revenue function for a product MR = 5 - 4x + 3x 2 . Then the total revenue function is
83. Evaluate : lim x→3 x 2 + 4x + 3 / x 2 + 6x + 9
84. In how many ways can an interview panel of 3 members be formed from 3 engineers, 2 psychologists and 3 managers if at least 1 engineer must be…
85. A = {a, b, p}, B = {2, 3}, C = {p, q, r, s} then n[(A∪C)×B] is :
86. If x = at 2 and y = a(t 3 - t) then dy / dx =
87. In certain code language 'CLOCK' is coded as 75276 and 'EARTH' is coded as 83491, then 'COAT' is coded as
88. Find the missing term of series 2, 7, 16, 29, ...., 67, 92
89. ∫(2x + 5) 7 dx
90. A committee of 3 members is formed from 5 women and 3 men in such a way that it consists at least 2 members who are women. In how many different…
91. Find the missing term CEGI, XVTR, GIKM, ________.
92. Raju started walking 10 kms towards east from his home. He turned right and walked 5 kms to the south to reach his school. In which direction is his…
93. A started walking from his house & walk 4 km north side then turns right & walk 3 km. If he turns right again, what is the direction now ?
94. In a certain language 'MENTION' is written as 'NFOUJPO', the code of 'MYSTIFY' is:
95. Find the odd man out from the following : Marriage, Wedlock, Divorce, Matrimony
96. Anil started walking 5 kms towards north then he turned left and walked 3 kms. Again he turned left and walked 5 kms. Then the total number of kms…
97. Five persons A, B, C, D and E are sitting in a circle facing centre. C is sitting immediate left of E. A is sitting in between E and D. Who is…
98. A man starts walking 10 km to the North. He turns right and walks 5 km, then turns right again and walks 10 km. In which direction is man now from…
99. In the morning Anika started walking from a point where her shadow falls in front of her. She walked 2 kms and then turned left and walked 2 kms.…
100. Eight persons A, B, C, D, E, F, G and H are sitting in two rows opposite to each other. Each row has 4 persons. B and C are sitting opposite side. C…