CA Foundation Quantitative Aptitude PYQ May 2026: 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 α & β are roots of the equations x 2 - 2x – 35 = 0, where (α ≥ β), then find the value of (α –…
2. The set of inequalities 2x + 3y < 9, 5x - y > 3 has ______ region.
3. The feasible region formed by linear inequalities is always a ______ region.
4. The system of equations 2x + y = 10 4x + 6y = 36 has solution with x =
5. One experienced person does 10 units of work per day, while a fresher does 5 units of work per day. The employer wants to maintain at least 50 units…
6. If the difference between the annually compounded interest and simple interest on a certain sum of money at 8% per annum for 3 years is ₹ 788. Then…
7. What will be the approximate future value of an annuity of ₹ 1000 made annually for 5 years at interest rate of 7% per annum, compounded annually?…
8. A machine depreciates at a rate of 10% per year on its beginning-of-year value. If it is sold for ₹ 6,000 after 9 years, what was its original…
9. Rakesh requires ₹ 1,00,000 to buy a scooter after 4 years. What will be the approximate present value of ₹ 1,00,000 if the interest rate is 10% per…
10. Raju deposit ₹ 20,000 in a nationalized bank for 3 years at an annual interest rate of 8%, with the interest compounded every quarter. Find out how…
11. Find the effective interest rate, if nominal rate is 12% per annum, quarterly compounding.
12. Find out the number of 5-digit even numbers that can be formed from digits 1 to 7 without repetition of any digit.
13. If the first term of a geometric progression exceeds the second term by 4 and the sum of its terms till infinity is 100, then the common ratio is…
14. The sum of the first n terms of an arithmetic progression (A.P.) is 4n 2 + 3n. The 10 th term of the A.P. is ______
15. If the sum of 4 th and 8 th term of an arithmetic progression (A.P.) is 120, then the 6 th term of the A.P. is ______
16. The sum of infinite terms of the geometric series 1 - 1 / 5 + 1 / 25 - 1 / 125 +.... will be ______
17. If x (m) = am 2 , y(m) = a / m 2 , then find the value of dy / dx
18. Calculate the integral ∫ x 2 / x dx
19. If x y = y x then dy / dx =
20. For a given Revenue function R(x) = 100x - 2x 2 , the maximum revenue occurs at x =
21. Find the next term in the series 11, 12, 14, 17, 22, 30, ______
22. Anil's house faces east. From the back-side of the house, he walks straight 50 meters, then turns to the right and walks 50 meters. Finally, he…
23. If A x B means A is to the south of B; A + B means A is to the north of B; A% B means A is to the east of B; A - B means A is to the west of B; then…
24. Vishal started from his house toward west. After walking a distance 30 meters, he turned towards right and walk 20 meters. He then turned left and…
25. Puru started from his house towards west. After walking a distance of 25 m, he turned to the right and walked 10 m. He then again turned to the…
26. Six students A, B, C, D, E and F are sitting in a bench facing north. C is sitting second to the right of F. A is sitting extreme left end of the…
27. Sharma points to a girl and says, "She is the mother of my son's wife's daughter". What is the relation of the girl with Sharma?
28. P is the sister of Q. R is the mother of Q. S is the father of C. R is the sister of S. T is the mother of S. What is the relation of P with T?
29. Dr. Madhu said, "The engineer who is my brother is the son of the only Professor in our family." If the Professor is Mr. Murli, how is Mr. Murli…
30. A is brother of B. P is the sister of Q. B is the son of P. How is A related to P?
31. Q's mother is the sister of P and daughter of S. A is the son of P and Brother of H. G is the father of H. How is G related to S?
32. Interview method is used for collection of ________.
33. An ogive represents cumulative frequencies on a graph. By what other name is this graphical form commonly known?
34. If the mean 40, k, 6k, 4k 2 , 8k-4k 2 is 20, then the value of k is ________.
35. The standard deviation is zero only if all the observations assumed by a variable are ________.
36. To add flexibility to the sampling process, the ________ is preferred.
37. In a sample survey, sampling error mainly arises because:
38. The mean of five observations is 28. Among the five observations, three observations are 10, 23 and 62. The difference between the remaining two…
39. Which of the followings is a property of Arithmetic Mean?
40. The probability of getting pass in an examination is x / 3 . If the probability of getting fail is 2 / 3 , then the value of x is ________.
41. Two dice are rolled. What will be the probability that one dice have multiple of 3 and other dice have multiple of 2?
42. The mean of 10 observations is 15. If one observation 12 is replaced by 22, what will be the new mean?
43. If f(x) = kx 2 , 0 ≤ x ≤ 1 is a probability density function of a random variable x, then the value of k is ________.
44. In a binomial distribution, the probability of success is 0.7. The variance for n = 15 is ________.
45. For a Binomial Distribution with mean = 4 and variance = 3, what are the values of n and p?
46. The covariance between two variables X and Y is 4. The standard deviation of X is 10 and the correlation coefficient between X and Y is 0.4. Find…
47. The mean and mean deviation of a normal distribution are 13.5 and 4.8 respectively. Then the third quartile of the normal distribution is ________.
48. The mean of a binomial distribution is 4 and the variance is 3.2. If p < 0.5, find the value of p.
49. If 2x + 3y + 2 = 0 is the regression equation of x on y and the arithmetic mean of y is -2, then arithmetic mean of x is ________.
50. A price index with base 2000 shows: Index for 2010: 140 Index for 2020: 210. What is the index for 2010 when base is shifted to 2020?
51. Which formula correctly represents Fisher's Price Index?
52. If ∑P 0 q 0 = 400 and ∑P n q 0 = 720 and Paasche's index number is 125, then the Fisher's index number is _____
53. What is the approximate real wage of a worker earning ₹ 12,500 nominal wage, when the cost of living index is 250 (base 100)?
54. The simplified value of b √a 6b x 4 × √(a 2 x -b ) -b will be _____
55. If a : b = 3: 4, then the value of 2a + 3b / 3a + 2b
56. The product of two numbers is 7644 and their ratio is 12:13. Then, the smaller of two numbers is _____
57. The value of log 3 16×log 4 3 / log 9 3×log 4 4
58. If x = 3 + √8, then the value of x + 1 / x is _____
59. The compound interest for ₹ 15,000 at 20% per annum for 2 years compounded semi-annually is _____
60. Mr. Amit bought a car for ₹ 3,00,000 by making a down payment ₹ 50,000 and decided to pay equal annual payment for 10 years. How much would be each…
61. The simple interest at the rate of p% per annum for p years will be ₹ p. Then, the principal is _____
62. The future value of an annuity of ₹ 2000 made annually for 8 years at interest rate of 14% per annum, compound annually is _____. (Given that (1.14)…
63. Ravi deposits some amount in bank for 5 1 / 2 years at the simple interest rate of 7% per annum. Ravi receives ₹ 66,480 at the end of term. Compute…
64. In how many years will ₹ 50,000 become ₹ 75,000 at 8% per annum compound interest? (Given log (1.5) = 0.1761 and log (1.08) = 0.0334)
65. If ₹ 50,000 grows to ₹ 80,525.5 in 5 years, the compound annual growth rate (CAGR) is _____
66. In how many ways 5 Indians and 5 Americans people are seated around a table so that no two Indians are in adjacent positions?
67. A loan of ₹ 1,00,000 is repaid in 3 equal annual instalments at 10% per annum interest, compounded annually. Find the amount of each instalment.…
68. A group consists of 7 men and 5 women. In how many ways can a group of 4 members be selected if the group has no women?
69. Four cards are drawn at random from a standard deck of 52 playing cards without replacement. In how many ways it can be done such that the selected…
70. In a class, 50 students have expressed that they like Mathematics, while 66 students like Accountancy. Among these, 36 students like both…
71. Relation on integers is defined by: aRb ↔ a - b is divisible by 5. This relation is _____
72. Let the function f : R → R is defined by f(x) = x 2 + 3, then f -1 (12) is _____
73. Evaluate lim x→∞ x 2 + 2x + 2 / 3x 2 + x + 1
74. If 'DOCTOR' is coded as 423527 and 'PATIENT' is coded as 8651905, then how is 'OPERATION' coded?
75. If the word 'CODE' is coded as 1357 and 'GAMER' is coded as 24678, what word does the number 84178 represent?
76. Ram started walking 2 kms towards the Sun in the morning. He turned right and walked 2 kms. Then, he turned right and walked 2 kms. Finally, he…
77. In a certain Language, 'SUBJECT' is written as 'UWDLGEV' then 'MENTION' will be written as
78. Find the next term of the series: 7, 8, 18, 57, 232, 1165,
79. Five persons A, B, C, D & E are sitting on a bench. A is immediately to the left of C. E is immediately to the left of D and right of A. D is to the…
80. Six friends A, B, C, D, E and F sit in a row facing north. A and B have two persons between them. C, who is at right end, is immediate right of A. D…
81. Six persons A, B, C, D, E, and F are seated at a round table facing outside the centre but not necessarily in the same order. A sits at the…
82. In a circular arrangement of 5 persons facing centre, A is sitting between B and C, D is sitting immediate right of C, and E is sitting immediate…
83. Which one of the following parts is used to show the units of measurement?
84. Data that is classified according to an attribute or characteristic of the items under study is referred to as _______
85. A researcher wants to study the effectiveness of a new treatment by surveying the most experienced doctors in a city. He selects 50 doctors based on…
86. Which of the following statement is true?
87. Mutually Exclusive classification of class intervals _______
88. The given frequency distribution is: X 1 2 3 4 5 6 7 Y 5 9 12 17 14 10 6 The arithmetic mean of the Frequency distribution is _______
89. What will be the mean deviation for the numbers {2, 4, 7, 8, 9, 12} from the mean?
90. If third quartile and first quartile are 64.5 and 22 respectively, then the quartile deviation is
91. The arithmetic mean (A.M.) of two positive numbers exceeds their harmonic mean by 30. If their A.M. is 45, Then, their geometric mean will be
92. Two groups of students have harmonic means of 50 and 30 for their test scores, with 10 students in the first group and 15 students in the second…
93. A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability that the card drawn is either a King or a Heart?
94. If the standard deviation of a Poisson distribution is 3, then P(X = 0) is
95. In a Shooting competition, A hit the target 6 out of 13 shots, and B hit 8 out of 11 shots. If they both try once, what is the probability that the…
96. A bag contains 5 red, 4 blue, and 3 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are of…
97. For a set of observations on variables x and y, the following summary statistics are given: n = 5, ∑x = 10, ∑y = 25, ∑xy = 70, ∑x 2…
98. The product of the price index and the quantity index are equal to the corresponding value index in _______
99. The Spearman's Rank correlation coefficient between Economics and Accountancy marks for a class student 75 / 99 is and the sum of Square of…
100. When the two regression coefficients are given as b xy = 0.6 and b yx = 0.9, determine the value of the coefficient of correlation.