CA Foundation Quantitative Aptitude PYQ January 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 a sum double itself in 8 years, then in how many years it will becomes four times, assuming that the simple interest is calculated.
2. Mr. XYZ is investing a certain amount at the end of each month in his account. He is supposed to get interest 12% per annum compounded monthly. If…
3. If an amount is compounded annually so that it tripled itself in 4 years, then the annual rate of interest is (Given that 3 1/4 = 1.316)
4. Bank B provides loans at 15% per annum compound interest. If Mr. XYZ borrowed ₹ 3,200 for 2 years from Bank B, then how much interest must Mr. XYZ…
5. An investor intends to purchase a three years bond at a price of ₹907.125 having nominal interest rate of 10%. What is the par value of the bond if…
6. A sinking fund is created for replacement of machine at the end of 20 years. Its present cost is ₹ 8,00,000. After 20 years cost of new machine…
7. The net asset value (NAV) of a Mutual Fund is calculated at the end of the financial year. For the last five years following values are computed.…
8. The third term of a geometric progression is 5. Then the product of first five terms is
9. The sum of infinity of the series 1 / 2 - 1 / 6 + 1 / 18 - 1 / 54 +........ is:
10. If the arithmetic mean of two numbers is 13 and the geometric mean is 12, then the difference between the two numbers is:
11. If f(x) = 3e x , then f'(x) – 2xf(x) + 1 / 6 f(0)-f'(0) is equal to
12. The cost of production of an item is given as C=50x – 5x 2 + x 3 / 6 where 'x' is number of items to be produced. If the average cost and marginal…
13. If A = {2, 3}, B = {4, 5} and C = {5, 6} then the A × (B ∩ C) is
14. The cost function of a company is given by C(x) = 600x – 10x 2 + x 3 / 2 where x denotes the output. Find the level of output (in nearest integer)…
15. Which of the followings is odd one?
16. Mr. ABC started walking down a road in the evening while facing the sun. After walking for a distance, he turned to his left, and then he turned to…
17. Find the odd number in the following series: 7, 11, 13, 15, 19, 23, ...
18. A boy is facing East. Turning to the right, he goes 20 m, then turning to the left he goes 20 m and turning to the right, he goes 20 m, then again…
19. In line, A sits 12 th from the left. B is sitting 20 th from the right and 5 th to the left of A. How many people are sitting in the line?
20. Eight persons P, Q, R, S, T, U, V, and W are sitting around a circular table facing the centre. Two persons sit between Q & W. V sits immediate…
21. Six friends P, Q, R, S, T and U are sitting around the hexagonal table each at one corner and are facing the centre of the hexagonal. P is second to…
22. Five friends P, Q, R, S, and T are sitting in row facing north. S is between T & Q and Q is to the immediate left of R. P is to be the immediate…
23. A market researcher divides a city into 5 regions, where variation within region is little and there is a maximum variation between regions and…
24. Frequency density of a class interval may be defined as the ratio of
25. P, Q, R, S, T, and U are six members of a family. R is spouse of Q. U is mother of T and S is daughter of U. P's daughter is T and R's son is P.…
26. During the tabular presentation of data, ______ is the entire upper part of table which includes columns and sub-column numbers, unit(s) of the…
27. This type of sampling method depends entirely on the discretion or judgement of the sampler
28. Which of the following sampling methods is completely free from sampler's biases
29. The diagrammatic representation of the cumulative frequency distribution is:
30. In two groups, unit one has 700 people with monthly salary of ₹ 2,500, unit two has 650 with salary of ₹ 2,750 then approximate combined arithmetic…
31. If the relationship between x and y is given by 5x - 3y = 15 and if range of x is given as 24 then the range of y is given by:
32. The two variables 'x' and 'y' are related by 2x - 3y - 3 = 0 If the mode of 'x' is 15, then the mode of 'y' is:
33. If mean of 5 observations x + 1, x + 3, x + 5, x + 7 and x + 9 is given as 125, then the value of x will be.
34. If two samples of size 30 and 20 have means as 55 and 60 and standard deviation 5 and 6 respectively then what would be the standard deviation of…
35. Find the probability that a 3-digit number formed using the digits 1, 3, and 5 (without repetition), is divisible by 3?
36. Ms. Radhika appeared in interview at three different companies. In the first company there are 5 candidates, in second company there are 12…
37. The odds in favour of Mr. A to solve a problem is 5:7 and odds against to Mr. B to solve the same problem is 9:6. What is the probability that if…
38. If the slope of the regression line is calculated to be 3.5 and the intercept 14 then the value of Y when X is 6 is
39. For the variables x and y, the regression equations are given as x + 2y - 5 = 0 2x + 3y - 8 = 0 and the arithmetic means of x and y are 1 and 2…
40. A quality control inspector finds that 20% of light bulbs are defective. If a batch of 5 light bulbs is tested, what is the probability that exactly…
41. If b yx = 1.6 and b xy = 0.4, then r xy will be:
42. The test of shift ability of the base is called?
43. The property of an index number that allows shifting of the base year without referring each time to the original base is tested by which of the…
44. Which of the following index does not satisfy the time reversal test?
45. If 3x × b 5 log b x = 192 then the value of x is
46. In India, an examination is conducted in two sessions. In the first session the ratio of boys to girls among 455 students is 8: 5. If 50 new girls…
47. If α and β are the roots of the equation 2x 2 -3x + 1 = 0 then the equation whose roots are 1/α and 1/β is:
48. One year ago, the ratio of ages (in years) of A and B was 5:4. The ratio of their ages, 4 years from now, will be 6:5. What will be the age of A (in…
49. Find the value of x (b+c-a) × x (c+a-b) × x (a+b-c)
50. If ₹ 80,000 grows to ₹ x in 3 years at compound interest compounded annually at 8% rate of interest per annum, then the value of x is:
51. The value of compound interest (in nearest ₹) if ₹ 30,00,000 is deposited in a bank for 1 year at the rate of 16% per annum compounded quarterly is:
52. The common region represented by inequalities: 2x + y ≥ 8, x + y ≥ 12, 3x + 2y ≤ 34, x ≥ 0 and y ≥ 0 is
53. The present value (in nearest ₹) of an annuity of ₹ 90,000 for 13 years at 5.5% compounded annually is (Given 1.005 13 = 2.0058)
54. Ms. Rina buys a refrigerator worth ₹ 25,000. She pays ₹ 5,000 upfront and agrees to settle the remaining amount through five equal annual…
55. A sum of money lent at compound interest for 2 years at 20% p.a. would fetch ₹ 482/- more if the interest was payable half yearly then if it was…
56. Mr. Ravi allocates a corpus of ₹ 50,000 into a term deposit account which accrues interest at a nominal annual rate of 10%, compounded on a…
57. Shiva invested an amount of ₹ 12,000 at the rate of 10% pa simple interest and another amount at the rate of 20% pa simple interest. The total…
58. If n C r-1 = 28, n C r = 56, n C r+1 = 70, then the value of n and r are
59. In a meeting, 5 analysts, 2 consultants, and 3 managers are to be seated in a row. If members of the same profession must sit together, in how many…
60. The total numbers greater than 2000 that can be formed with the digits 1, 2, 3, 4, 5 and no digits being repeated in any number are:
61. How many 3-digit number can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digit is repeated?
62. If f(x) = 1 + 1 / x , then the value of f(f( 1 / x )) is
63. The function f(x) = x 2 - 25 / x - 5 is undefined at x = 5 what value must be assigned to f(5) if f(x) is to be continuous at x = 5?
64. A GP series consists of 2n terms. If the sum of the terms occupying the odd places is S 1 and that of the terms in even places is S 2 , the common…
65. Let R is the set of real numbers such that the function f: R → R and g: R → R are defined by f(x) = x 2 + 3x - 1 and g(x) = 2x + 3 then…
66. The next term of the series 1, 7, 17, 31, 49, 71, ____ is
67. If in a certain code language PAINT is coded as 74128 and ACCEPT is coded as 455978, what will be the code for PATIENT?
68. Evaluate the integral ∫ 0 1 (2x 2 - x 3 ) dx
69. If in a certain language, MONKEY is coded as NNOJFX, how is PUZZLE coded in that language?
70. A man drives 10 km towards north; from there he turns towards right and drive 3 Km. then he takes right turn and drives 6 km. How far and in which…
71. A, B, C, D and E are sitting on a bench. A is sitting next to B, C is sitting next to D, D is not sitting with E who is on the left end of the…
72. Mr. Q walks 20 km north, then walks 14 km south, and then walks 8 km east. How far is he from his starting point?
73. If west is replaced with north-east then south will be replaced by which of the following direction?
74. A is the son of C; C and Q are sisters; Z is the mother of Q and P is the son of Z. Which of the following statements is true?
75. 'A+B' means A is the father of B. 'A - B' means A is the wife of B. 'A × B' means A is the brother of B. 'A/B' means A is the daughter of B.…
76. Pointing to a photograph of a boy Suresh said, "He is the son of the only son of my mother." How is Suresh related to that boy?
77. A and B are sisters, B is the wife of C, D is the son of E, F is the daughter of B, G is the husband of A, E is the father of B. Who is the brother…
78. According to the _______ if a sample of fairly large size is drawn from the population under discussion at random, then on an average the sample…
79. On _______ the frequency, starting from a rather low value, gradually reaches the maximum value, somewhere near the central part and then gradually…
80. In the Stratified Sampling, When the strata-variances differ significantly among themselves, we take recourse to "Neyman's allocation" where:
81. If arithmetic mean of two numbers is 64 and harmonic mean is 16 then geometric mean is
82. In continuous frequency distribution, the median of the data is 32. If each observation is increased by 7, then the new median will be:
83. If mean is 21 and median is 25 then value of mode is
84. Calculate the coefficient of quartile deviation for 11, 55, 65, 22, 33, 98, 88,
85. If two variables 'x' and 'y' are related to 3x + 4y - 7 = 0 and mean & mean deviation about mean of 'x' are 1.2 and 0.4 respectively then the…
86. If in a class, 50% of the student study mathematics and science and 70% of the student study mathematics, then the probability of a student studying…
87. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a…
88. If two dice are rolled, then the probability of getting a greater number on the first die than the one on the second, given that the sum should be…
89. For a binomial distribution, if the mean is 10 and the standard deviation is 3, find n. (number of trials)
90. If a binomial distribution has n = 25 and p = 0.2 what is its mean?
91. If X is a Poisson variate such that P(X = 1) = 0.3 P(X = 2) = 0.2 then P(X = 0) =
92. If the first quartile (Q 1 ) and third quartile (Q 3 ) of a normal distribution are 22 and 28, what is the median of the distribution?
93. The coefficient of rank correlation in a beauty contest of 10 candidates by two judges A & B was found to be 0.5. If it was later discovered that…
94. Fisher's Ideal Price Index is defined as the ______ Index and the Paasche's Index. of the Laspeyres'.
95. The coefficient of correlation between 'x' and 'y' is 0.6. If 'u' & 'v' variables are defined as 2u-x+3 = 0 and 3v+y-2 = 0 then the coefficient of…
96. Which index number method uses current year quantities as weights?
97. If 2x + 3y = 34 and x + y / y = 13 / 8 , find the value of 7x + 5y.
98. The solution of the inequality 5 - 2x / 3 ≤ x / 6 - 5 is
99. The value of √(5 + √(5 + √(5 + √(5 + ... ∞)))) is
100. Solve the system and 5 - 2x / 4 ≤ x / 8 - 5 and x + 4 / 3 ≤ 6.