CA Foundation Quantitative Aptitude PYQ September 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. The value of x in log x (4) +log x (16) + log x (64) = 12 is
2. XYZ invested ₹ 1,68,000 in a business. After a few months, MNP joined in the business by investing ₹ 1,12,000 in the business. At the end of year,…
3. The value of log √a (√(a√(a√(a√a)))) is
4. The ratio of 1 / 2 √35 : 1 / 3 √140 is equal to the ratio
5. If α and β are the roots of the equation x 2 -x-6=0, then the value of α 3 +β 3 + α 2 +β 2 + α+β is…
6. The roots of the equation ( x / x-1 ) 2 - 5( x / x-1 ) + 6 = 0 are:
7. If α and β are the roots of the equation 2x 2 -6x+3=0, then the equation with the roots α / β and β / α is
8. Which of the following is a solution of the inequality 5x / 3 x / 6 - 5?
9. The number of solutions of 5-2x / 4 x / 8 - 5 - 3 - 2x are where x is a real number.
10. The region specified by the inequalities 10x+29y≥40 and 15x-4y≤25 includes the point
11. The compound interest on ₹ 1,00,000 compounded quarterly, for 9 months at 4% per annum is
12. The difference between the compound interest and the simple interest on a certain sum at 12% per annum for 2 years is ₹ 90, when the interest is…
13. A machine is depreciated at the rate of 15% on the reducing balance. The original cost of machine was ₹ 2,00,000. In approximately how many years,…
14. Mohan invests ₹ 25,000 every year starting from today for next 5 years. Interest rate is 7% per annum compounded annually. The future value of the…
15. Mr. X borrowed ₹ 6000 from Mr. Y at 10% per annum simple interest. After two years Mr. X wanted to repay this amount, Mr. Y is insisted on paying…
16. If ₹ 2,470 is obtained as an interest in 4 years and 4 months at the rate of 3% per annum simple interest rate in bank deposit, how much amount was…
17. The compound interest of ₹ 4,900 is ₹ 1661 for 2 years at a certain rate of interest, compounded annually. What is the rate of interest per annum in…
18. If Mr. XYZ is investing ₹ 86,000 in a bank fixed deposit scheme where interest will be payable at 12% per annum, compounded half-yearly, what will…
19. Ms. Y invested ₹ 2,00,000 in a mutual fund equity scheme. She redeemed entire investment after 96 months and received ₹ 6,00,000 after redemption.…
20. A loan of ₹ 5,000 is lent for three years at the rate of 10% per annum, compounded semi-annually. The future value of the money is ₹ (Given: 1.05 6…
21. One person wants to have ₹ 20,000 at the end of six years. Hence, he deposits ₹ (rounded in rupee) in a fund that pays 3% per annum, compounded…
22. Suppose you deposit ₹ 1,000 today, ₹ 2,000 after one year from today and ₹ 3,000 after two years from today, in a deposit that pays 10% per annum,…
23. You are interested in an investment of ₹ 5,000 in a fund that promises ₹ 50 at the end of each year, forever. What is the annual interest rate on…
24. An investment was priced at ₹ 100 per share in year 0, priced at ₹ 150 per share in the end of the first year, and priced ₹ 200 per share in the end…
25. How many different words from the letters of the word MATHEMATICS can be formed so that all the vowels always come together in any word?
26. Find n if n P 5 = 20 n P 3
27. In a school, for a class monitor selection, there are 6 candidates, and students need to choose up to 3 monitors. A student can vote for 1 or 2 or 3…
28. Different words are made with rearrangement of letters of the word “TROPICAL" in a way that the vowels occupy odd places when counted from left. How…
29. The common difference of the arithmetic progression 1 / 3 , 1-3b / 3 , 1-6b / 3 , ... is
30. If the numbers x, 2x + 2 and 3x + 3 are in the geometric progression, then the fourth term of the progression is
31. The sum of all natural numbers between 200 and 600 those are divisible by 13 is
32. The sum of first two terms of a geometric progression is 14 and its infinite sum i.e. sum up to infinity is 32. What is the common ratio of the…
33. For a relation R, aRb represents that a is related to b. If for all a, b, c, aRb and bRc gives that aRc, then the relation is
34. Let S = {a, b, c, d, e}. The number of non-empty proper subsets of S is
35. If f(y)= 1 / 1+y and g(y) = y-1 / y then fog(y)=
36. The inverse of the function f(x) = 2+3x / x+5 by taking f(x) as y, is
37. Find dy / dx for x 2 y 2 +y = 0.
38. The cost function of an organisation as C(x) = 500-5x 2 + x 3 / 3 , where x denotes the output. Find the level of output at which marginal cost is…
39. The value of ∫ 0 4 x+3 / x+2 dx is
40. The value of ∫ 2x / 1+x 2 dx is
41. Complete the given series: 0, 6, 24, 60, 120, 210, _____.
42. Find the odd one out in the series: 2, 5, 10, 17, 26, 37, 50, 64.
43. If in a certain language, MADRAS is coded as NBESBT. How is DELHI coded in that language?
44. In a certain code, GLAMOUR is written as IJCNMWP and MISRULE is written as OGUSSNC, then how will MUSICAL be written in that code?
45. In the following series, one term is wrong. Find out the wrong term. 48, 50, 82, 170, 290
46. Suresh started walking 4 km west from his office. Then he turned right and walked 2 km. Again he turned right and walked 2 km to reach his house. In…
47. Mr. PQR walked 50 metres towards east, took a right turn and walked 40 metres. Then he took a left turn and walked 30 metres. In which direction is…
48. Starting from point A, PQ walked 40 metres south. She turned left and walked 40 metres. She then turned left and walked 40 metres. She again turned…
49. Two persons, P and Q, start walking from a meeting point towards North. After walking 100 metres, P turns left and Q turns right. P, after walking…
50. A hunter is chasing a deer, by running 200 metres in east direction, turns to his right, runs 100 metres and turns to his right, runs 90 metres.…
51. Six persons A, B, C, D, E and F are sitting in a circle facing the centre. A is facing D. C is left of A and right of E. D is between B and E. F is…
52. Six persons A, B, C, D, E and F are sitting in two rows with 3 persons in each row facing same side. C is sitting in the middle of first row. B is…
53. Six people, A, B, C, D, E and F are sitting in a hexagonal shape. All the sides of the hexagon so formed are of same length. A is not adjacent to B…
54. Seven persons with names T, B, L, A, P, Z and R are standing in a row, facing East. It is given that T is to the right of R; A is between B and Z,…
55. Eight friends with names P, Q, R, S, T, U, V and W are sitting on a bench and facing North. U is sitting between S and V; Q is sitting between W and…
56. A girl introduced a boy as the son of daughter of the father of her uncle. The boy is girl's
57. A and B are Brothers. C and D are Sisters. A's son is D's Brother. How is B related to C?
58. Ms. X told Ms. Y, "The girl I met yesterday at the market was the youngest daughter of the brother-in-law of my friend's mother." How is the girl…
59. There are six members, named as, A, B, C, D, E and F. It is given that E is the brother of A's husband; F is the mother of E; B is the daughter of D…
60. It is given that a person named as A is married to B; the person E is a brother of D and the person B is the mother of C whose sister is D. How is D…
61. Sampling method which belongs to the category of Mixed sampling is
62. Number of students in a college is an example of
63. For manifold classification, this method of presentation of data cannot be recommended:
64. The most commonly used distribution is ______ in which the maximum frequency is at the central part and the frequency decreases when one moves away…
65. Which of the followings is not a basic principle of sample survey?
66. After a singing competition on a live TV show, the winner is selected according to the number of likes each candidate has received on a messaging…
67. A bar chart can be drawn for the data having numbers on
68. An investigator collects information on salaries received by 1000 persons. From this collection, the data on women are extracted. Now the data is…
69. Two sales-persons present their numbers of sales per week for a month. An appropriate diagram that can be drawn for this data is ______
70. If X and Y are related by 4X+3Y+5=0 and Mean of X is 10, then the Mean of Y is
71. For a moderately skewed distribution of marks in English for a group of 145 students the mean marks and median marks were found to be 55.10 and…
72. If there are two groups with 10 and 12 observations and harmonic mean of the two groups are 3 and 5 respectively, then the combined Harmonic mean is
73. Best measure of Dispersion for open-end classification is the ______ which does not change with the change of ______
74. Coefficient of range of 84, 93, 53, 70, 82, 65 is
75. Calculate the Harmonic Mean of 1, 1 / 3 , 1 / 6 and 1 / 9
76. Find the Coefficient of variation for the following numbers; 7,5,9,3,6
77. A set contains seven numbers whose average is 12. The average of four greater numbers is 18 and the average of four smaller numbers is 8. Which of…
78. If the sum of ten values is 20 and sum of squares of these values is 80, then the standard deviation is ____
79. A data set has first eleven positive multiples of 6. The semi inter-quartile range is ____
80. The number of tosses of a coin, that are needed so that the probability of getting at least one head is 0.875, is
81. Two-person X and Y appear in an interview for two vacancies for the same post. The probability of X's selection is 1 / 5 and that of Y's selection…
82. A number is selected at random from the first 50 natural numbers. What is the probability that it would be either a two-digit prime number or a…
83. Some dice with six faces have numbers written from Four to Nine. Two such dice are thrown simultaneously. Find the probability that the sum of…
84. Three components A, B and C are manufactured separately and then assembled into a finished product. While producing the three components, it is…
85. Two persons are playing a set of matches. The winner of 4 matches is declared as the winner. Any player has 50% chance to win a match. The…
86. The Mode of binomial distribution B (7, 1 / 3 ) is
87. An emergency room receives an average of 3 patients per hour. What is the probability that exactly 2 patients arrive in an hour? (Given: e 0 = 1, e…
88. If a binomial distribution has n = 20 and p = 0.3 what is its variance?
89. It is given that X has normal distribution with mean zero and standard deviation one. Also given that P [- 2 < X < 2] = 0.95, P[- 2 < X…
90. The probability mass function of a distribution is given below in a tabular form: x | 0 | 1 | 2 | 3 | 4 p(x) | k | 2k + k 2 | 3k | 2k + k 2 | k…
91. For a group of students, the sum of squares of differences in ranks for Maths and Physics marks are found to be 60, which is 120 times the value of…
92. If two variables move in the same direction i.e. an increase (or decrease) on the part of one variable introduces an increase (or decrease) on the…
93. If m + 3x=10 and 2y + 5n=25 and regression coefficient of y on x is 0.80, what is the regression coefficient of n on m?
94. If the regression coefficient b yx is greater than one, then the regression coefficient b xy
95. The sum of squares of the differences between two ranks awarded by two judges on 10 candidates is ____ if the rank correlation coefficient is 0.8.
96. Two indices that is current on base and base on current should be reciprocals of each other in
97. If ∑p 0 q 0 = 160.7 and ∑p 1 q 0 = 178.6, then the cost of living index is
98. Which sampling technique can be used for the construction of Index numbers?
99. From the year 2015 to 2025, Consumer price index increased from 125 to 196. During this period, salary of the employees as per 7th pay commission…
100. If the consumer price index number is 750, then the purchasing power of one rupee is ____