CA Foundation Quantitative Aptitude MTP September 2026: Question Paper and Solutions

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

1. If 15(x 2 − y 2 ) = 7xy and x, y are positive, then find x : y
2. A Person has asset worth of ₹ 1,48, 200. He wants to divide among his wife, son and daughter in the ratio 3:2:1. Find the share of the son
3. If 4 × 2 n × 16 / 2 n/2 × 64 = 64, then the value of n will be
4. If log x / y−z = log y / z−x = log z / x−y , then find value x x .y y .z z
5. If x=2 + 2 1 / 3 + 2 2 / 3 , then the value of x 3 -6x 2 +6x is
6. The ratio of the speeds of two trains is 2:5. If the distances they travel are in the ratio 5:9, find the ratio of the times taken by them.
7. If α and β are the roots of the equation x 2 −5x+6=0 then the value of α 2 +β 2 +α+β
8. A Invested ₹1,80,000 at the start of the year. B joined later with ₹2,40,000. The profits were shared in the ratio 9 : 5.After how many months from…
9. The region represented by x+y≥4,x≥1 contains
10. If a, b, c are in continued proportion, then a 2 + b 2 / b 2 +c 2 is equal to:
11. If α and β are the roots of the equation x 2 −5x+6=0 then the equation whose roots are (α+1) and (β+1) is:
12. The sum required to earn a monthly interest of ₹1,500 at 12% p.a. simple interest is:
13. A company wants to accumulate ₹1,00,000 after 5 years to replace a machine. If the fund earns 10% compound interest per annum, the annual amount to…
14. A person deposits ₹10,000 at the end of each year for 3 years in a fund earning 10% per annum compound interest. The amount accumulated at the end…
15. A person wishes to receive ₹5,000 per year for 4 years. If the rate of interest is 10% per annum, the present value of the annuity is approximately:
16. The difference between Compound Interest and Simple Interest on a sum for 2 years at 15% p.a., compounded annually, is ₹225. The principal is:
17. A machine costing ₹3,00,000 depreciates at 20% p.a. on the reducing balance method. Its value after 3 years is
18. The compound interest on ₹10,000 for 2 years is ₹2,100, compounded annually. The rate of interest is
19. A bank offers 8% p.a., compounded quarterly. The effective annual rate is
20. An investment grows from ₹3,00,000 to ₹4,39,230 in 5 years. (Given 1.08 5 =1.4693). Then Compound Annual Growth Rate (CAGR) is
21. A loan of ₹20,000 is borrowed for 2 years at 12% p.a., compounded annually. The future value is
22. An investor purchases a perpetuity that pays ₹12,000 per year forever. If the required rate of return is 8% per annum, the present value of the…
23. A project requires an initial investment of ₹40,000 and is expected to generate a cash inflow of ₹55,000 after one year. If the discount rate is 10%…
24. A person expects to receive ₹1,10,000 after one year. If the inflation rate is 10% per annum, the present purchasing power of this amount is:
25. Six bulbs, of which four are defective, are to be tried in two light points in a dark room. In how many trials will the room be lightened?
26. The Indian Cricket team consists of 16 players. It includes 2 wicket keepers and 5 bowlers. In how many ways can a cricket eleven be selected if we…
27. Find sum to n terms of the series 1 / 1.2 + 1 / 2.3 + 1 / 3.4 + 1 / 4.5 +....:
28. The sum of the first n terms of an A.P is 3n 2 -2n+1. The common difference is
29. If the 3rd term of a G.P. is 12 and the 6th term is 96, then the common ratio is:
30. Find the value of lim x→3 (x 2 −4) is:
31. A function f: A→B is one-one if:
32. The relation R={(1,1),(2,2),(3,3)} on A={1,2,3} is:
33. If A={1,2,3} and B={a,b}, then the number of elements in A×B is:
34. If y=x 3 -5x 2 +4x+7, then dy / dx is:
35. The total cost function of a firm is C(x)=x 3 −6x 2 +15x+20, The marginal cost at x=2 units is:
36. The marginal cost function of a firm is, MC=6x+4. If the fixed cost is ₹100, then the total cost function is:
37. ∫(2x+1) 5 dx = (2x+1) n / m + C , then the value of m+n is
38. If f(x)=x 2 -3x+2, then f(2)+f(3) is
39. The number of arrangements of the letters of the word ACCOUNT in which all the vowels are together is
40. In a class of 80 students, 45 study Mathematics, 40 study Statistics and 15 study neither. The number of students studying both Mathematics and…
41. Identify the odd one out:
42. If DELHI is coded as 45 and MUMBAI as 54, then CHENNAI is coded as:
43. Find missing term of the alphabet letter series ABD, DGK, HMS, MTB, SBL, ?
44. If ROAD = URDG, then MILK = ?
45. Find next term of the series 7, 26, 63, 124, 215, 342, ?
46. P is the mother of Q. R is the husband of P. S is the sister of Q. T is the son of R. How is S related to T?
47. In a family of six persons A, B, C, D, E and F, there are two married couples. (i) D is the father of B. (ii) B is the husband of C. (iii) A is the…
48. All the six members of a family A, B, C, D, E and F are travelling together. B is the daughter of C, but C is not the father of B. (i) A and C are a…
49. A, B, C, D, E and F are members of a family. B is the brother of D. C is the mother of B. A is the husband of C. E is the father of A. F is the wife…
50. A, B, C, D, E and F are members of a family. (i) B is the son of C. (ii) A and C are a married couple. (iii) D is the daughter of A. (iv) E is the…
51. Seven students P, Q, R, S, T, U and V are sitting in a row facing North. (i) Q is third to the left of T. (ii) P is at one of the ends. (iii) R is…
52. Eight friends P, Q, R, S, T, U, V and W are sitting around a circle facing the centre. (i) P is between Q and R. (ii) S is opposite P. (iii) T is to…
53. Directions (Q. 53–55): Seven athletes—A, B, C, D, E, F, and G—are standing in a line to receive medals. (i) B is standing to the…
54. Directions (Q. 53–55): Seven athletes—A, B, C, D, E, F, and G—are standing in a line to receive medals. (i) B is standing to the…
55. Directions (Q. 53–55): Seven athletes—A, B, C, D, E, F, and G—are standing in a line to receive medals. (i) B is standing to the…
56. Directions (Q. 56–57): A person starts walking from Point A towards the East. After walking 20 meters, he then turns Right and walks 10…
57. Directions (Q. 56–57): A person starts walking from Point A towards the East. After walking 20 meters, he then turns Right and walks 10…
58. It is 3'o clock in a watch. If the minute hand points towards the North-East then the hour hand will point towards the
59. A man is facing East. He turns 180° clockwise and then 90° clockwise. Which direction is he facing?
60. A, B, C and D are playing carrom. A and D are partners. B is to the right of A. If A is facing East, then C is facing:
61. Which of the following is a relative measure of dispersion (dimensionless/unitless)?
62. If a constant value k = 5 is added to every observation in a dataset, how does the Standard Deviation change?
63. If every value in a dataset is multiplied by a constant k=-3, how does the variance of the new dataset relate to the original variance σ 2 ?
64. The distribution of heights of adult men generally follows:
65. The median of a frequency distribution can be obtained from:
66. If the GM and AM for 10 observations are both 15, then the value of HM.
67. The price of a commodity doubles in a period of 4 year, what is the average percentage increase per year?
68. If the AM and GM for two numbers are 6.50 and 6 then the two numbers are
69. Find the third quartile (Q 3 ) of the data:12, 15, 18, 20, 22, 25, 28, 30, 35
70. The mean of 50 observations was found to be 30. Later, it was discovered that 42 was wrongly entered as 24. The correct mean is:
71. The arithmetic mean and coefficient of variation of a data set are 20 and 25 respectively. The variance of 5+3x is:
72. The geometric mean of three numbers 25, 16 and x is 20. The value of x is:
73. Two cards are drawn without replacement. What is the probability that both are Red cards?
74. If three coins are tossed simultaneously, what is the probability of getting two heads together?
75. A class has 12 boys and 18 girls. One-third of the boys and one-half of the girls wear spectacles. What is the probability that a randomly selected…
76. A device consists of two independent components A and B. The probabilities that A and B are defective are 0.10 and 0.15 respectively. Find the…
77. If P(A)=0.6, P(B)=0.5,P(A∩B)=0.3, find P(B|A).
78. If a number is selected at random from the first 60 natural numbers, what is the probability that it is a multiple of both 4 and 5?
79. For a Poisson distribution, if P(x=1) =P(x=2), then the mean is:
80. For a binomial distribution with n=25, p=0.4, q=0.6, the standard deviation is:
81. The skewness of a perfectly symmetrical distribution is:
82. If the first quartile is 40 and the third quartile is 70, then the coefficient of quartile deviation is:
83. Regression equations given by x+2y-8=0, 3x+y-9=0. Find Mean of x and Mean of Y
84. Correlation from Regression Coefficients are b yx =0.64 and b xy =0.49. Find the correlation coefficient.
85. Ranks obtained by 5 students in two subjects are: Student A B C D E Maths 1 2 3 4 5 Statistics 2 1 4 3 5 Find Spearman's rank correlation.
86. Given: r = 0.75, σ x = 6, σ y = 9 . Find regression coefficient of y on x.
87. The two regression lines are: 2x+5y-9=0, 4x+5y-15=0. Find the coefficient of determination
88. If Laspeyres Price Index = 144 and Paasche Price Index = 121, then Fisher's Ideal Index is:
89. The index used to measure changes in the cost of living of consumers is:
90. When a new commodity is added to an index series, the method generally used is:
91. Given: ∑P 1 Q 0 = 420,∑P 0 Q 0 = 350 ∑P 1 Q 1 = 480,∑P 0 Q 1 = 400. Find Fisher's Ideal Index.
92. The quantity sold increases from 200 units to 250 units. The quantity relative Index is:
93. If Fisher's Index = 150 and Paasche's Index = 144, then Laspeyres Index is:
94. If the variance of a distribution is 16 and the mean is 20, then the coefficient of variation is:
95. A game consists of tossing a fair coin. If a head appears, a player wins ₹50; if a tail appears, the player loses ₹20. The expected gain of the…
96. If r = 0.5, Cov(x,y) = 20, and σ x =8, then σ y is: Find Standard Deviation
97. The median of the observations 18, 25, 12, 30, 20, 15, 28, 22, 35, 40 is:
98. Given that ∑x 2 =2450, N=50,σ=5, then mean is:
99. Two series have the following characteristics: Series A: Mean = 40, S.D. = 8, and for Series B: Mean = 50, S.D. = 12, which series is more consistent?
100. Which of the following graphical methods is most suitable for representing a frequency distribution of continuous data?
101. The fourth proportional to (a 2 – ab + b 2 ), (a 3 + b 3 ) and (a-b) is equal to ______
102. A person has assets worth ₹1,80,000. He wants to divide them among his wife, son and daughter in the ratio 4: 3 : 2. Find the share of the son.
103. Find the value of p from (√4) -6 × (√2) -4 = 2 p .
104. If p q = q p then value of ( p / q ) p / q - p p / q reduces to
105. The value of log x (0.00001) = − 5, then x is
106. The sum of a number and its reciprocal is (41/20). The number is
107. Solve for x, 4 x - 3.2 x+2 + 2 5 =0
108. The equation y 3 – 7y + 6 = 0 is satisfied by
109. The roots of the equation 2 2x-y + 2 y-2 – 3 = 0 are
110. If 5 = √(x + √(x + √(x.......∞))), then value of x is
111. The sum of the digits of a two digit number is 12. If the digits are reversed, the number is decreased by 18. Find the number.
112. Solve for x, x-3≥2x+9
113. If 4x+3>19, then x belongs to:
114. ₹20,000 is invested at an annual rate of interest of 10% p.a. The amount after 2 years, compounded annually, is:
115. At what interest rate will a sum doubles itself in 7 years, if the interest is compounded annually.
116. A machine for which the useful life is estimated to be 5 years, Cost ₹ 5000 and Rate of depreciation is 10% p.a. The scrap value at the end of its…
117. The sum required to earn a monthly interest of Rs 1200 at 18% per annum Simple Interest is
118. On what sum will the compound interest at 5% per annum for two years compounded annually be ₹1640?
119. Find the future value of an annuity of ₹500 is made annually for 7 years at interest rate of 14% compounded annually. Given that (1.14) 7 = 2.5023.
120. The effective rate of interest corresponding to a nominal rate 3% p.a payable half yearly is
121. If the simple interest on ₹ 1,200 be more the interest on ₹ 1,000 by ₹ 30 in 3 year. Find the rate percent per annum.
122. If the present value of future cash inflows is ₹ 75,000 and the initial investment is ₹ 60,000, the NPV is:
123. A perpetuity provides an annual cash flow of ₹ 8,000. If the required rate of return is 8% p.a., its present value is:
124. A company's revenue increases from ₹ 50 lakh to 72 lakh in 2 years. The CAGR is:
125. Find the value of n if (n+1)! = 42 (n−1)!
126. Every two person shakes hands with each other in a party and the total number of hand shakes is 66. The number of guests in the party is
127. In ______ ways can 4 Americans and 4 English men be seated at a round table so that no 2 Americans may be together?
128. A box contains 7 red, 6 white and 4 blue balls. How many selections of three balls can be made so that none is red?
129. The sum of the following 5, 9, 13, 17............. 25 terms in AP is
130. The 4th term of series whose sum to n terms is 5n 2 +2n is
131. The series 1 / 3 + 1 / 3 2 + 1 / 3 3 + 1 / 3 4 + ...... to ∞ is
132. Find the f o g for the functions f (x) =x 2 , g (x) = x+ 1
133. If a function in x is defined by f(x) = x / x 2 +1 , X ∈ R then f(1/x) =
134. If f(x)=x 2 -1 and g(x) = x+1 / 2 , then f(3) / f(3)+g(3) is
135. lim x→1 x 2 - 4x + 3 / x 2 -6x + 5 =
136. If lim x→3 x n -3 n / x-3 = 405, then value of n is equal to
137. Evaluate result of ∫(x 2 −1) 2 dx is
138. If u = (x 3 +1) 5 and y = (x 3 + 5x+7) then du / dy is
139. Find dy / dx of ( x 2 / a 2 + y 2 / b 2 = 1)
140. If y = e x - e -x then dy / dx √(y 2 + 4) is equal to
141. Find the odd one out: 3, 8, 15, 24, 35, 48, 62, 80
142. In a certain code, GARDEN is written as ICTFGP. How will FLOWER be written?
143. Find the wrong term of the series 5, 11, 25, 51, 103, 207
144. If in a certain language, TABLE is coded as UBCMF, how is CHAIR coded?
145. Complete the given series: 1, 6, 15, 28, 45, 66, ?
146. Ravi walks 6 km towards North from his office. He then turns right and walks 4 km. He again turns right and walks 6 km. In which direction is he…
147. A person walks 40 meters towards East, turns left and walks 30 metres, then turns left again and walks 40 metres. How far and in which direction is…
148. A man walks 30 m North, turns right and walks 40 m, turns right and walks 20 m, then turns left and walks 30 m. In which direction is he from his…
149. A person starts facing East. He turns 45° anticlockwise, then 90° clockwise, and finally 135° anticlockwise. What is his final direction?
150. A hunter is chasing a deer, by running 200 metres in the east direction, turns to his right, runs 100 metres and turns to his right, runs 90 metres.…
151. Six persons P, Q, R, S, T and U are sitting in two rows of three each, all facing north. P is in the middle of the first row. Q is to the left of P.…
152. Seven persons P, Q, R, S, T, U and V are standing in a row facing north. P is to the right of Q. R is third to the left of P. S is at the extreme…
153. Eight persons A, B, C, D, E, F, G and H are sitting in two rows of four each, facing each other. A, B, C and D are in the first row. E, F, G and H…
154. Eight persons A, B, C, D, E, F, G and H are sitting in a circle facing the centre. A is second to the right of B. C is immediately right of A. D is…
155. Six persons A, B, C, D, E and F are sitting at the six vertices of a regular hexagon. A is not adjacent to B or C. D is not adjacent to C or E. B…
156. A man said, "The daughter of my mother's only son is the sister of this boy." How is the man related to the boy?
157. A family consists of 10 members P, Q, R, S, T, U, V, W, X and Y. • P is the father of Q. • R is the wife of P. • Q is the brother of S. • S is the…
158. If: P @ Q means P is the son of Q, P # Q means P is the daughter of Q, P $ Q means P is the brother of Q and P% Q means P is the sister of Q. Then…
159. Pointing to a boy, Neha said, “He is the son of the only daughter of my mother's only son.” How is the boy related to Neha?
160. A and B are brother. C is the sister of A. D is the mother of B. E is the father of D. How is E related to A?
161. When the data are classified in respect of successive time points, they are known as ______
162. The following data relate to the incomes of 100 persons: Income (₹) No. of persons 500-999 10 1,000-1,499 25 1,500-1,999 40 2,000-2,499 25 What…
163. Find the number of observations between 100 and 200: Value No. of observations More than 50 95 More than 100 75 More than 200 45 More than 300 20
164. Which of the following is an example of bivariate data?
165. Data obtained from census reports, government publications and published reports are generally:
166. The width of each of 12 classes is 2.5. If the lower class boundary of the lowest class is 7.5, the upper class boundary of the highest class is:
167. In a group of 40 persons, the average weight is 60 kg. If the average weight of males and females is 75 kg and 50 kg respectively, find the ratio of…
168. The class interval having the highest frequency is called:
169. For a moderately skewed distribution, which relationship holds?
170. The sum of deviations of observations from their arithmetic mean is always:
171. If A.M. = 20 and H.M. = 12 for two positive numbers, their G.M. is:
172. The average of 7 numbers is 18. If one number is replaced by 30, the average increases to 20. The number that was replaced is:
173. If the standard deviation of x is 4, what will be the standard deviation of 3x-7?
174. The third decile of the following observations is: 14,8,21,17,11,25,19,10,13
175. If the range of x is 15, then the range of 3x-7 / 2 is:
176. If the overall percentage of success in an examination is 70%, what is the probability that out of a group of 5 students, at least one student has…
177. If the mode of a data set is 18 and its mean is 24, then the median is:
178. The median of the following numbers, which are given is ascending order is 25. Find the Value of X. 11,13,15,19, (x+2), (x+4), 30,35,39,46.
179. If 5 is subtracted from each observation of some certain item then its co-efficient of variation is 10% and if 5 is added to each item then its…
180. A letter is selected at random from the word RANGE and another letter is selected at random from the word PAGE. The probability that the two letters…
181. If one of the regression coefficients is ______ unity, the other must be ______ unity.
182. Which of the following regression equations represents the regression line of Y on X? 7x+2y+15=0 2x+5y+10=0
183. The coefficient of rank correlation of marks obtained by 10 students in English and Economics was found to be 0.5. It was later discovered that the…
184. Two random variables have the following regression lines: 3x+2y=26 and 6x+y=31. The coefficient of correlation between x and y is:
185. The probability of a girl getting a scholarship is 0.6 and the probability of a boy getting a scholarship is 0.8. Find the probability that at least…
186. The odds in favour of A solving a problem are 5 : 7, and the odds against B solving the same problem are 9 : 6. What is the probability that, if…
187. The daily demand for calculators has the following probability distribution: Demand X 1 2 3 4 5 6 Probability P(X) 0.10 0.15 0.20 0.25 0.18 0.12…
188. An urn contains 9 balls, of which 2 are red, 3 are blue, and 4 are black. Three balls are drawn at random. The probability that all three balls are…
189. A sample of 100 dry battery cells was tested to find the length of life. The mean life was found to be 12 hours and the standard deviation was 3…
190. If 5% of the families in Kolkata do not use gas as a fuel, what will be the probability of selecting 10 families in a random sample of 100 families…
191. Suppose the weather records show that, on an average, 5 out of 31 days in October are rainy days. Assuming a binomial distribution, with each day of…
192. The probability density function of a normal random variable X, with mean μ and standard deviation σ, is given by:
193. Correlation Co-efficient is ______ of the units of measurements
194. A ______ distribution is a theoretical distribution that expresses the functional relation between each of the distinct values of the sample…
195. Simple random sampling is very effective if ______
196. The test of shifting the base is called
197. If with rise of 10% in prices the wages are increased by 20%. Find the percentage of real wage increase
198. For factor reversal test: P 01 × Q 01 = ∑P 1 Q 1 / ∑P 0 Q 0 = True Value Ratio (T.V.R.) This is
199. Between 2024 and 2025, the price of a commodity increased by 60% while the production decreased by 30%. By what percentage did the value index of…
200. Expenditure of a family on three items are in the ratio of 2: 5: 3. The prices of these commodities rise by 30%, 20% and 40% respectively. By what…