CA Foundation Quantitative Aptitude MTP May 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 (4) 3 × (√2) 2n = 2 n , then n is
2. The values of x for the equation x 2 + 9x + 18 = 6 – 4x are
3. The solution of the equation (p+2) (p−3) + (p+3) (p−4) = p (2p−5) is
4. The denominator of a fraction exceeds the numerator by 7 and if the 2 is added to the denominator, then the fraction becomes 3 / 4 . Find the…
5. The value of √(6+√6+√6+.......∞) is
6. log p 2 / qr + log q 2 / pr + log r 2 / pq =
7. A bag contained 25 paise, 10 paise and 5 paise are in the ratio 3:2:1. The total value of ₹ 40, the number of 5 paise coins is
8. If 2 x × 3 y × 5 z = 720 then the value of x, y, z?
9. A man wants to cut three lengths from a single piece of board of length 91 cm. The Second length is to be 3 cm longer than the shortest and third…
10. A labour can be paid under two methods of given below: (i) ₹ 600 fixed and ₹ 50 per hour (ii) ₹ 170 per hour If a labour job work takes 'r' hours to…
11. The time required to produce a unit of product A is 3 hours and that for product B is 5 hours. The total available time is 220 hours. If x and y are…
12. What must be added to each term of the ratio 49:68. So that it becomes 3:4?
13. Find future value of annuity of ₹ 1000 made annually for seven years at interest rate 16% compounded annually. [Given that (1.16) 7 = 2.8262]
14. Assuming that the discount rate is 7% is p.a. How much would you pay to receive ₹ 500. Growing at 5% annually forever?
15. Rajesh deposits ₹ 3,000 at the start of each quarter in his savings account. If the account earns interest 5.75% per annum compounded quarterly, how…
16. The annual rate of simple interest is 12.5%. In how many years does principal doubles?
17. ₹ 5000 is paid every year for 10 years to pay off a loan. What is the loan amount of interest rate be 14% p.a. compounded annually?
18. ₹ 800 is invested at the end of each month in account paying interest 6% per year compounded monthly. What is the future value of annuity after 10…
19. Certain sum of money borrowed at simple interest to ₹ 2688 in three years and to ₹ 2784 in four years at the rate per annum equal to
20. Ravi made of an investment of ₹ 15,000 in a scheme and at the time of maturity the time of maturity the amount was ₹ 25,000. If Compound Annual…
21. Madhu takes a loan of ₹ 50,000 from ABC Bank LTD. The rate of interest is 10% per annum. The first instalment will be paid at the end of five year.…
22. Rajesh invests ₹ 20,000 per year in a stock index fund, with earns 9% per year, for the next ten years. What would be closest value of accumulated…
23. An investment is earning compounded interest ₹ 100 invested in the year 2 accumulated to ₹ 105 by year 4. If ₹ 500 invested in the year 5, will…
24. An investor is saving to pay off an obligation of ₹ 15,250 which will due in seven years, if the investor is earning 7.5% simple interest rate per…
25. The value of scooter is ₹ 1,00,000 find its depreciation is 10% p.a. Calculate total depreciation value at the end of seven years.
26. Effective rate of interest does not depend upon
27. The number of triangles that can be formed by choosing the vertices from a set of 12 points, Seven of which lie on the same lie on the same straight…
28. Five bulbs of which three are defective are to be tired in two light-points in a dark-room. In how many trails the room shall be lightened?
29. In how many ways can a party of 4 men and 4 women be seated at a circular table, so that no two women are adjacent?
30. How many words can be formed with the letters of the word ‘ORIENTAL’. So that A and E always oocupy odd places:
31. The number of ways of painting the faces of a cube by 6 different colours is
32. The sum of an AP, whose first is -4 and last term is 146 is 7171. Find the value of n
33. In a geometric progression, the second term is 12 and sixth term is 192. Find 11 th term.
34. The first and last terms of an arithmetic progression are 5 and 905. Sum of the terms is 45,955. The number of terms is
35. The sum of first eight terms of geometric progression is five times the sum of the first four terms. The common ratio is
36. If the sum of n terms of an AP is (3n 2 -n) and its common difference is 6, then its 1 st term is
37. Two finite sets have m and n elements. The total number of sub sets of first set is 56 more than the total number of subsets of the second set. The…
38. Evaluate Lim x→a (x + 2) 5/3 – (a+2) 5/3 / x-a is
39. Determine f(x), given that f'(x) =12x 2 -4x and f(-3) =17
40. ∫ 0 1 x.e x dx
41. Find the missing term in each of the following series : 6, 13, 25, 51, 101, ?
42. Find the missing term in each of the following series : 28, 33,31,36, 34,39, ?
43. In a certain code, TEACHER is written as VGCEJGT, How is CHILDREN written in that code?
44. In a certain code language, '253' means 'books are old'; '546' means 'man is old' and '378' means 'buy good books'. What stands for 'are' in that…
45. If SUMMER is coded as RUNNER, the code for WINTER will be
46. From home Neha goes towards North for her college and then she turns left and then turns right, and finally she turns left and reaches college. In…
47. Y is to the East of X, which is to the North of Z. If P is to the South of Z, then P is in which direction with respect to Y.
48. Five villages P, Q, R, S, and T are situated close to each other. P is to the west of Q, R is to the south of P. T is to the north of Q and S is to…
49. If South-West becomes North, then what will North-East be?
50. In a clock at 12: 30, hour needle is in North direction while minute needle is in South direction. In which direction would be minute needle at 12:45?
51. Five students are standing in a circle. Abhinav is between Alok and Ankur. Apurva is on the left of Abhishek. Alok is on the left of Apurva. Who is…
52. How many persons are there to the right of D?
53. Which of the following is sitting to the left of D?
54. Who is at the immediate left of C?
55. Five persons are sitting on a bench to be photographed, S is to the left of N and to the right of B. M is to the right of N. R is between N and M.…
56. B is the brother of A whose only sister is mother of C, D is maternal grandmother of C How is A related to D?
57. If X+Y means X is the mother of Y; X-Y means X is the brother of Y; X%Y means X is the father of Y and X×Y means X is the sister of Y, Which…
58. 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?
59. 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?
60. Pointing to a photograph. Bajpai said, "He is the son of the only daughter of the father of my brother." How Bajpai is related to the man in the…
61. Which sampling technique is most appropriate when a person wants to ensure that subgroups are proportionally represented?
62. Non-probability Sampling is also known as:
63. The number of possible samples of size n out of N population units without replacement is
64. Finite population correction is
65. In a group of persons, average weight is 60 kg. If the average of males and females taken separately is 80 kg and 50 kg respectively, find the ratio…
66. A train covered the first 5 km of its journey at a speed of 30km/hr and next 15 km at a speed of 45 km/hr. The average speed of the train was:
67. If 2x + 3y + 4 = 0 and v(x) = 6 then v (y) is:
68. If the standard deviation of 1, 2, 3, 4, ...... 10 is σ, then the standard deviation of 11, 12, 13, 14, ...... 20 is:
69. What is the standard deviation of the following series : Measurements: 0-10, 10-20, 20-30, 30-40 Frequency: 1, 3, 4, 2
70. If the difference between Mean and Mode is 69, then the difference between Mean and Median will be _____
71. If all observations in a distribution are increased by 6, then the variance of the series will be _____
72. Which measure of dispersion is base on the absolute deviation only?
73. Calculate the value of 3 rd quartile from the following data 40, 35, 51, 21, 25, 16, 29, 27, 32
74. The mean of 100 students was 45. Later on, it was discovered that the marks of two students were misread as 85 and 54 instead of 58 and 45. Find…
75. The arithmetic mean and coefficient of variation of data set x are respectively, 10 and 30. The variance of 30-2x is
76. The approximate ratio of SD, MD, QD is
77. The geometric mean of three numbers 40, 50 and x is 10, the value of x is
78. Difference between upper limit and lower limit of class is known as
79. If P(A) = 1 / 3 , P(B) = 1 / 2 and P(A∪B) = 5 / 6 , then events A and B are
80. A and B two events such that P(A∪B) = 3 / 4 , P(A∩B) = 1 / 4 and (P(A) c ) = 2 / 3 , then P(A∩B) is equal to
81. Five persons A, B, C, D and E are standing in a queue of a ration shop. The probability A and B are always together -
82. A card is drawn from a pack of playing cards and then another card is drawn without the first being replaced. What is the probability of getting two…
83. The probability of a man hitting the target is 1 / 4 . If he fires 7 times, the probability of hitting the target at least twice is :
84. If 5% of the electric bulbs manufactured by a company are defective, use Poisson distribution to find the probability that in a sample of 100 bulbs,…
85. In a non- leap year, the probability of getting 53 Sundays or 53 Tuesdays or 53 Thursdays is:
86. Examine the validity of the following: Mean and standard deviation of a binomial distribution are 10 and 4 respective:
87. For a Poisson variate X, P(x=1) =P(x=2), what is the mean of x ?
88. Thirty balls are serially numbered and placed in bag. Find chance that the first ball drawn is a multiple of 3 or 5
89. For a normal distribution, the first and third quartile are given to be 37 and 49, the mode of the distribution is.
90. The odds in favour of event A in a trail is 3:1. In a three independent trails, the probability of non-occurrence of the event A is
91. If 4y - 5x = 15 is the regression line of y on x and the coefficient of correlation between x and y is 0.75, what is the value of the regression…
92. If the regression line of y on x and of x on y are given by 2x+ 3y = -1 and 5x + 6y = -1 then the arithmetic means of x and y are given by.
93. For a PxQ bivariate frequency table, the maximum number of marginal distribution is
94. The maximum value of correlation coefficient is
95. The regression coefficients remain unchanged due to a
96. Consumer Price Index Number goes up from 100 to 200 and salary of a worker is also raised from 300 to 500, then Real Wage is
97. The Circular Test is known as:
98. In the data group Bowley's and Laspyre's index number is as follows. Bowley's index number =150, Laspyre's index number = 180 then Paasche's index…
99. Laspyres index number is a weighted aggregate method by taking _______ as weights.
100. Find the Paasche's Index number for prices from the following Commodity Base year Price Base year Commodity Current year Price Current year…
101. Salries of Ravi and Suneet are in the ratio 2:3. If the salary of each is increased by ₹ 4000, the new ratio becomes 40:57. What is Suneet's present…
102. The price of scooter and moped are in the ratio 7 : 9. The price of moped is ₹ 16000 more than that of scooter. Then the price of moped is:
103. 1 / 2 log 10 25-2log 10 3+log 10 18=
104. 1 / log xy xyz + 1 / log yz xyz + 1 / log zx xyz
105. Roots of the equation x 3 +9x 2 - x - 9 = 0.
106. if α + β= -2 and α .β= -3 then α and β are the roots of the equation , which is
107. U 5x = V 5y = W 5z and U 2 = vw, then the value of xy+xz-2yz_will be :
108. Find the value of k in 3x 2 - 2kx + 5 = 0, if x = 2.
109. The difference between the roots of the equation x 2 -7x-9= 0 is
110. The solution of the Inequality 8x+6<12x+4 is :
111. On solving the inequalities 2x +5y ≤20,3x +2y ≤12, x≤ 0, y ≤0, we get the following situation
112. Find the effective rate of interest on ₹ 10,000 on which interest is payable half yearly at 5% p.a.
113. Find the effective rate of interest at 10% p.a. when interest is payable quarterly.
114. What will be the population after 3 years when present population is 1,25,000 and population increases at the rate of 3% in 1 st year, at 4% in 2 nd…
115. The value of scooter is ₹ 100,000. Find its value after 7 years if rate of depreciation is 10% p.a.
116. SI = 0.125 P at 10% p.a. Find Time.
117. How much amount is required to be invested every year as to accumulate ₹ 6,00,000 at the end of 10 years, if interest is compounded annually at 10%…
118. The difference between the CI and SI for 2 year is 21. If the rate of interest is 5%, the final principal is:
119. Present value of a scooter is ₹ 72,000. If its value decreases every year by 10%, then its value before 3 years is equal to:
120. Mr. X lent some amount of money at 4% S.I. and he obtained ₹ 520 less than he lent in 5 years. The sum lent is
121. ₹ 8,829 is invested into three different sectors in such a way that their amounts at 4% p.a. S.I. after 5 years; 6 and 8 years are equal. Find each…
122. A ₹ 1000 bond paying annual dividends at 8.5% will be redeemed at par at the end of 10 years. Find the purchase price of this bond if the investor…
123. Mr. X invest ₹ 10,000 every year starting from today for next: 10 years suppose interest rate is 8% per annual compounded annually. Calculate future…
124. Three girls and five boys are to be seated in a row so that no two girls sit together. Total No. of arrangements are:
125. A garden having 6 tall trees in a row. In how many ways 5 children stand, one in a gap between the trees in order to pose for a photograph?
126. In how many ways can 4 people be selected at random from 6 boys and 4 girls if there are exactly two girls?
127. Find the number of arrangements in which the letters of the word ‘MONDAY' be arranged so that the words thus formed begin with 'M' and do not end…
128. A sum of Money doubles itself at compound interest in 10years. In how many years will it become eight times
129. If the sum of n terms of an A.P be 2n 2 + 5 n, then its 'nth' term is:
130. Sum of x terms of two AP's are in the ratio (3x + 5) : (5x + 3) then ratio of their 10 th term is
131. The sum of the first eight terms of a G.P. is five times the sum of the first four terms; then the common ratio is -
132. If the p th term of an A.P. is 'q' and the q th term is 'p', then its r th term is:
133. If A = {1, 2, 3, 4, 5}, B = {2, 4} and C = {1, 3, 5} then (A – C) × B is:
134. Let A = {1,2, 3}, then the relation R = {(1,1), (2, 3), (2, 2), (3, 3), (1,2)} is:
135. 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. Find…
136. Find the positive value of k for which the equations: x 2 + kx + 64 = 0 and x 2 – 8x + k = 0 will have real roots:
137. If x = c t, y = c/t, then dy/dx is equal to :
138. Find the gradient of curve y = 3x 2 -5x+4 at the point (1, 2)
139. If f'(x) = 3x 2 +2 & f(0) = 0 then find f(2).
140. ∫2 3x × 3 2x × 5 x dx =
141. If HEALTH is written as GSKZDG, then how will NORTH be written in that code ?
142. In a certain code, TEACHER is written as VGCEJGT. How is CHILDREN written in that code ?
143. Find odd man out of the following:
144. In the following series, which number will replace the question mark: 23, 29, 31, 37, 41, 43, ?
145. In a certain code language, '253' means 'books are old'; '546' means 'man is old' and '378' means 'buy good books'. What stands for 'are' in that…
146. Sangeeta leaves from her home. She first walk 30 metres in North-West direction, and then 30m in South West direction, next she walks 30 metres in…
147. Shweta moved a distance of 75 metres towards the north. She then turned to the left and walking for about 25 metres, turned left again and walked 80…
148. Varun faces towards north. Turning to his right, he walks 25 metres. He then turns to his left and walks 30 metres. Next, he moves 25 metres to his…
149. Pankaj is facing west. He turns 45° in the clockwise direction and then again another turns with 180° in the same direction i.e. clockwise…
150. A man is facing north. He turns 45 degree in the clockwise direction and then another 180 degree in the same direction and then 45 degree in the…
151. In a straight line there are six persons sitting in a row. B is between F and D. E is between A and C. A does not stand next to F or D, C does not…
152. Eight leaders P, Q, R, S, T, U, V and W are sitting on a bench facing towards North. (i) T is fourth to the left of P (ii) S is fourth to the right…
153. There are four children P, Q, R, S sitting in a row. P occupies seat next to Q but not next to R. If R is not sitting next to S? Who is occupying…
154. Five boys A, B, C, D and E are sitting in a row. A is to the right of B, and E is to the left of B but to the right of C. A is to the left of D. Who…
155. Five persons are standing in a line. One of the two persons at the extreme ends is a professor and the other a businessman. An advocate is standing…
156. Pointing to a photograph, a man said “His mother husband's sister is my aunt”. Then what is relation between a man and he?
157. If P + Q means P is the mother of Q. P × Q means P is the father of Q. P – Q means P is the sister of Q. Then which of the following…
158. Ram and Mohan are brothers, Shankar is Mohan's father. Chhaya is Shankar's sister. Priya is Shankar's niece. Shubhra is Chhaya's grand daughter.…
159. Pointing to a man in a photograph, a woman said, “the father of his brother is the only son of my grandfather", how is the woman related to the man…
160. Suresh introduce a man as "he is the son of the woman who is the mother of the husband of my mother". How is Suresh is related to the man?
161. The number of times a particular items occurs in a class interval is called its:
162. An Ogive is a graphical representation of:
163. From the following data, cumulative frequency for the class 20 – 30 is Class | Frequency 0-10 | 4 10-20 | 6 20-30 | 20 30-40 | 8 40-50 | 3
164. In tabulation, source of data, if any is shown in the :
165. From the following data find the number of class intervals if class length is given as 5. 73, 72, 65, 41, 54, 80, 50, 46, 49, 53
166. Find Q 1 for the following observations: 7,9,5,4,10,15,14,18,6,20
167. Histogram is useful to determine graphically the value of:
168. Data are said to be ____________ if the investigator himself is responsible for the collection of data.
169. A suitable graph for representing the portioning of total into sub parts in statistics is:
170. The AM of 15 observations is 9 and the AM of first 9 observations is 11 and then AM of remaining observations is:
171. In a moderately skewed distribution the values of mean and median are 12 and 8 respectively. The value of mode is:
172. Which of the following is positional average?
173. For a symmetric distribution:
174. For the distribution X | f 1 | 6 2 | 9 3 | 10 4 | 14 5 | 12 6 | 8 The value of median is:
175. The QD of six numbers 15, 8, 36, 40, 38, 41 is equal to:
176. SD of first five consecutive natural numbers is:
177. If the profit of a company remain same for the last 10 months then the SD of profit of the company would be:
178. Coefficient of Quartile Deviation is 1 / 4 then Q 3 /Q 1 =?
179. The sum of mean and SD of a series is a + b, if we add 2 to each observation of the series then the sum of mean and SD is :
180. The overall percentage of failure in a certain examination is 0.30. What is the probability that out of a group of 6 candidates at least 4 passed…
181. In a certain manufacturing process, 5% of the tools produced turn out to be defective. Find the probability that in a sample of 40 tools, at most 2…
182. What is the mean of X having the following density function? f(x) = 1 / √(2π) e - (x-10) 2 / 32 for - ∞ < x < ∞
183. If mean and variance are 5 and 3 respectively then relation between p and q is:
184. In a Poisson distribution if P(x=4) = P(x= 5) then the parameter of Poisson distribution is:
185. Two events A and B are such that they do not occur simultaneously then they are called events.
186. If a coin is tossed 5 times then the probability of getting Tail and Head occurs alternatively is:
187. When 2 dice are thrown simultaneously then the probability of getting at least one 5 is:
188. The probability that a leap year has 53 Wednesday is:
189. Ram is known to hit a target in 2 out of 3 shots whereas Shyam is known to hit the same target in 5 out of 11 shots. What is the probability that…
190. In a box carrying one dozen of oranges, one third has become bad. If 3 oranges are taken out from the box at random, what is the probability that at…
191. For a (m×n) classification of bivariate data, the maximum number of conditional distributions is
192. If two variables x and y are related by 2X + 3Y – 7 = 0 and the mean and mean deviation about mean of X are 1 and 0.3 respectively, then the…
193. Correlation Co-efficient is of the units of measurements
194. 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…
195. The prices and quantities of 3 commodities in base and current years are as follows: Po P1 Qo Q1 12 14 10 20 10 8 20 30 8 10 30 10 The Laspyre's…
196. The cost of living index number in year 2015 and 2018 were 97.5 and 115 respectively. The salary of a worker in 2015 was 19500. How much additional…
197. Fisher's method for construction of Index Numbers uses
198. Consumer price index is commonly known as
199. Circular Test is satisfied by :
200. The consumer price index in 1990 increases by 80- per cent as compared to the base 1980. A person in 1980 getting ₹ 60,000 per annum should now get