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

How to Prepare for CA Foundation Quantitative Aptitude

Solving past MTPs, RTPs, and suggested answers from previous examination windows is essential to mastering time management under the time limit applicable to your exam paper. Review step-by-step working notes, legal case precedents, and accounting disclosures with instant 24/7 AI tutor assistance via CApex.

Question directory and available solutions

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

1. In an examination there four multiple choice questions and each question has four choices. Number of ways fails to get all answer correct is
2. In a party every person shakes hands with every other person. If there are 105 handshakes in total, find the number of persons in the party.
3. The Sum of an Infinite GP is 10, -8, 6.4....is
4. if n th term of an AP is 2n+1, the sum of its first 20 terms of this A.P Is
5. Let a, b, c be in A.P. If P is A.M between a and b and q is the A.M. between b and c, then b is equal to
6. If the sum of two extreme numbers of an A.P. with four terms is 8 and the product of remaining two middle terms is 15, then the greatest number will…
7. If A = {1,2,3,4,5}, B = {2,4,6} and C = {3,4,6} then (A∪B)∩C is
8. if A= {a, b}, B= {x, y, z} then the number of relations from B to A
9. In an election, two candidates A and B contested. y% of the total voters voted for A and (y+30)% for B. if 20% of the voters did not vote, then y =
10. Which of the following relations is a function?
11. The slope of the tangent to the curve y = x 2 -x at the point where line y=2 cuts the curve in first quadrant is
12. if the total cost producing x units of a commodity given by C(x) = 1 / 3 x 3 + 2x 2 - 5x + 10, then the marginal cost when x= 5 is
13. If the total cost function of producing x units of a commodity is given by 360-12x+2x 2 , then the level of output at which the total cost is…
14. if the cost function of a product is given by MC = 10-4x+3x 2 and fixed cost is ₹ 500, then the total cost function is
15. if the Marginal revenue function of a commodity is MR = 2x-9x 2 , then the revenue function is
16. Find the next term of the series; 1, 5, 14, 30, 55, 91,?
17. Find the missing value in the series; 51, 52, 60, 87, 151,..........., 492.
18. In a certain code language, if TOUR is written as 1234, CLEAR is written as 56784 and SPARE is written as 90847. Find the code for TEARS.
19. In a certain code, RIPPLE is written as 613382 and LIFE is written as 8192. How is PILLER written in that code?
20. In a series of letters, which one is the odd one out: BDFH, JLNP, RTVX, ZBDE?
21. Laxman went 15 km to the north, then he turned west and covered 10 km. Then he turned south and covered 5 km, finally turning to east he covered 10…
22. Manu wants to go to the market. He starts from his house towards the north and reaches a crossing after 30 m. He turns towards east, goes 10 m till…
23. Deepika starts walking straight towards East. After walking 65m, she turns to the left and walks 25m straight. Again she turns to be left and walks…
24. Mr. X walks 14 km towards north. From there he walks 8 km towards south. Then he walks 8 km towards the west. How far and in which direction is he…
25. Sunitha walked 30m towards the east, took a right turn and walked 40m, then she took a left turn and walked 30m. In which direction is she now from…
26. Six persons M, N, O, P, Q and R are sitting in two rows with three persons in each row. Both the rows are in front of each other. Q is not at the…
27. 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.…
28. Five players named as A, B, C, D and E are sitting on a bench, facing South and are waiting to be interviewed by a selector. The person C is an…
29. Six friends A, B, C, D, E and F are sitting in a row facing towards North. C is sitting between A and E. D is not at the end. B is sitting immediate…
30. Six girls, named P, Q, R, S, T, and V, are seated in a circle, all facing the center. The following statements are given: 1. T is not seated between…
31. A husband and wife had five married sons and each of these had four children. How many members are there in the family?
32. Pointing to the lady in the photograph, Seema said, “Her son's father is the son-in-law of my mother." How is Seema related to the lady?
33. A is B's brother. C is D's father. E is B's mother. A and D are brothers. How is E related to C?
34. A is the mother of D and sister of B. B has a daughter C who is married to F. G is the husband of A. How is G related to D?
35. If "A # B" means A is father of B, “A* B” means A is brother of B, “A @ B" means A is mother of B, then which of the following is correct about G @…
36. What does an Ogive represent?
37. Frequency density corresponding to a class interval is the ratio of
38. The Secondary data is collected by:
39. Standard Error can be described as
40. If the difference between Mean and Mode is 69, then the difference between Mean and Median will be ____
41. Cost of sugar in a month under the heads raw materials, labour, direct production and others were 12, 20, 35 and 23 units respectively. What is the…
42. The mean of a group X is 70 and the mean of group Y is 85. If the number of observations in group Y is five times that of group X, then the combined…
43. Which of the following is not a type of sampling?
44. Exit polls are an example of which method of collecting data?
45. A Professor has given assignment to students in a Statistics class. A student Jagan computes the arithmetic mean and standard deviation for a set of…
46. 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…
47. If x and y are related by y = 2x + 5 and SD and AM of x are known to be 5 and 10 respectively, then the coefficient of variation of y is
48. The arithmetic mean and coefficient of variation of data set x are respectively 10 and 30. The variance of 30 - 2x is
49. The quartiles of a variable are 45, 52 and 65 respectively. Its quartile deviation is
50. If the quartile deviation is 12 and the first quartile is 25, then the value of the third quartile is
51. In a city with a crime rate of 60%, the probability that among a group of 5 incidents, at least 4 are reported accurately is
52. A coin with probability for head as 1 / 5 is tossed 100 times, then the standard deviation of the number of heads turned up is
53. When p = 0.5, the distribution is
54. If mean and standard deviation of a binomial distribution is 10 and 2 respectively, q will be _____
55. For a normal distribution, the ratio of mean deviation to the standard deviation is:
56. If X and Y are two independent normal variables with means 10 and 12, and standard deviations (S.D.) 3 and 4 respectively, then (X + Y) is normally…
57. If Origin is shifted by 5, what will happen?
58. For the first 20 natural numbers, the standard deviation is
59. A machine is made of two parts A and B. The manufacturing process of each part is such that probability of defective in part A is 0.08 and that B is…
60. If P(A∪B) = 5 / 6 , P(A)= 1 / 2 and P(B)= 2 / 3 what is P (A∪B)?
61. The chance of getting 7 or 11 in a throw of 2 dice is
62. Let P be the probability function on S = (X 1 , X 2 , X 3 ) if P(X 1 ) = 1 / 4 and P(X 3 ) = 1 / 3 , then P(X 2 ) is equal to
63. Ticket numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is…
64. The Interval (μ – 3σ, μ + 3σ) covers
65. The two lines of regression are given by 8x + 10y = 25 and 16x + 5y = 12 respectively. If the variance of x is 25, what is the standard deviation of…
66. The equations of two lines of regression are 4x + 3y + 7 = 0 and 3x + 4y + 8 = 0. Find the correlation coefficient between x and y.
67. Out of the following, which one affects the regression co-efficient?
68. For n pairs of observations, the coefficient of concurrent deviation is calculated as 1 / √3 if there are six concurrent deviations then n =
69. The correlation between two variables x and y is found to be 0.4. What is the correlation between 2x and (-y)?
70. Which of the following is not a test of adequacy in the context of index numbers?
71. Fisher's index number is called as ideal index number because it satisfies
72. Circular test is satisfied by which of the following index?
73. During this period, the salary of employees as per pay commission recommendations was received from ₹ 23,000 to ₹ 29,500. In real terms, an employee…
74. If Laspeyer's index is A and Fisher's index is B. Find the value of Paasche's index.
75. In price index, when a new commodity is required to be added, which of the following index is used?
76. If (4) 3 × (√2) 2n = 2 n , then n is
77. The value of log 5 (1 + 1 / 5 ) + log 5 (1 + 1 / 6 ) + ......+ log 5 (1 + 1 / 624 )
78. If x = log 24 12, y = log 36 24, z = log 48 36, then xyz + 1 = ?
79. If roots of equation x 2 + x + r = 0 are 'α' and 'β' and α 3 + β 3 = - 6. Find the value 'r'?
80. If |x - 2| + |x - 3| = 7 then, 'x' will be equal to
81. Solve for x of the Inequalities 2 ≤ 3x-2 / 5
82. A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was ₹ 1500 after 4 years of service and ₹…
83. The salaries of A, B and C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what…
84. One root of the equation; x 2 – 2(5 + m) x + 3(7 + m) = 0 is reciprocal of the other. Find the value of m.
85. The solution of the following system of linear equation 2x – 5y + 4 = 0 and 2x + y − 8 = 0 will be
86. On solving the inequalities 6x + y ≥ 18; x + 4y ≥ 12; 2x + y ≥ 10, we get the following situation:
87. A person invested ₹8,000 at the rate of 10% compounded annually. Find the compound interest gained in 3 years.
88. Find the effective rate of interest if an amount of 30,000 deposited in a bank for 1 year at the rate of 10% per annum compounded semi-annually.
89. What will be the population after 3 years, when present population is 1,00,000 and the population increase at 3% in 1 st year, at 4% second year and…
90. Determine the present value of perpetuity of ₹50,000 per month at the rate interest 12% per annum is
91. Mr. A borrows ₹5,00,000 to buy a house. If he pays equal instalments for 20 years and 10% interest on outstanding balance, then what will be the…
92. How much money 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%…
93. Ranju wants to accumulate ₹4,91,300 in her savings account after three years. The rate of interest offered by bank is 16 1 / 4 % per annum…
94. If the difference between the compound interest compounded annually and simple interest on a certain amount at 10% per annum for two years is ₹372,…
95. How much amount is required to be invested every year so as to accumulate ₹30,000 at the end of 10 years if the interest compounded annually at 10%?…
96. A perpetuity has a cash flow of ₹625 and a required rate of return of 8%. If the cash flow is expected to grow at a constant rate of 4% per year,…
97. In an account paying interest at the rate of 9% per year compounded monthly, ₹200 is invested at the end of each month. What is the future value of…
98. Suppose Mr. X invested ₹5000 every year starting from today in mutual fund for next 10 years. Assuming that average return compounded annually is at…
99. How many 4 letter words with or without meaning can be formed out of the letter of the word 'LOGARITHMS', if repetition of letters is not allowed?
100. If there are 40 guests in a party. If each guest takes a shake hand with all the remaining guests. Then the total number of hands shake is
101. A fruit basket contains 7 apples, 6 bananas and 4 mangoes. How may selections of 3 fruits can be made so that all 3 are apples?
102. n articles are arranged in such a ways that 2 articles never come together. The number of such arrangement is
103. If the fourth term of an Arithmetic Progression (A.P.) series is zero, then what is the ratio of the twenty-fifth term to the eleventh term?
104. The 3rd term of arithmetic progression is 7 and Seventh term is 2 more than thrice of third term. The common difference is
105. If the A.M. and G.M. for two numbers are 6.50 and 6 respectively then the two numbers are
106. The 4 arithmetic means between -2 and 23 are
107. The numbers x, 8, y in Geometric Progression (G.P) and the numbers x, y, -8 are in Arithmetic Progression (A.P). Find the values of x and y…
108. If A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}, then value of A – (B U C) is
109. Let R is the set of real number, 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…
110. If f(x) = x 2 + 2, then the given function is
111. The range of the function f(x) = 3x – 2 is
112. If xy × yx = 16, then the value of dy/dx at (2, 2) is:
113. The maxima and minima of the function y = 2x 3 – 15x 2 + 36x + 10 occurs respectively at
114. The equation of the curve in the form y = f(x) if the curve passes through the point (1, 0) and f '(x) = 2x – 1, then f(x) is:
115. The equation of the curve which passes through the point (1, 2) and has the slope 3x - 4 and the point of (x, y) is
116. In a certain code language. 'CLOCK' is coded as 75276' and 'EARTH' is coded as '83491', then 'COAT is coded as
117. In certain system of code STATEMENT is coded as TNEMETATS, then how the word can POLITICAL be coded?
118. In the following series, which number will replace the question mark 23, 29, 31, 37, 41, 43,?
119. The number in place of question mark in: 7, 26, 63, 124, 215, ?, 511 is
120. Which of the following is odd one?
121. Arun started walking 5 km towards North, then he turned left and walked 3 km. Again, he turned left and walked 5 km. Then the total number of km he…
122. Ravi started walking 10 km towards East from his home. He turned right and walked 5 km to the South to reach his school. In which direction is his…
123. A person is facing towards the North. He moves 70°clockwise direction. Again he is moving 300° clockwise direction. Now, in which direction…
124. Shrikant is facing East and turns 120° in the clockwise direction and then turns 180° in the anticlockwise direction. Which direction is…
125. A and B start moving towards each other from two places apart. After walking 60 m, B turns left and goes then 20 m then he turns right and goes 40…
126. Seven friends O, P, Q, R, S, T and U are watching movie sitting in a row. S is sitting at one extreme end. Q is sitting second to the right of S. P…
127. Six friends A, B, C, D, E and F are sitting in a row facing towards North. C is sitting between A and E. D is not at the end. B is sitting at…
128. Who are the neighbours of B?
129. What is the position of A?
130. Who are the left to C?
131. Pointing to the old man Kailash said “his son is my son's uncle! How is Kailash related to an old man?
132. A reads a book and finds the name of the author familiar. The author 'B' is the paternal uncle of C. C is the daughter of A. How is B related to A?
133. If "A #B" means A is father of B, “A * B” means A is brother of B, “A @ B” means A is mother of B, then which of the following is correct about G @T…
134. A family has a man, his wife, their four sons and their wives. The family of every son also has 3 sons and one daughter. Find out the total number…
135. Read the following information and answer the question 'A + B' means 'A is the daughter of B'. 'A × B' means 'A is the son of B'. 'A - B'…
136. In tabular presentation of data, stub is ______.
137. A less than ogive curve is drawn by plotting
138. Consider the following data where class length is given as 5. Calculate the number of class intervals; 59, 68, 78, 57, 44, 73, 40, 60, 70, 47
139. The following data relate to the wages of a group of workers: Wages (in ₹) No. of workers Below 100 15 Below 200 38 Below 300 65 Below 400 90
140. What is the purpose of stratified random sampling?
141. If from a population with 20 members, a random sample without replacement of 2 members is taken, the number of all such samples is
142. The mean salary of a group of 50 persons is ₹5850. Later on it discovered that the salary of one has been wrongly taken as ₹ 8000 instead of ₹ 7800.…
143. A Professor has given assignment to students in a Statistics class. A student Jagan computes the arithmetic mean and standard deviation for a set of…
144. In a dataset, 25 percent of values are smaller than 30 and one-fourth of values are larger than 70, then the coefficient of quartile deviation is…
145. If x and y are related as 4x + 2y + 12 = 0 and mean deviation of x is 4. 5, then the mean deviation of y is
146. The Arithmetic Mean (A.M.) and Mode of the data are 32 and 26 respectively, then find the median of the data.
147. Consider the data sets; X = {−6, 2, −2, 6}, Y = {4, 8, 2, 6} and Z = {103, 100, 102, 101}. Let S x , S y & S z be the standard deviations of the…
148. For the first 20 natural numbers, the standard deviation is
149. If 2x + 3y + 4 = 0 and v(x) = 6, then v(y) is
150. Find out the mode from the following data: 100, 110, 125, 225, 325, 125, 90, 80, 455, 375,125
151. If the mode of a data is 18 and mean is 24, then median is
152. The mean of three numbers is 135. Among the three numbers, the biggest number is 180. The difference between the remaining two numbers is 25, then…
153. Which of the following measure of central tendency depends on the position of the observation?
154. Which one of the following measures of central tendency is based on only fifty percent (50%) of the central values?
155. Two dice are thrown simultaneously. Find the probability that the sum of digits on the two dice would be 8 or more.
156. Which of the following pairs of events are mutually exclusive?
157. A number is selected at random from the set {1, 2, ..., 99}. The probability that it is divisible by 9 or 11 is
158. A random variable X has the following probability density function; f (x) = 6x(1 – x), 0 ≤ x ≤ 1, then the mean is
159. The probability of success of three students in CA Foundation examination are 1 / 5 , 1 / 4 and 1 / 3 respectively. Find the probability that at…
160. If 3 percent of ceramic cup manufactured by a company are known to be defective. What is the probability that a sample of 100 cups are taken from…
161. If 5% of the families in large population city do not used gas as a fuel, what will be the probability of selecting 10 families in a random sample…
162. The number of accidents in a year attributed to taxi drivers in a locality follows Poisson distribution with average 2. Out of 500 taxi drivers of…
163. The mean deviation of normal distribution is approximately equal to____.
164. Poisson probability distribution is appropriately applied in
165. If the points of inflexion of a normal curve are 6 and 14, then standard deviation of the distribution is
166. For 9 college students group, the sum of squares of differences in ranks for History and Hindi marks was found to be 62, then what is the value of…
167. Which one of the following statements is correct regarding limit of the two regression coefficient?
168. If r = 0.8, b yx = 0.6, b xy = 0.5, x = 5 and y = 3, then the regression equation y on x is
169. The two lines of regression are given by 8x + 10y = 25 and 16x + 5y = 12 respectively. If the variance of x is 25, what is the standard deviation of…
170. If the rank correlation coefficient between marks in Management and Mathematics for a group of students is 0.6 and the sum of the squares of the…
171. Fisher index number is ______ of Laspeyres and Paasche's Index Number.
172. Weighted geometric mean of relative formula satisfies ______ test while Factor Reversal test is satisfied by ______.
173. The Laspeyre's index number is a weighted aggregate method by taking ______ as weight.
174. The simple index number for the current year using simple aggressive method for the following data Commodity base Base Year Price (P 0 ) Base Year…
175. The cost-of-living index number in year 2015 and 2018 were 97.5 and 115 respectively. The salary of a person in 2015 was ₹195000. How much…
176. If x = 3 √28 and y = 3 √27 find the value of x + y - 1 / x 2 + xy + y 2
177. Solve the following equation for x: log x (8x-3) - log x 4 = 2
178. The product of √2 . 3 √2 . 4 √32 equals
179. If 2 x = 4 y = 8 z and 1 / 2x + 1 / 4y + 1 / 6z = 24 / 7 then the value of z is
180. Three types of wheat costing ₹ 18 per kg, ₹ 20 per kg and ₹ 25. per kg mixed together. If the mixed variety sold at ₹ 22 per kg, then the ratio in…
181. The age of a man is four times the sum of the ages of his two sons and after 10 years, his age will be double the sum of their ages. The present age…
182. What will be the value of k, if the roots of the equation (k – 4)x 2 – 2kx + (k + 5) = 0 are equal?
183. The roots of the cubic equation x 3 – 7x + 6 = 0 are
184. If arithmetic mean between roots of a quadratic equation is 8 and the geometric mean between them is 5, the equation is.
185. The shaded area is represented by which of the following option ?
186. A dietician recommends mixture of two kinds of foods to a person so that mixture contains at least 45 units of carbs, 25 units of protein, 15 units…
187. The present value of sequence of payments of ₹ 800 made at the end of every 6 month and continuing forever, if money is worth 4% p.a. compounded…
188. What sum of money invested now could establish a scholarship of ₹ 2500, which is to be awarded at end of every month forever, if money is worth 4%…
189. In how many years will a sum of money becomes four times at 12% p.a. simple interest?
190. Manoj invests ₹ 12,000 at 6% per annum simple interest to obtain a total amount of ₹ 14,880. What is the time for which the amount was invested
191. The simple interest if the principal is ₹ 2,000 and the rate and time are roots of the equation x 2 - 11x + 30 = 0
192. The effective rate of interest does not depend upon
193. The future value of an annuity of ₹ 5,000 is made annually for 8 years at interest rate of 9% compounded annually is [Given that, (1.09) 8 = 1.99256]
194. Suppose your parent decides to open a PPF account in a bank towards your name with ₹ 10,000 every year starting from today for next years. When you…
195. What will be the future value of an annuity ₹ 2500 made annually for 12 years at an interest rate of 5% compounded annually? If (1.05) 12 = 1.7958
196. The Earning Per Share (EPS) of a company for five years is given below: Year 2019 2020 2021 2022 2023 EPS 40 25 40 60 90 Calculate the compounded…
197. If the initial investment of ₹ 4,00,000 becomes ₹ 6,00,000 in 24 months, then the compound Annual Growth Rate (CAGR) is:
198. How much money 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%…
199. The number of 4 letter words with or without meaning that can formed out of the letters of the word 'WONDER' if repetition letters not allowed
200. The number of six-digit numbers can be formed by using the digits 1,2,1,2,0,2 is