CA Foundation Quantitative Aptitude MTP September 2024: 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. What is the value of p+q / p-q if p / q = 7
2. If 2 x+y = 2 x-y = √8, then the value of x and y are
3. The equation x 3 - 3x 2 - 4x + 12 = 0 has three real roots, they are:
4. If α and β are roots of the equation x² - 8x + 12 = 0 then 1 / α + 1 / β = _____
5. The roots of the equation x² – 7x + 10 = 0 are:
6. Given that log 10 2 = x and log 10 3 = y, the value of log 10 120 is expressed as
7. If four numbers 1 / 2 , 1 / 3 , 1 / 5 , 1 / x are proportional then x =
8. If x = 2 +√3 and y = 2 - √3 then value of x² + y² =
9. If the ratio of the roots of the Equation 4x²-6x+p=0 is 1:2 then the value of p is:
10. The ratio of number of boys and number of girls in a school is found to be 15: 32. How many boys and equal number of girls should be added to bring…
11. If 2x+5>3x+2 and 2x-3≤4x-5, then x takes which of the following value ?
12. Solve for x of the Inequalities 2≤ 3x-2 / 5 ≤ 4 where x∈N
13. The amount charged for a defined length of time for uses of principal, generally on year basis is known as
14. The sum required to earn a monthly interest of ₹ 1200 at 18% p.a. Simple Interest is –
15. Sachin deposited ₹ 1,00,000 in his bank for 2 years at simple interest of 6%. How much interest would be he earns? How much final value of deposit
16. The ratio of principal and the compounded interest value for three years (Compounded annually) is 216:127. The rate of interest is:
17. The Compounded interest ₹8000 for 6 months at 12% p.a payable quarterly is:
18. The annual birth and death rates per 1,000 are 39.4 and 19.4 respectively. The number of years in which the population will be doubled assuming…
19. The simple interest on sum of money at 6% p.a. for 7 years is equal to twice of simple interest on another sum for 9 years at 5 p.a. The ratio will…
20. Nominal rate of Interest is 9.9 % p.a. If interest is compounded monthly, what will be effective rate of Interest.
21. The population of a town increases by 2% of the population at the beginning of the year. The number of years by which the total increases in…
22. A stock pays annually an amount of ₹ 10 from 6 th year onwards. What is the present value of perpetuity, if the rate of return is 20%
23. A sum of money invested in compounded interest doubles itself in four years. In how many years it becomes 32 times of itself as the same rate of…
24. Sinking fund factor is the reciprocal of _____
25. If the nominal rate of growth is 17% and inflation is 9% for the five years. Let P be the Gross domestic Product (GDP) amount at the present year…
26. If the interest rate on a loan as 1% per month, the effective annual rate of interest is:
27. A user wants to create a password using 4 lowercase letters (a-z) and 3 uppercase letters (A-Z). No letter can be repented in any form. In how many…
28. In how many ways can 5 boys and 3 girls sit in a row so that no two girls are together
29. In how many ways the letters of the word "STADIUM" be arranged in such a say that the vowels all occur together?
30. How many ways can 5 different trophies can be arranged on a shelf if one particular trophy must always be in the middle?
31. The 3 rd term of a G.P is 2 / 3 and 6 th term is 2 / 81 , then the first term is
32. If the sum of n terms of an A.P. is (3n 2 – n) and its common difference is 6, then its first term is:
33. In a survey of 300 companies, the number of companies using different media- Newspapers (N), Radio (R) and Television (T) are as follows: n(N) =…
34. If f(x)= x+2, g(x) = 7x, then g of (x) =
35. The relation R = {(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)} on the set A = {1,2,3} is:
36. If f(x) = (x + 1) x+1 then find f'(0)
37. if f(x) = x(x 2 -2) then dy / dx
38. 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
39. The slope of the tangent to the curve y=x 2 -x at the point where the line y=2 cuts the curve in the first quadrant is
40. ∫ 2 3x ·3 2x ·5 x dx =
41. Find the missing value in the series: 51, 52, 60, 87, 151, ________. 492.
42. Find missing term of the series ABD, DGK, HMS, MTB, SBL, ?
43. In a certain code TEACHER is written as VGCEJGT, how is CHILDREN written in that code.
44. In a certain code INACTIVE is written as VITCANIE, how is COMPUTER written in the same code
45. Choose the odd numerical pair group
46. Gopal started from the house towards West. After walking a distance of 30 metres, he turned towards right and walked 20 metres. He then turned left…
47. Namita walks 40 metres towards west Namita walks 14 metres towards west, then turns to her right and walks 14 metres and then turns to her left and…
48. The door of Aditya's house faces the East. From the back side of his house, he walks straight 50 m, then turns to the right and walks 50 m again.…
49. Maya starts at point T, walks straight to point U which is 4 ft. away. She turns left, at 90° and walks to W which is 4 ft. away. turns 90°…
50. There are four towns P, Q, R and T.Q is to the South-west of P, R is to the east of Q and South-east of P and T is to the north of R in line with…
51. All the six members of a family A, B, C, D, E and F are travelling together. B is the son of C but C is not the mother of B. A and C are a married…
52. T, S and R are three brothers. T's son Q is married to K and they have one child Rahul blessed to them. M the son of S is married to H and this…
53. Six persons M, N, O, P, Q and R are sitting in two rows with three persons in each row. Both the row are in front of each other. Q is not at the end…
54. The length and breadth of a room are 8 metre and 6 metre respectively. A cat runs along all four walls and finally along diagonal order to catch a…
55. Ravi left home and cycled 10 km towards South, then turned right and cycled 5 km and then again turned right and cycled 10 km. After this he turned…
56. If A+B means B is the brother of A; A×B means B is the husband of A; A-B means A is the mother of B and A% B means A is the father of B, which…
57. Read the following instructions: P $ Q means P is the brother of Q; P # Q means P is the mother of Q; P * Q means P is the daughter of Q If the code…
58. (58-59.) There are seven members A, C, D, E, F, G and H in a family. There are two fathers, one mother two sisters and four brothers. E is the…
59. How many male members in the family?
60. A is B's sister. C is B's mother. D is C's father. E is D's mother. Then how A is related to D.
61. The following set of data cannot be presented in a table
62. According to the empirical rule, if the data form a "bell-shaped “distribution, then the maximum and minimum frequencies occur at _______ and…
63. The Mean of a set of 20 observations on 18.3. The mean is reduced by 0.6 when a new observation is added to the set. The new observation is:
64. In a graphical representation of data, the largest numerical value is 4 the smallest numerical value is 25. If classes desired are 4 then which…
65. Histogram is used for finding
66. The median following numbers, which are given in ascending order is 25. Find the value of x 11, 13, 15, 19, (x+2), (x+4), 30, 35, 39, 46
67. The mean salary of a group of 50 persons is ₹5850. Later on it is discovered that the salary of one has been wrongly taken as ₹8000 instead of RS.…
68. If the mode of a data is 18 and mean is 24, then median is
69. If the first Quartile is 142 and semi-inter quartile range is 18, then the value of median is:
70. Orgin is shifted by 5, what will happen
71. The third decile for the numbers 15, 10, 25, 18, 111, 9 and 12 is
72. The Harmonic mean H of two numbers is 4 and their arithmetic means A and the geometric mean G satisfy the equation 2A+G 2 = =27, the numbers are:
73. If mean and coefficient of variation of the marks of 10 students is 20 and 80 respectively. What will be the variance of them?
74. If the same amount is added or subtracted from all the of an individual series then the standard deviation and variance both shall be _______
75. The algebraic sum of the deviations of set of values from their arithmetic mean is:
76. The AM of 15 observations is 9 and the AM of first 9 observations is 11 and then AM of remaining observations is
77. Which of the following is not a type of sampling?
78. In connection with random experiment, it is found that P(A) =2/3, P(B) = 3/5 and P(AUB)=5/6 Find P(A'/B)
79. If a card is drawn at random from a pack of 52 cards, what is the chance of getting spade or an ace?
80. The chance of getting a sum of 10 in a simple single throw is
81. A random variable has the following probability distribution: X 2 3 5 P K 2K 2K Find K
82. A number is selected at random from the set {1, 2,.....,99}. The probability that it is divisible by 9 or 11 is
83. A random variable X follows Binomial Distribution With E(X) = 2 and V(x) =1.2, then the value of n is
84. The mean of Poisson distribution is 4. The probability of two-successes in
85. The mean deviation abut median of standard normal variate is
86. If the Quartile Deviation of a normal distribution with mean 10 and SD 4 is
87. If the two Quartiles N(μ,σ 2 ) are 14.6 and 25.4 respectively. What is the standard deviation of the distribution?
88. When 'p' is large than 0.5, the Binomial Distribution is:
89. A die is thrown 100 times if getting an even number is considered a success then the variance number of success.
90. Two regression lines are perpendicular each other of r =
91. if r = 0.6, then the coefficient of non-determination is:
92. The sum of the squares of differences in ranks of marks obtained in Physics and Chemistry by 10 students in a test is 150, then the coefficient of…
93. If one regression coefficient is ____ unity, the other must be ____ Unity
94. For lines of regression 4x-2y=3 and 2x-3y=5, find bxy
95. if the coefficient of correlation between x and y is 0.5, the covariance is 16 and if the standard deviation of x is 4 then Standard deviation of y…
96. Fisher index number is ____of Laspyres and Paasches Index Number
97. Circular test is satisfied by which of the following index?
98. ∑P 0 Q 0 =1360, ∑P n Q 0 = 2000, then the Laspyres Index number is:
99. If Laspyres Index number is 250 and Paasches Index number is 160, then Fishers Index number is:
100. If the prices of all commodities in the base year are twice the values of the respective commodities in the current year, then the Fisher's ideal…
101. A bag contains 23 number of coins in the form of 1 rupee, 2 rupee and 5 rupee coins. The total sum of the coins is ₹43. The ratio between 1 rupee…
102. On Simplification 1 / 1+z a-b +z a-c + 1 / 1+z b-c +z b-a + 1 / 1+z c-a +z c-b would reduces to
103. (18) 3.5 ÷ (27) 3.5 × 6 3.5 = 2 x , then the value of x is:
104. The value of (243) 0.13 ×(243) 0.07 / (7) 0.25 ×(49) 0.075 ×(343) 0.2 is:
105. The number of prime factors in 6 12 ×(35) 28 ×(15) 16 / (14) 12 ×(21) 11 is:
106. log a bc / a - log a c 2 / b 2 + log a ab / c =
107. 1 / log xy (xyz) + 1 / log yz (xyz) + 1 / log xz (xyz) =?
108. 4 tables and 3 chairs, together, cost ₹2,250 and 3 tables and 4 chairs cost ₹1950. Find the cost of 2 chairs and 1 table.
109. If n = m! where (' m' is a positive integer > 2) then the value of: 1 / log m n + 1 / log 2 n + 1 / log 4 n + .....+ 1 / log m n
110. Aman walks a certain distance with certain speed. If he walks 1 / 2 km an hour faster, he takes 1 hour less. But, if he walks 1 km an hour slower,…
111. If α; β are the roots of the quadratic equation 3x 2 -4x+1= 0; the equation having roots β / α ; α / β is
112. The shaded region represents:
113. The solution of the inequality (5-2x) / 3
114. The simple interest on a certain sum of money is 1 / 25 times of principal, the rate of interest when rate of interest and time are equal is
115. At what time a certain sum of money amounts to ₹ 400 at 10% p.a. S .1. and to ₹ 200 at 4% p.a. S.I.
116. ₹ 6,400 amounts to ₹ 7840 in two years at simple interest. How much will a sum of ₹ 84 invested at the same rate of simple interest amount in four…
117. A person gave a loan of ₹ 200 to Mr. X and recovered it at the rate of 35 for eight months, commencing from the end of first month. What is the…
118. If the compound Interest on a certain sum of money for 2 years at 4% p.a. be ₹510, then its simple Interest (S.I.) of same time at same rate of…
119. On what sum will the difference between the S.I. and C.I. for 3 years at 6% p.a. amount to ₹ 13.77?
120. Mr. X bought an electronic item for ₹1000. What would be the future value of the same item after two years, if the value is compounded semi-annually…
121. The Partners A & B together lent ₹3903 at 4% p.a interest compounded annually. After a span of 7 years, A gets the same amount as B gets after 9…
122. If X = {a, b, c, d}; the elements of power set P (X) are
123. X = {x, y, w, z}; Y = {1,2, 3, 4}; H = {(x, 1); (y, 2);(y, 3);(z, 4);(x, 4)}
124. Mr. A borrows ₹ 5,00,000 to buy a house. If he pays equal instalments for 20 years and 10% interest on outstanding balance what will be the equal…
125. Invests ₹ 10,000 every year starting from today for next 10 years. Suppose interest rate is 8% per annum compounded annually calculate future value…
126. The present value of an annuity which pays ₹200 at the end of each 3 months for 10 years, assuming money to be worth 5% converted quarterly
127. The value of the present value of a sequence of payments of ₹ 80 made at the end of each 6 months and continuity for ever, if money is worth 4%…
128. Mr. X Invests ₹10,000 every year starting from today for next 10 years suppose: interest rate is 8% per annum compounded annually. Calculate future…
129. A company establishes a sinking fund to provide for the payment of ₹ 2,00,000 debt maturing in 20 years. Contributions to the fund are to be made at…
130. A candidate is required to answer 6 out of 10 questions, which are divided into two groups each containing 5 questions and he is not permitted to…
131. If 1 / 9! + 1 / 10! = X / 11! The value of x is
132. The value of n-1 P r + r. n-1 P r-1 is
133. If n C 7 = n C 5 , the value of 'n.' is
134. If 2n C 3 : n C 3 = 11:1, the value of 'n.'is
135. The nth term of the series whose sum to n terms is 3n 2 + 2n is:
136. What is the value of lim y→2 y 2 -4 / y-2
137. Given x = 2t + 5; y = t 2 -2, then dy / dx is calculated as:
138. If f'(x) = x - 1, the equation of the curve y = f(x) passing through the point (1,0) is given by
139. ∫x 2 e 3x dx is:
140. ∫ 1 2 2x / 1+x 2 dx:
141. If A = 26, SUN = 27, then CAT = ?
142. In a certain code language PREMONITION is written as 68530492904, how will the word MONITOR be written that code language?
143. In a certain code language, '123' means 'bright little boy', '145' means 'tall big boy' and '637' means 'beautiful little flower'. Which digit in…
144. Find next term of the series 1, 3, 4, 8, 15, 27, ?
145. Find next term of the series 1, 5, 14, 30,55, 91, ?
146. Q's mother is sister of P and daughter of M. S is daughter of P and sister of T. How is M related to T?
147. E is the son of A. D is the son of B. E is married to C. C is B's daughter. How is D related to E ?
148. (48-50) There are six persons A, B, C, D, E and F. C is the sister of F. B is the brother of E's husband. D is the father of A and grandfather of F.…
149. How many male members are there in the group?
150. How F is related to E
151. Distance between E and I is _____
152. Distance between E and G is _____
153. Distance between A and F is _____
154. Seven villages A, B, C, D E, F and G are situated as follows: E is 2 km to the west of B F is 2 km to the north of A C is 1 km to the west of A D is…
155. If 'South-east' is called 'East', 'North-west' is called 'West', 'South-west' is called 'South' and so on, what will 'North' be called?
156. Who are the neighbours of B?
157. What is the position of A?
158. who are the left of C
159. Who among the following is to the immediate left of F ?
160. How many persons are seated between K and F
161. For a moderately skewed distribution, quartile deviation and the standard deviation are related by:
162. Data are said to be _____ if the investigator if the investigator himself responsible for collection of data
163. Which of the following is suitable for cumulative frequency distribution?
164. The left part of the table providing the description of row is called.
165. The following data relate to the marks of group of students: Marks Below 10 Below 20 Below 30 Below 40 Below 50 No. of Students 15 38 65 84 100 How…
166. The probability of a blue-chip company is showed by _____
167. if all the observations are increased by 6, then the variance of the series will be
168. if the mode of the data is 18 and mean is 24, then median is,
169. If the first Quartile is 142 and semi-Inter quartile range is 18, then the value of median is
170. Which measures of dispersions is not affected by the presence of extreme observations?
171. If the SD of x is 3, what us the variance of (5–2x)?
172. If x and y are related by y = 2x+ 5 and the SD and AM of x are known to be 5 and 10 respectively, then the coefficient of variation is:
173. If the relationship between two variables u and v are given by 2u + v +7 = 0 and if the AM of u is 10, then the AM of v is
174. If x and y are related by x-y–10 = 0 and mode of x is known to be 23, then the mode of y is
175. There are two boxes containing 5 white and 6 blue balls and 3 white and 7 blue balls respectively. If one of the boxes is selected at random and a…
176. A box contains 5 white and 7 black balls. Two successive drawn of 3 balls are made (i) with replacement (ii) without replacement. The probability…
177. If P (A) = 1 / 2 , P(B) = 1 / 3 and P(A∩B) = 1 / 4 , what is P A' / B' ?
178. X and y are stand in a line with 6 people. What is the probability that there are three persons between them ?
179. For two events A and B, P(A ∪ B) = P(A) + P(B) only when
180. If x is a binomial variable with parameters n and p, then x can assume
181. The probability density function of a normal variable x is given by
182. What is the first quartile of X having the following probability density function? f(x) = 1 / √(72π) e - (x-10) 2 / 72 for – μ…
183. The average weekly food expenditure of a group of families has a normal distribution with mean ₹ 1,800 and standard deviation ₹ 300. What is the…
184. X is a binomial variable such that 2 P(X = 2) = P(X = 3) and mean of X is known to be 10/3. What would be the probability that X assumes at most the…
185. For a standard normal distribution, the points of inflexion are given by
186. If two random variables x and y are related by y = 2 – 3x, then the SD of y is given by
187. Probability of getting a head when two unbiased coins are tossed simultaneously is
188. If x and y are random variables having expected values as 4.5 and 2.5 respectively, then the expected value of (x−y) is
189. The interval (m - 3s, m + 3s) covers
190. What is spurious correlation?
191. The two lines of regression become identical when
192. 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…
193. 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
194. If y = 3x + 4 is the regression line of y on x and the arithmetic mean of x is 1, what is the arithmetic mean of y?
195. When the product of price index and the quantity index is equal to the corresponding value index then the test that holds is
196. The formula for conversion to current value
197. If the index number of prices at a place in 2018 is 280 with 2008 as base year, then the prices have increased on average by
198. In 1980, the net monthly income of the employee was ₹800/- p. m. The consumer price index number was 160 in 1980. It rises to 200 in 1984. If he has…
199. Consumer price index number goes up from 110 to 200 and the Salary of a worker is also raised from ₹325 to ₹500. Therefore, in real terms, to…
200. The prices of a commodity in the year 1975 and 1980 were 25 and 30 respectively taking 1980 as base year the price relative is :