CA Foundation Quantitative Aptitude MTP January 2025: Question Paper and Solutions

How to Prepare for CA Foundation Quantitative Aptitude

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

1. log 4 (x 2 + x) – log 4 (x + 1) = 2. find x.
2. If x = log 24 12; y = log 36 24; z = log 48 36 then xyz + 1 = ?
3. In a two digits number; the digit in the ten's place is twice the digit in the unit's place. If 18 be subtracted from the number the digits are…
4. For a certain commodity the demand equation giving “y” units for a price “p” in rupees per unit is y = 100 (10 – p). The supply equation giving the…
5. The age of a person is 8 years more than thrice the age of the sum of his two grandsons who were twins. After 8 years his age will be 10 years more…
6. Roots of the equation 3x 2 – 14x – k = 0 will be reciprocal of each other if:
7. It roots of equation x 2 + x + r = 0 are 'α' and 'β' and α 3 + β 3 = -6. Find the value of 'r'?
8. Find the value of: [1 – {1 – (1 − x 2 ) -1 } -1 ] -1/2 is
9. The value of (3 n+1 +3 n )/ (3 n+3 - 3 n+1 ) is equal to:
10. If u 5x = v 5y = w 5z and u 2 = vw then xy + zx – 2yz
11. The shaded region represents
12. Which of the following graph represents the in equality x + y ≤ 6 is
13. The time by which a sum of money is 8 times of itself if it double itself in 15 years.
14. What is the rate of simple interest if a sum of money amount ₹ 2,784 in 4 years and ₹ 2,688 in 3 years ?
15. In how many years, a sum will become double at 5% p.a. compound interest.
16. 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…
17. The difference between simple and compound interest on a sum of ₹ 10000 for 4 years at the rate of interest 10% per annum is
18. How much will ₹ 25,000 amount to in 2 years at compound interest if the rates for the successive years are 4% and 5% per year:
19. The value of furniture depreciates by 10% a year, if the present value of the furniture in an office is ₹ 21870, calculate the value of furniture 3…
20. The effective rate of interest does not depend upon
21. If p. i 2 = 96, and R = 8% compounded annually then P =
22. If a bank pays 6% interest compounded quarterly what equal deposit have to be made at the end of the each quarter for 3 years if you want to have ₹…
23. Find 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?
24. 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…
25. 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…
26. Suppose your mom decides to gift you ₹ 10,000 every year starting from today for the next sixteen years. You deposit this amount in a bank as and…
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 straight line, is:
28. A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics part-II unless…
29. An examination paper consists of 12 questions divided into two parts A and B. Part A contains 7 questions and part B contains 5 questions. A…
30. In how many ways can the letters of the word FAILURE be arranged so that the consonants may occupy only odd positions?
31. 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 ?
32. The sum of the series: 0.5 + 0.55 + 0.555+ ..... to n terms is:
33. (x + 1), 3x, (4x + 2) are in A.P. Find the value of x.
34. The 4 th term of an A.P. is three times the first and the 7 th term exceeds twice the third term by 1. Find the first term 'a' and common difference…
35. There are 40 students, 30 of them passed in English, 25 of them passed in Maths and 15 of them passed in both. Assuming that every Student has…
36. If A = {1, 2, 3, 4, 5}, B = (2, 4) and C = (1, 3, 5) then (A – C) × B is:
37. If A= {1,2,3} then the relation R = {(1,1), (2,3), (2,2), (3,3), (1,2)} on A is:
38. The cost function for the production of x units of a commodity is given by C(x) = 2x 3 − 15x 2 + 36x + 15, The cost will we minimum when 'x'…
39. A seller makes an offer of selling certain articles that can be described by the equation x = 25 – 2y where x is price per unit and y denotes the…
40. ∫ xe x dx is:
41. Find odd man out of the following:
42. In a certain code, TEACHER is written as VGCEJGT. How is CHILDREN written in that code ?
43. If HEALTH is written as GSKZDG, then how will NORTH be written in that code?
44. If HONEY is coded as JQPGA, which word is code as VCTIGVU?
45. Which of the following is odd one?
46. 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…
47. A man is facing East, then he turns left and goes to 10 metres then turns right and goes 5 metres then goes 5 metres to the South and from there 5…
48. Rahim started from point X and walked straight 5 km. East, then turned left and walked straight 2 km. and again turned left and walked straight 7…
49. 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…
50. A person is facing towards North. He moves 70° clock-wise direction. Again he is moving 300° clock-wise direction. Now, in which direction…
51. 8 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 of W…
52. The flats of which of the other pairs than SU, are diagonally opposite to each other ?
53. Which of the following combinations gets South facing flats ?
54. A, B, C, D, E and F are sitting around a round table. A is between E and F, E is opposite to D, and C is not in either of the neighbouring seats of…
55. 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…
56. A prisoner introduced a boy who came to visit him to the jailor as “Brothers and sisters, I have none, he is my father's son's son”. Who is the boy ?
57. 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…
58. How is G is related to P ?
59. If M is a Female, then How is H is related to M?
60. There are two couples in a family. K has two children. M is wife of O, who is brother of B. F is daughter of K. U is sister of S, who is son of O. T…
61. The graphical representation of a cumulative frequency distribution is called.
62. A table has ______ parts:
63. Out of 1000 persons, 25 per cent were industrial workers and the rest were agricultural workers. 300 persons enjoyed world cup matches on T.V. 30…
64. The column headings of a table are known as:
65. Arrange the dimensions of Bar diagram, Cube diagram, Pie diagram in sequence
66. In a class of 11 students, 3 students were failed in a test. 8 students who passed secured 10,11,20,15,12,14,26 and 24 marks respectively. What will…
67. Suppose a population A has 100 observations 101,102,103,200 and another population B has 100 observations 151, 152, 153, ........ 250. If V A and V…
68. Out of these, which is not a probability sampling?
69. With the increase in sample size, the error also ______
70. For a moderately skewed distribution, which of the following relationship holds?
71. If mean and coefficient of variation of the marks of n students is 20 and 80 respectively. What will be variance of them
72. A company's past 10 years average earnings is ₹ 40 crores. To have the same average earning for 11 years including theses 10 years, how much earning…
73. Origin is shifted by 5, then
74. Two unbiased dice are thrown. The expected value of sum of numbers on the upper side is
75. An example of bi-parametric continuous probability distribution.
76. 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…
77. A bag contains 3 white and 5 black balls and second bag contains 4 white and 2 black balls. If one ball is taken from each bag, the probability that…
78. If the difference between mean and mode is 63, then the difference between Mean and Median will be _______
79. A lady travel at a speed of 20km/h and returned at quicker speed. If her average speed of the whole journey is 24km/h, find the speed of return…
80. Three identical dice are rolled. The probability that the same number will appear on each of them is:
81. The theory of compound probability states that for any two events A and B:
82. In a non-leap year, the probability of getting 53 Sundays or 53 Tuesdays or 53 Thursdays is :
83. A card is drawn from a well shuffled pack of 52 cards. Let E 1 , “a king or a queen is drawn" & E 2 : “a queen or a jack is drawn”, then:
84. 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…
85. A manufacturer, who produces medicine bottles, finds that 0.1% of the bottles are defective. The bottles are packed in boxes containing 500 bottles.…
86. The probability than a man aged 45 years will die within a year is 0.012. What is the probability that of 10 men, at Least 9 will reach their 46 th…
87. Shape of Normal Distribution Curve:
88. The mean of Binomial distribution is 20 and Standard deviation is 4 then;
89. In a Poisson distribution if P(x = 4) = P(x = 5) then the parameter of Poisson distribution is :
90. If the rank correlation co-efficient between marks in Management and Mathematics for a group of students is 0.6 and the sum of the squares of the…
91. Correlation coefficient between X and Y will be negative when
92. Two variables X and Y are related as 4x + 3y = 7 then correlation between x and y is _______.
93. Given the regression equations as 3x + y = 13 and 2x +5y = 20. Find regression equation of y on x.
94. Regression coefficient are _______.
95. If one of regression coefficient is _______ unity, the other must be _______ unity.
96. Circular test is satisfied by which index number?
97. Which of the following statement is true ?
98. Monthly salary of an employee was ₹ 10,000 in the year 2000 and it was increased to ₹ 20,000 in the year 2013 while the consumer price index number…
99. Purchasing power of money is _______
100. In the year 2010 the monthly salary was ₹ 24,000. The consumer price index number was 140 in the year 2010 which rises to 224 in the year 2016. If…
101. The ratio of the prices of two Fans was 16: 23. Two years later when the price of the first has increased by 10% and that of the second by ₹ 477,…
102. If a: b = 3: 4, the value of (2a+3b): (3a+4b) is
103. The third proportional to 49 and 21
104. Given that log 10 2 = x and log 10 3 = y, the value of log 10 60 is expressed as
105. What should be added to 4x 2 +4x, so that it becomes perfect square?
106. The sum of two numbers is 62 and their product is 960. The sum of their reciprocals is
107. Three persons Mr. Roy, Mr. Paul and Mr. Singh together have ₹ 51. Mr. Paul has ₹ 4 less than Mr. Roy and Mr. Singh has got ₹ 5 less than Mr. Roy.…
108. The roots of the quadratic equation x 2 -4x+k = 0 are coincident if
109. The three roots of the cubic equation x 3 +9x 2 -x-9=0 is
110. Given the quadratic equation 2x 2 + 2x -1 =5. Its roots are.
111. The wages of 8 men and 6 boys amount to ₹ 33. If 4 men earn ₹ 4.50 more than 5 boys determine the wages of each man and boy.
112. The roots of the equation x 2 + (2p−1)x + p= 0 are real if.
113. On solving the inequalities 2x +5y ≤20,3x +2y ≤12, x≤ 0, y ≤0, we get the following situation
114. On the average experienced person does 5 units of work while a fresh one 3 units of work daily but the employer has to maintain an output of at…
115. A sum of ₹ 46,875 was lent out at simple interest and at the end of 1 year 8 months the total amount was ₹ 50,000. Find the rate of interest percent…
116. A = ₹ 5,200, R = 5% p.a., T = 6 years, P will be
117. The time by which a sum of money would treble itself at 8% p. a C. I is
118. The present value of an annuity of ₹ 80 for 20 years at 5% p.a is [Given (1.05) 20 = 2.6533]
119. A person bought a house paying ₹ 20,000 cash down and ₹ 4,000 at the end of each year for 25 yrs. at 5% p.a. C.I. The cash down price is[ Given…
120. A man purchased a house valued at ₹3,00,000. He paid ₹ 2,00,000 at the time of purchase and agreed to pay the balance with interest at 12% per annum…
121. A person desires to create a fund to be invested at 10% CI per annum to provide for a prize of ₹ 300 every year. Using V = a/I find V and V will be
122. A person invests ₹500 at the end of each year with a bank which pays interest at 10% p.a C.I. annually. The amount standing to his credit one year…
123. A machine depreciates at 10% of its value at the beginning of a year. The cost and scrap value realized at the time of sale being ₹ 23,240 and ₹…
124. The compound interest on half-yearly rests on ₹ 10,000 the rate for the first and second years being 6% and for the third year 9% p.a. is
125. The present value of ₹ 10,000 due in 2 years at 5% p.a. compound interest when the interest is paid on half-yearly basis is
126. The effective rate of interest corresponding to a nominal rate 3% p.a payable half yearly is
127. The number of ways the letters of the word ‘COMPUTER' can be rearranged is
128. 5 persons are sitting in a round table in such way that Tallest Person is always on the right-side of the shortest person; the number of such…
129. An examination paper with 10 questions consists of 6 questions in Algebra and 4questions in Geometry. At least one question from each section is to…
130. If 12 school teams are participating in a quiz contest, then the number of ways the first, second and third positions may be won is
131. Three numbers are in AP and their sum is 21. If 1, 5, 15 are added to them respectively, they form a G. P. The numbers are:
132. The sum of three numbers in G.P. is 70. If the two extremes by multiplied each by 4 and the mean by 5, the products are in AP. The numbers are
133. The first and the last term of an AP are –4 and 146. The sum of the terms is 7171. The number of terms is
134. (A∪B)' is equal to
135. If f(x) = x / 1-x and g(x) = x-1 / x , then gof(x) is
136. A town has a total population of 50,000. Out of it 28,000 read the newspaper X and 23,000 read Y while 4,000 read both the papers. The number of…
137. ∫e ax dx
138. The gradient of the curve y = 2x 3 –5x 2 – 3x at x = 0 is
139. Evaluate ∫ 1 4 (2x+5) dx and the value is
140. If f(x) = x 2 -6x+8 then f'(5) – f'(8) is equal to
141. Find the wrong term of the series 121, 143, 165, 186, 209
142. Find missing term 7, 26, 63, 124, 215, 342?
143. Find odd man out of the series 145, 197, 257, 325,399
144. Find missing term of the alphabet series ABD, DGK, HMS, MTB, SBL?
145. In a certain language, FLOWER is coded UOLDVI, then how is TERMINAL coded in that language?
146. Pointing to a lady, a man said, “The son of her only brother is the brother of my wife". How is lady is related to man?
147. A family has a man, his wife, their four sons and their wives. The family of every son also 3 sons and one daughter. Find out the total number of…
148. Given that 1. A is mother of B. 2. C is son of A. 3. D is brother of E. 4. E is daughter of B. The grandmother of D is
149. 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' means…
150. In a certain code, TELEPHONE is written as ENOHPELET. How is ALIGATOR written
151. Who is C to A
152. How many male members are in the family
153. At what position A is sitting?
154. What is position of B?
155. What is position of D?
156. Six Children 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…
157. A man is facing towards East and turns through 45°clockwise again 180° clock wise and then turns through 270° anti-clock wise. In which…
158. Facing towards North, Ravi walks 35 m. He then turns left and walks 55 m. He again turns left and walks 35 m. How far is from original position and…
159. Ram start moving from a point, facing in East direction. After walking 15 m, he turned to his left and walked 25m, before turning to his right.…
160. Five Friends are sitting on a bench. A is to the left of B but on the right of C, D is to the right of B but one the left of E. Who are at the…
161. Find the number of observations between 250 and 300 from the following data: Value: More than 200 More than 250 More than 300 More than 350 No. of…
162. The difference between Upper limit and lower limit of a class is called
163. The following data relate to the marks of a group of students: Marks: Below 10 Below 20 Below 30 Below 40 Below 50 No. of students: 15 38 65 84 100…
164. Median of a distribution can be obtained from
165. For open-end classification, which of the following is the best measure of central tendency?
166. In case of an even number of observations which of the following is median?
167. Standard Error can be described as
168. Two variables x and y are given by y= 2x – 3. If the median of x is 20, what is the median of y?
169. 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
170. The appropriate measure of dispersion for open-end classification is
171. If R x and R y denote ranges of x and y respectively where x and y are related by 3x+2y+10=0, what would be the relation between x and y?
172. If x and y are related by 2x+3y+4 = 0 and SD of x is 9, then SD of y is
173. The quartiles of a variable are 45, 52 and 75 respectively. Its quartile deviation is
174. If x and y are related as 3x+4y = 20 and the quartile deviation of x is 16, then the quartile deviation of y is
175. If x and y are related by y = 2x+ 5 and the SD and AM of x are known to be 5 and 10respectively, then the coefficient of variation of y is
176. What is spurious correlation?
177. When r = 1, all the points in a scatter diagram would lie
178. If the coefficient of correlation between two variables is 0.8 then the percentage of variation unaccounted for is
179. If for two variable x and y, the covariance, variance of x and variance of y are 40, 16 and 256 respectively, what is the value of the correlation…
180. If the relation between x and u is 3x + 4u + 7 = 0 and the correlation coefficient between x and y is −0.6, then what is the correlation…
181. Three events A, B and C are mutually exclusive, exhaustive and equally likely. What is the probably of the complementary event of A?
182. What is the chance of picking a spade or an ace not of spade from a pack of 52cards?
183. Find the probability that a four-digit number comprising the digits 2, 5, 6 and 7 would be divisible by 4.
184. The probability that an Accountant's job applicant has a B. Com. Degree is 0.85, that he is a CA is 0.30 and that he is both B. Com. and CA is 0.25…
185. Rupesh is known to hit a target in 5 out of 9 shots whereas David is known to hit the same target in 6 out of 11 shots. What is the probability that…
186. In connection with a random experiment, it is found that P(A) = 2 / 3 , P(B) = 3 / 5 and P(A∪B) = 5 / 6 , find P(A/B)
187. In a business venture, a man can make a profit of ₹ 50,000 or incur a loss of ₹ 20,000. The probabilities of making profit or incurring loss, from…
188. Find the probability of a success for the binomial distribution satisfying the following relation 4 P (x = 4) = P (x = 2) and having the parameter n…
189. An experiment succeeds thrice as after it fails. If the experiment is repeated 5times, what is the probability of having no success at all?
190. If the two quartiles of a normal distribution are 47.30 and 52.70 respectively, what is the mode of the distribution? Also find the mean deviation…
191. X follows normal distribution with mean as 50 and variance as 100. What is P(x≥ 60)? [Givenφ(1) = 0.8413]
192. Number of misprints per page of a thick book follows:
193. If for a Poisson variable X, f(2) = 3 f(4), what is the variance of X?
194. If the points of inflexion of a normal curve are 40 and 60 respectively, then its mean deviation is:
195. Fisher's index number satisfies the ______ tests
196. Fisher's ideal index number is:
197. If r = 0.6 then coefficient of non-determination is:
198. The Cost-of-Living Index (CLI) is always
199. The Paasches and Fishers index numbers are 169 and 156 respectively, then Laspyre's Index number is:
200. The whole sale price index number or agricultural commodities in a given region at a given date is 280. The percentage increase in prices of…