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

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1. The triplicate ratio of 8/3 and 16/5 is
2. if 2/5A = 3/7 B, then B:A is
3. If (3x + 2y)/(4x - 3y) = 3/2, then find x:y
4. The roots of the quadratic equation 9x 2 + 3kx + k = 0 are coincident, if
5. if (x-1) is a factor of the cubic equation x 3 - 9x 2 + 23x - 15 = 0, then roots of the cubic equation are
6. log p 2 / qr + log q 2 / pr + log r 2 / pq =
7. log a √3 = 1 / 6 , find the value of a
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 boaard of length 91 cm. The Second length is to be 3 cm longer than the shortest and third…
10. The sum of three numbers is 98. If the ratio of the first to second number is 2: 3 and that of the second to third is 5: 8, then the second number is
11. On solving the inequalities 6x + y ≥ 18, x + 4y ≥ 12, 2x + y ≥ 10; which of the following are correct solutions?
12. Side is 4 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.
13. Find future value of annuity of ₹ 1000 made annualy for seven yeras at interest rate 16% compounded annaualy. [ 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 accaount earns interest 5.75% per annuam compounded quarterly,…
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 annualy?
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 instalmennt 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 become…
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. Calculte total depreciation value at the end of seven years.
26. Effective rate of interest does not depend upon
27. The number of traingles that can be formed by choosing the vertices from a set of 12 ponts, 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 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. If f(p) = 1 / 1-p , then f -1 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,?
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 in the East of X which is in the North of Z. If P is in the South of Z, then in which direction of Y, is P?
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…
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 photo graphed, S is to the left of N and to the right of B.M is to the right of N. R is between N amd 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 maens 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. Rohan's mother is ______ to Anita's mother.
59. Prateek's and Anita's mother are ______
60. Rohan is Prateek's ______
61. The distribution of profits of a company follows:
62. Median of a distribution can be obtained from:
63. Frequency density corresponding to a class interval is the ratio of
64. 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…
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. Calculaue 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 maen and coefficienct 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 classs is known as
79. Let P be a 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 :
80. A speaks truth in 60% of the cases and B in 90% of the cases. In what percentage of cases are they likely to contradict each other in stating the…
81. A candidate is selected for interview for 3 posts. For the first there are 3 candidates, for the second there are 4 and for the third there are 2.…
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 proabibility 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. If correlation co-efficient r between x and y is 0.5 then r between x and -y is
94. For a positive and perfectly correlated random varaiables, one of the regression coefficeint is 1.4 and the standard devation of X is 2, the…
95. For n pairs of of observations, the coefficient of concurrent devation is calculated as 1 / √3 . If there are six concurrent deviations, n =
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. From the following data, find out an Index number for 2022 taking 2021 as base (using simple aggregative method): Commodities Price in 2021 Price in…
98. From the following chain base index numbers based on 2015, find out new chain base index number for the year 2022 by shifting the base year 2019.…
99. Laspyres índex number is aweighted aggregate method by taking ________ as weights.
100. Find the Paasche's Index number for prices from the following Commodity Base year Current year Price Commodity Price Commodity A 5 25 6 30 B 3 8 4…
101. Find the value of [log 10 √25 - log 10 (2 3 ) 2 + log 10 (4) 2 ]
102. If A: B = 2:5, then (10A + 3B): (5A + 2B) is equal to
103. The ratio compounded of 4:5 and sub-duplicate of a:9 is 8:15. Then value of "a" is
104. If 1 / 2 , 1 / 3 , 1 / 5 and 1 / x are in proportion, then the value of x will be
105. If P = x 1/3 + x -1/3 then find value of 3p 3 - 9p
106. Fourth proportional to x, 2x, (x+1) is:
107. The value of (3 n+1 + 3 n ) / (3 n+3 - 3 n+1 ) is equal to
108. Lim x→3 x 2 -9 / x-3 is equal to
109. Let f(x) = x 2 -6x+9 / x-3 , x≠3, f(3) = 0, then f(x) is
110. If 3x-2 / 5x-6 is the duplicate ratio of 2 / 3 then the value of 'x' is
111. If α and β are the roots of the equation x 2 + 7x + 12 = 0, then the equation whose roots (α + β) 2 and (α - β) 2…
112. Roots of the equation 2x 2 + 3x + 7 = 0 are α and β then the value of αβ -1 + βα -1 is
113. On solving the inequalities 5x + y ≤ 100, x + y ≤ 60, x≥ 0, y ≥ 0, we get the following situation:
114. The rules and regulations demand that the employer should employ not more than 5 experienced hands to 1 fresh one and this fact is represented by…
115. In what time will be a sum of money doubles itself at 6.25% p.a simple interest?
116. 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…
117. The difference between the simple and compound interest on a certain of 3 years at 5% p.a is ₹ 228.75. The compound interest on the sum of for 2…
118. How much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum
119. The time in by which a sum of money is 8 times of itself if it doubles itself in 15 years interest compounded annually.
120. Present value of a scooter is ₹ 7290, if its value decreases every year by 10% then the value before 3 years is equal to
121. Find the effective rate of interest at 10% p.a when the interest is payable quarterly.
122. The difference between in simple interest on a sum invested of ₹ 1500 for 3 years is ₹ 18. The difference in their rate is
123. What will be the population after 3 years. When the population increases at the rate 3% in I year, 4% in II year and 5% in III year.
124. If ₹ 10,000 is invested at 8% per annum, then compounded quarterly.Then value of investment after 2 years is .
125. In how many years will a sum of money become double at 5% p.a compound interest
126. The future value of an annuity of ₹ 1,000 is made annually for 5 years at interest rate of 14% compounded annually [Given that (1.14) 5 = 1.92541]…
127. The number of ways of arranging 6 boys and 4 girls in a row so that all 4 girls are together is:
128. 15C 3r = 15C r+3 then 'r' is equal to
129. If n P 4 = 20 ( n P 2 ) then the value of 'n' is _____
130. How many different words can be formed with the letters of the word “LIBERTY”
131. If x, y and z are the terms in G.P, then the term x 2 +y 2 , xy + yz, y 2 + z 2 are in
132. In a G.P. if fourth term is 3 then the product of first seven terms is
133. In a G.P. If the third term of a GP is 2 / 3 and 6 th term is 2 / 81 , then the first term is
134. Sum upto infinity series 1 / 2 + 1 / 3 2 + 1 / 2 3 + 1 / 3 4 + 1 / 2 5 +.....
135. If f(x) = 2+x / 2-x , then f -1 (x) :
136. If f : R→R is a function, defined by f(x) = 2x; then f(x+y) is
137. If f(x) = x+2, g(x) = 7 x , than g of (x) =
138. Given x = 2t + 5; y = t 2 -2, then dy / dx is calculated as:
139. Evaluate ∫(e x - e -x )dx
140. if xy =1 then y 2 + d 2 y / dx 2 = ?
141. The missing term of the series 11, 10 _____ 27, 66.5, 198.5
142. What comes at last place in R, U, X, A, D, ?
143. If Z = 52 and ACT = 48, then BAT will be equal to
144. If ROSE is coded as 6821, CHAIR is coded as 73456 and PREACH is coded as 961473, what will be the code for SEARCH?
145. If E = 5 and READ is coded as 7, then what is the code of 'DEAR'?
146. M is to the East of D, F is to the South of D and K is to the West of F. M is in which direction with respect to K?
147. A cyclist goes 30 km to North and then turning to goes 40 km. Again he turns to his right and goes 20 km. After this he turns to his right and goes…
148. A boy from his home, first walks 20 m in North-West direction then 20 m in South - West direction. Next, he walks 20m South - East direction.…
149. Raju leaves his house and walks 12 km towards North. He turns right and walks another 12 km. He turns right, walks 12 km more and turns left to walk…
150. A child goes 50 meter towards South and then turning to his right, he goes 50 meter. Then, turning to his left, he goes 30 meter. Again he turns to…
151. D is daughter of E. A is son of D . C is brother of A and B is sister of A. F is brother of D. How F is related to B?
152. Introducing a boy a girl said, “He is the son of the daughter of the father of my uncle". Who is the boy to the girl?
153. It is given that “A is the mother of B; B is the sister of C; C is the father of D”. How is A related to D?
154. Rita told Mani, "The girl I met yesterday at the beach was the youngest daughter of the brother-in-law of my friend's mother."How is the girl…
155. Sanjay has three daughters, and each daughter has a brother. How many male members are there in the family?
156. Who is sitting to the left of S?
157. Which of the following pairs of people are sitting at the extreme ends?
158. Five girls are sitting on a bench to be photographed. Seema is to the left of Rani and to the right of Bindu. Mary is to the right of Rani. Reeta is…
159. Who is immediate neighbor of B?
160. Who is sitting left of A
161. Median of a distribution can be obtained from
162. The ______ the size of the sample more reliable is the result.
163. The Standard deviation of the ______ distribution is called standard error.
164. For a set of observations, the sum of absolute deviations is ______, when the deviations are taken from the median.
165. For open-end classification, which of the following is the best measure of central tendency?
166. The quartiles of a variable are 45, 52 and 65 respectively. Its quartile deviation is
167. 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
168. For a moderately skewewd distribution, the median is twice the mean, then the mode is ______ times the median.
169. If average marks for agroup of 30 girls is 80, a group of boys is 70 and combined average is 76, then how many boys are in the group?
170. The median value of the set of observations 48, 36, 72, 87, 19, 66, 56 and 91
171. If two vriables a and b are related by c= ab then GM.of c =
172. If there are three obsewrvations 15, 20, 25 then the sum of devation of the observations from their AM is.
173. The mean weight of 15 students is 110 kg. The mean weight of 5 of them is 100 kg. and of another five students is 125 kg. then the mean weight of…
174. If the Arithmetic mean between two numbers is 64 and the Geometric mean between them is 16. The Harmonic Mean between them is ______.
175. The regression coefficients remain unchanged due to
176. If the plotted points in a scatter diagram lie from upper left to lower right, then the correlation is
177. The covariance between two variables is
178. If the coefficient of correlation between two variables is -0.9, then the coefficient of determination is
179. For a probability of a random variable x is given below : X: 1 2 4 5 6 P: 0.15 0.25 0.2 0.3 0.1 What is the Standrard deviation of x ?
180. Given that for two events A and B, P (A) = 3 / 5 , P (B) = 2 / 3 and P (A∪B) = 3 / 4 , what is P (A/B)?
181. If 2x + 3y + 4 = 0 and V(x) = 6 then V(y) is
182. X and Y stand in a line with 6 other people. What is the probability that there are 3 persons between them?
183. Four unbiased coins are tossed simultaneously. The expected number of heads is : X: 0 1 2 3 4 P(x): 1 / 16 4 / 16 6 / 16 4 / 16 1 / 16
184. Assume that the proabailityfor rain on a day is 0.4. An umbrella salesman can earn ₹ 400 per day in case of rain on that day will lose ₹100 per day…
185. The covraince between two variables X and Y is 8.4 and their variances are 25 and 36 respectively.Calculate Karl Pearson's coefficient of…
186. What is the probability of getting 3 heads if 6 unbaised coins are tossed simultaneously?
187. The mode of the binomial distribution for which the mean is 4 varaince 3 is equal to?
188. For Poisson Distribution :
189. If avaraiate x has, mean>variance, then the distribution will be
190. An example of a bi-parametric continuous probability distribution
191. For a poisson variate X, P(x=2) =3 P(x=4), then the standard deviation of X is
192. What is the mean of X having the following density function? f(x) = 1 / 4√(2Π) e -(x-10) 2 / 32 for -∞ < x < ∞
193. The divations are minimum when taken from
194. Histogram is useful to determine graphically the value of
195. If x and y are related as 3x-4y = 20 then the Quartile divation of x is 12, then the Quartile deviation of y is :
196. The base year____
197. 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…
198. Find the Paasche's Index number for prices from the following Commodity | Base year Price | Base year Commodity | Current year Price | Current year…
199. Index numbers are not helpful in
200. The weight average of price relatives of commodities when the weight is equal to the value of commodities in base year yields ____ index number