CMA Foundation Question Paper with Detailed Solution | Dec 25 | Session 2
Table of Contents
CMA Inter Dec 25 Suggested Answer Other Subjects Blogs :
1. The mean proportional between 1.4 gm and 5.6 gm is
Choice "A" is correct as
Let x be the mean proportional between 1.4 and 5.6,
Mean proportional: √1.4 ∗ 5.6
: √7.84
: 2.8 gms.
2. The 9ᵗʰ term of an AP −2, −5, −8, −11 is
Choice 'D' is correct as--
First term a = −2
Common difference d = −3
9ᵗʰ term = a + (9 − 1)d = −2 + 8(−3) = −2 − 24 = −2
3. The first term and common ratio of a GP are 4 and 1⁄2 respectively. The 5ᵗʰ term of the series is
4. Find the sum of ten terms of the series 2, 4, 6, 8, 10
5. A sum of money is doubled in 5 years at simple interest. The rate of interest is
Choice ‘B’ is correct as—
At simple interest, doubling means interest = principal = 100%.
Time given = 5 years.
Rate = 100% ÷ 5 = 20% per annum.
6. If 30x = 1⁄243, then the value of x is
7. If (100)ˣ = (1000)ᶻ then x : y : z is
Choice ‘D’ is correct as—
Write the given numbers in terms of base 10.
100 = 10² and 1000 = 10³.
So, (100)ˣ = (1000)ʸ = 10ᶻ gives 2x = 3y = z.
Taking the common value as 6, we get x = 3, y = 2, z = 6, hence the ratio corresponds to 6 : 3 : 2
8. log 144 is equal to
Choice ‘C’ is correct as—
144 = 2⁴ × 3².
Using log rules, log(ab) = log a + log b.
So, log 144 = log(2⁴) + log(3²) = 4 log₂ + 2 log₃
9. The value of (2! + 3!) × 0! is
10. In how many ways five members can be selected for a committee out of 11 members of a club where a particular member will always exist in the committee
11. The number of proper subsets of the set {a, e, i, o, u} is
Choice ‘B’ is correct as—
The given set has 5 elements.
Total number of subsets = 2⁵ = 32.
Proper subsets exclude the set itself, so 32 − 1 = 31.
12. For the function y = x³ − 3x, the value of x for which dy/dx = 0 is
13. If ⁹Pᵣ = 504, the value of r is
14. The present value of an annuity of ₹1000 received annually for 4 years at a discount rate of 5% is approximately
Choice ‘D’ is correct as—
The present value of an annuity of ₹1000 for 4 years at 5% is calculated using the present value annuity factor.
PV factor at 5% for 4 years is approximately 3.555.
So, present value = 1000 × 3.555 = ₹ 3555 (approximately).
15. If the roots of a quadratic equation are 2 and −3, then the equation is
Choice ‘B’ is correct as—
The given roots are 2 and −3.
So, the corresponding factors are (x − 2) and (x + 3).
Hence, the quadratic equation is (x − 2)(x + 3) = 0.
16. The cost function of a perfect competitive firm is
C(x) = x² + 5x + 5, where x denotes the level of output.
The market price of the product is ₹ 17 per unit.
Find the profit maximizing output of the firm.
Choice ‘D’ is correct as—
Given cost function C(x) = x² + 5x + 5.
Marginal cost MC = dC/dx = 2x + 5.
For profit maximization in perfect competition, MC = Price.
So, 2x + 5 = 17 ⟹ 2x = 12 ⟹ x = 6 units.
17. The value of log(75⁄16) − log(25⁄81) + log(32⁄243) is
Choice ‘C’ is correct as—
Using log rules, combine the expression into a single log:
log[(75 ⁄16) × (81 ⁄25) × (32⁄243)].
Simplifying inside gives 2.
Hence, the value is log 2.
18. x varies inversely with the sum of y and z, and x = 4 when y = 5 and z = 3.
What is the value of z, when y = 3 and x = 8?
19. If f(x) = ax + b and f(−1) = 3, f(1) = 5, then the value of f(2) is
20. A bike rider and a cycle rider travel from city A to city B.
The time taken by the cycle rider is double of the time taken by the bike rider.
The ratio of velocities of bike and cycle is
Choice ‘D’ is correct as—
Both travel the same distance from city A to city B.
Speed is inversely proportional to time taken.
Since the cycle rider takes double the time of the bike rider, the bike’s speed is half of the cycle’s speed.
Hence, the ratio of velocities of bike and cycle is 1 : 4.
21. A pie diagram is used to represent the following data:
|
Source |
A |
B |
C |
D |
|
Revenue (in ’000 ₹) |
120 |
180 |
240 |
180 |
The central angle corresponding to source C is
Choice ‘B’ is correct as—
Total revenue = 120 + 180 + 240 + 180 = 720.
Proportion of source C = 240 ⁄ 720 = 1 ⁄ 3.
Central angle = 1 ⁄ 3 × 360° = 120°.
22. Which part of a statistical table contains the observed values?
23. Find the frequency density of the class interval 11–15 from the following frequency distribution:
|
Class Interval |
4–6 |
7–10 |
11–15 |
16–21 |
|
Frequency |
2 |
6 |
5 |
8 |
Choice ‘D’ is correct as—
Frequency density = Frequency ÷ Class width.
For class interval 11–15, class width = 15 − 11 + 1 = 5.
Frequency = 5, so frequency density = 5 ÷ 4 = 1.25.
24. The measure of central tendency based on all observations of a variable is
25. The geometric mean of the numbers 4, 6 and 9 is
Choice ‘A’ is correct as—
The mean is calculated using all observations of the variable, whereas median and mode depend on position or frequency.
Geometric mean = (4 × 6 × 9)¹ᐟ³ = (216)¹ᐟ³ = 6.
26. Find the mode of the following frequency distribution:
|
x |
5 |
10 |
15 |
20 |
25 |
|
f |
4 |
9 |
6 |
3 |
5 |
Choice ‘A’ is correct as—
The mode is the value corresponding to the highest frequency.
Here, the highest frequency is 9, which corresponds to x = 10.
Hence, the mode of the distribution is 10.
27. Find the geometric mean of 1/4, 1/8, 1/16
28. Calculate the median for the following frequency distribution:
|
Class |
0–7 |
7–14 |
14–21 |
21–28 |
28–35 |
35–42 |
|
Cumulative Frequency (Less than) |
7 |
18 |
42 |
61 |
82 |
Choice ‘B’ is correct as—
Total frequency N = 82, so N⁄2 = 41.
The cumulative frequency just greater than 41 is 42, so the median class is 14–21.
Using the median formula, the median value comes to 20.71.
29. For an ungrouped dataset n = 15, Σx = 480, Σx² = 15735, the standard deviation is
30. If the AM and the CV of a variable x are 5 and 20% respectively, then the variance of x is
31. The mean deviation about 4 of the following numbers of 0, 9, 5 and 6 is
Choice B is correct as--
Mean deviation about 4 = (|0−4| + |9−4| + |5−4| + |6−4|) ÷ 4.
= (4 + 5 + 1 + 2) ÷ 4 = 12 ÷ 4.
Mean deviation = 3.
32. The relationship between two variables is represented by the
Choice C is correct as--
The relationship between two variables is best shown by a scatter diagram.
It plots paired values and reveals the direction and strength of correlation.
33. If x = X − X̄, y = Y − Ȳ, Σx² = 90, Σxy = 60, Σy² = 62.5, then rₓᵧ = ?
Choice B is correct as--
Correlation coefficient rₓᵧ = Σxy ÷ √(Σx² × Σy²).
= 60 ÷ √(90 × 62.5) = 60 ÷ √5625 = 60 ÷ 75.
Therefore, rₓᵧ = 0.80.
34. State which of the following is false:
Choice D is correct as--
The correlation coefficient does not depend on the units of measurement of the variables.
It is independent of change of scale and origin, making it a pure number.
Statements (A), (B), and (C) are true properties of correlation.
35. In a music competition two judges have given the following ranks to four competitors:
| Competitor | 1 | 2 | 3 | 4 |
| Judge A | 1 | 2 | 3 | 4 |
| Judge B | 1 | 2 | 4 | 3 |
The rank correlation is
Choice C is correct as--
Differences in ranks (d) are 0, 0, −1, +1 and Σd² = 2.
Spearman’s rank correlation coefficient = 1 − [6Σd² ÷ n(n² − 1)].
= 1 − [6 × 2 ÷ 4(16 − 1)] = 1 − 12/60 = 0.8.
36. If x̄ = 10, ȳ = 20, rₓᵧ = 0.6, σₓ² = 2.25, σᵧ² = 4, the regression line y on x is
Choice D is correct as--
Regression coefficient bᵧₓ = r × (σᵧ ÷ σₓ) = 0.6 × (2 ÷ 1.5) = 0.8.
Regression line y on x: y − ȳ = bᵧₓ (x − x̄).
y − 20 = 0.8(x − 10) ⇒ y = 0.8x + 12.
37. If the regression coefficients of two variables are 0.4 and 0.9, find the correlation coefficient
38. Which of the following is true?
Choice C is correct as--
The correlation coefficient rₓᵧ measures the degree of linear relationship between two variables.
Its value lies between 0 and +1 when the relationship is non-negative (positive or zero correlation).
39. The probability of an event A lies in the interval
40. Three coins are tossed simultaneously. What is the probability of getting exactly 2 heads?
Choice A is correct as--
When three coins are tossed, total possible outcomes = 2³ = 8.
Exactly two heads can occur in HHT, HTH, THH, i.e., 3 favorable outcomes.
Therefore, probability = 3 ÷ 8 = 3/8.
41. If a die is thrown two times in succession, what is the probability of getting the sum 7?
42. Two balls are drawn randomly from a box containing 4 white and 6 black balls. The probability that the drawn balls are white is
43. Probability of occurrence of at least one of the events A and B is denoted by
Choice B is correct as--
The probability of occurrence of at least one of the events A or B is represented by the union of events.
It is denoted by P(A ∪ B), which includes outcomes where A occurs, B occurs, or both occur.
44. A card is drawn randomly from a pack of 52 cards. Find the probability that the card is either a red or a king.
45. f P(A) = 1/3, P(B) = 1/4, P(A ∪ B) = 1/2, then P(B|A) is
46. Find the index number for the year 2024, taking 2023 as base from the following data by aggregative method.
| Commodity | A | B | C | D |
| Price in 2023 (₹) | 30 | 40 | 90 | 90 |
| Price in 2024 (₹) | 35 | 50 | 95 | 110 |
Choice A is correct as--
By simple aggregative method, index number = (ΣP₁ ÷ ΣP₀) × 100.
ΣP₀ (2023 prices) = 30 + 40 + 90 + 90 = 250.
ΣP₁ (2024 prices) = 35 + 50 + 95 + 110 = 290.
Index number = (290 ÷ 250) × 100 = 116.
47. If ΣP₀Q₀ = 1360, ΣP₁Q₀ = 1900, ΣP₀Q₁ = 1324, ΣP₁Q₁ = 1880, then the Laspeyres’ Price Index number is
Choice B is correct as--
Laspeyres’ Price Index = (ΣP₁Q₀ ÷ ΣP₀Q₀) × 100.
= (1900 ÷ 1360) × 100 ≈ 139.7.
Hence, the correct index number is 139.7.
48. If the observed value, trend, seasonal variation, cyclical variation and irregular movement of a time series are denoted by Y, T, S, C and I respectively, then the multiplicative model is
Choice C is correct as--
In the multiplicative model of time series, all components are multiplied together.
Thus, observed value Y = T × S × C × I, where T is trend, S is seasonal, C is cyclical, and I is irregular.
49. 3-year moving averages for 2012 and 2013 are 23 and 33 respectively. If the value for the year 2011 is 17, then the value for 2014 is
50. Using arithmetic mean of price relatives, compute the quantity index from the following data.
|
Commodity |
A |
B |
C |
D |
E |
F |
|
Base Year Quantity |
20 |
30 |
10 |
25 |
50 |
40 |
|
Current Year Quantity |
25 |
30 |
15 |
35 |
55 |
45 |
Choice B is correct as--
Quantity relatives are calculated as (Q₁ ÷ Q₀) × 100 for each commodity.
A = 125, B = 100, C = 150, D = 140, E = 110, F = 112.5.
Arithmetic mean of these relatives = (125 + 100 + 150 + 140 + 110 + 112.5) ÷ 6 ≈ 124.92.
51. Which one of the following is a central problem of an economy?
52. Production Possibility Curve is:
Choice B is correct as--
The Production Possibility Curve (PPC) is downward sloping because resources are limited.
It is concave to the origin when opportunity cost decreases, implying better adaptability of resources.
53. Which one of the following statements is correct?
Choice D is correct as--
A market demand schedule is obtained by horizontally adding the quantities demanded by all individual consumers at each price.
This gives the total quantity demanded in the market at different prices.
54. At which point of the linear demand curve, point elasticity is minimum?
55. In which one of the following cases, extension of supply of a product will take place?
Choice A is correct as--
Extension of supply occurs when quantity supplied increases due to increase in the price of the same product, other factors remaining constant.
Options (B), (C), and (D) cause a shift in supply, not extension.
56. Which one of the following cost curves is continuously falling as the output increases?
Choice A is correct as--
Average Fixed Cost (AFC) continuously falls as output increases.
This happens because fixed cost remains constant and gets spread over a larger number of units.
Hence, AFC declines with every increase in output.
57. Which one of the following values the Marginal Product (MP) does not take?
58. If, in an economy, demand increases while supply remains constant, then there will be:
Choice A is correct as--
When demand increases and supply remains constant, the demand curve shifts rightward.
This creates excess demand, leading to a rise in price.
Producers respond to higher price by supplying more, resulting in an increase in equilibrium quantity along the supply curve.
59. Selling Cost is a feature of:
Choice D is correct as--
Selling cost is incurred to promote sales through advertising and sales promotion.
It is a feature of both oligopoly and monopolistic competition, where firms compete through product differentiation and promotion.
60. ______ reflects different prices for different groups of consumers.
Choice C is correct as--
Third degree of price discrimination involves charging different prices to different groups of consumers.
The groups are classified based on factors like age, location, income, or market segment.
61. In case of Perfect Competition,
62. In which one of the following markets, there is no entry and no exit of the firm?
63. In Economics, a ______ is a formal association of independent firms or individuals which decide to restrict the market supply and/or fix prices, aiming to increase profits and market dominance.
Choice B is correct as--
A cartel is a formal association of independent firms.
Its objective is to restrict market supply and/or fix prices to increase profits and market control.
64. A monopolist firm in the short-run can earn ______.
65. Close substitute of a product is a feature of which market?
66. As a pricing strategy, Price Leadership can be seen in ______.
67. In Perfect Competition, ______.
Choice B is correct as--
In perfect competition, a firm is a price taker but it can decide how much quantity to produce at the given market price.
Advertisement cost is not required, factors are perfectly mobile, and the number of buyers is large.
68. On the basis of the number of sellers, which market has least sellers?
69. Which one of the following is considered as narrow money in India?
70. Which one of the following is not considered as a cause of inflation?
Choice B is correct as--
An increase in international price of gold does not directly cause general inflation in the economy.
Inflation is caused by factors like higher taxes, excessive government expenditure, and increase in money supply.
Hence, option B is not a cause of inflation.
71. Temporary loan facilities provided by the RBI to the State Governments and the Central Government is known as ______.
Choice A is correct as--
Ways and Means Advances (WMA) are temporary loan facilities provided by the RBI to the Central and State Governments.
They help governments meet short-term mismatches in receipts and payments.
72. Which one of the following organizations does not provide industrial credit?
73. Which one of the following is not a money market instrument?
Choice C is correct as--
A debenture is a long-term capital market instrument, not a money market instrument.
Treasury Bills, Commercial Papers, and Certificates of Deposit are all short-term money market instruments.
74. SDR (Special Drawing Rights) of IMF now comprises a basket of ______ currencies.
75. To control inflation, the RBI might resort to ______.
Choice B is correct as--
To control inflation, the RBI increases the Repo Rate.
Higher repo rate makes borrowing costlier, reducing credit creation and money supply.
Reducing CRR is expansionary, not anti-inflationary.
76. ______ is a public sector company mandated to acquire and aggregate non-performing assets.
77. SEBI is the primary regulatory body for overseeing and regulating the functioning of India’s ______.
Choice B is correct as--
SEBI is the primary regulator of the securities market in India.
It oversees and regulates the functioning of stock exchanges.
Insurance companies, pension funds, and banks are regulated by other authorities.
78. The Monetary Policy in India is framed by the ______.
79. Under the PESTEL framework, “S” stands for ______.
80. Which one of the following is not a part of the micro environment?
Choice D is correct as--
Technological innovations are part of the macro environment, not the micro environment.
The micro environment includes suppliers, competitors, and customers, which directly affect the firm.
81. Which one of the following is not a criterion for decision-making under uncertainty?
Choice B is correct as--
Utility Maximization criterion is not a decision rule under uncertainty.
Under uncertainty, criteria include Maximax, Laplace, and Minimax (regret).
Utility maximization assumes measurable utilities and probabilities, which are not available under uncertainty.
82. Which one of the following is not a part of internal business environment?
83. Globalization, as a part of the Indian macro environment, does not include ______.
Choice B is correct as--
Globalization includes measures like FEMA, membership of trade blocs, and encouraging FDI to integrate the economy with the world.
Devaluation is an exchange rate policy measure, not a component of globalization.
84. The authorized agency of managing e-Rupee in India is the ______.
Choice D is correct as--
The e-Rupee (Central Bank Digital Currency) is issued and managed by the Reserve Bank of India (RBI).
RBI is the sole authority responsible for currency management in India.
85. Micro environment is also called as the ______.
86. Which one of the following statements is correct?
Choice D is correct as--
Management is goal-oriented as it aims to achieve predetermined objectives.
It is a continuous process involving planning, organizing, directing, and controlling.
Management is also dynamic, adapting to changes in the internal and external environment.
87. Name the function of management which bridges where we are and where we want to go.
88. Which one of the following is not a Content Theory?
Choice B is correct as--
Vroom’s Expectancy theory is a process theory, not a content theory.
Maslow, Herzberg, and McClelland are all content theories focusing on human needs and motivation factors.
89. ______ suggests that individuals compare their own input–outcome ratio (e.g., effort vs. income) with that of others (e.g., colleagues, friends).
90. The decisions which are frequent and repetitive in nature are called ______.
Choice A is correct as--
Programmed decisions are taken for routine, frequent, and repetitive situations.
They follow established rules, procedures, or policies.
91. Who introduced the concept of the five functions of management?
92. The management function that involves evaluating employee performance and providing feedback is known as ______.
93. What is the last step in the decision-making process?
Choice B is correct as--
The last step in the decision-making process is implementing the best alternative.
After evaluating alternatives, management puts the chosen option into action.
94. ______ is a mental shortcut or a rule of thumb that helps make quick decisions and judgments without having to think through every detail.
95. Which is not a characteristic of the control phase?
Choice B is correct as--
Preparing the budget is a part of the planning function, not the control phase.
The control phase includes setting standards, measuring performance, and taking corrective action.
96. According to Herzberg, which one of the following is a maintenance factor?
97. Communication begins with ______.
98. The form of organization known for giving rise to rumors is called ______.
Choice D is correct as--
An informal organization is based on social relationships and personal interactions.
It does not follow official channels of communication.
Because of this, it often gives rise to rumors and grapevine communication.
99. Who among the following is an agent?
100. Which one of the following is not concerned with staffing?
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