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Free CA Quantitative Aptitude Practice Questions & Answers
500 exam-style Quantitative Aptitude questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 31
If a : b = 2 : 3 and b : c = 4 : 5, then a : c is:
Select an option first.
Correct answer: A — 8 : 15
Explanation: Multiply the corresponding terms: a/c = (a/b) x (b/c) = (2/3) x (4/5) = 8/15. Alternatively make b common - a : b = 8 : 12 and b : c = 12 : 15 - which also shows a : b : c = 8 : 12 : 15. The compound ratio shortcut works whenever the linking term appears once in each ratio.
Question 32
Rs.10,000 is invested at 12% per annum compounded QUARTERLY. The amount at the end of one year is:
Select an option first.
Correct answer: B — Rs.11,255.09
Explanation: With quarterly compounding the rate per period is 12/4 = 3% and there are 4 periods, so the amount is 10,000 x (1.03)^4 = Rs.11,255.09. Distractor A is the simple interest answer and distractor D applies 12% as if compounded annually on a larger base. Divide the rate and multiply the periods - never one without the other.
Question 33
The value of k for which x squared + kx + 9 = 0 has equal roots is:
Select an option first.
Correct answer: B — Plus or minus 6
Explanation: Equal roots require the discriminant to vanish: k squared - 4(1)(9) = 0, so k squared = 36 and k = plus or minus 6. Both signs are valid, giving (x + 3) squared = 0 and (x - 3) squared = 0 respectively. Distractor A discards the negative root, which is the standard omission when a square root is taken.
Question 34
If a/3 = b/4 = c/7, then the value of (a + b + c)/c is:
Select an option first.
Correct answer: C — 2
Explanation: Put each ratio equal to k, so a = 3k, b = 4k and c = 7k. Then (a + b + c)/c = 14k/7k = 2. Introducing a single constant of proportionality is the standard technique for a continued ratio - it converts three unknowns into one and the constant cancels in any ratio of the quantities.
Question 35
In linear programming, the corner point method is used to:
Select an option first.
Correct answer: B — Find the optimal value of the objective function
Explanation: Because the objective function is linear and the feasible region convex, the optimum must occur at a vertex. Evaluating the objective at each corner and picking the best is therefore sufficient. For an unbounded region the existence of the optimum must be checked separately before this is relied on.
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Question 36
The number of POSITIVE INTEGERS satisfying 2x is less than 11 is:
Select an option first.
Correct answer: B — 5
Explanation: Dividing gives x less than 5.5, and the positive integers below that are 1, 2, 3, 4 and 5 - five values. Distractor C wrongly includes 6, and an answer of 6 would also arise from including zero, which is not positive. Note where the inequality is strict and whether zero is admitted - both change the count.
Question 37
The value of the integral of 6x with respect to x, from 1 to 2, is:
Select an option first.
Correct answer: C — 9
Explanation: The integral of 6x is 3x squared, evaluated from 1 to 2 as 12 - 3 = 9. Distractor B is the value at the upper limit alone, with the lower limit forgotten - subtracting F(a) is the step most often skipped. Geometrically this is the area of a trapezium of parallel sides 6 and 12 and width 1.
Question 38
The value of the integral of 3x squared with respect to x, from 0 to 1, is:
Select an option first.
Correct answer: A — 1
Explanation: The integral of 3x squared is x cubed, evaluated from 0 to 1 as 1 - 0 = 1. Distractor C integrates without the coefficient 3. Differentiating the antiderivative should return the integrand: the derivative of x cubed is indeed 3x squared.
Question 39
The value of a definite integral taken from a to b, where a equals b, is:
Select an option first.
Correct answer: A — Zero
Explanation: By the fundamental theorem the integral equals F(b) - F(a), and with a = b that difference is zero. Geometrically, the area under a curve over an interval of zero width is zero. The result holds whatever the function, which is what makes it a definition-level question rather than a computation.
Question 40
The value of the definite integral of 2x with respect to x, from 0 to 3, is:
Select an option first.
Correct answer: D — 9
Explanation: The integral of 2x is x squared, evaluated from 0 to 3 as 9 - 0 = 9. No constant of integration appears in a definite integral, since it cancels between the two limits. Geometrically this is the area under the line y = 2x between x = 0 and x = 3, a triangle of base 3 and height 6, whose area is indeed 9.
Question 41
The number of solutions of the system x + y = 5 and 2x + 2y = 10 is:
Select an option first.
Correct answer: A — Infinitely many
Explanation: The second equation is simply twice the first, so the two represent the SAME straight line and every point on it satisfies both - infinitely many solutions. Had the constants been inconsistent, for instance 2x + 2y = 12, the lines would be parallel and there would be no solution at all.
Question 42
If y = 3x to the power 4 minus 2x, the value of dy/dx at x = 1 is:
Select an option first.
Correct answer: A — 10
Explanation: Differentiating gives 12x cubed - 2, which at x = 1 equals 12 - 2 = 10. Distractor B forgets the second term, and distractor C is the value of the FUNCTION at x = 1, namely 3 - 2 = 1. Differentiate every term, including the linear one, before substituting.
Question 43
The derivative of e raised to the power x with respect to x is:
Select an option first.
Correct answer: A — e raised to the power x
Explanation: The exponential function is its own derivative - the only function with that property, which is what makes e the natural base. Distractor B wrongly applies the POWER rule, which governs x raised to a constant, not a constant raised to x. Identify which of the two forms you are facing before differentiating.
Question 44
For a loan of a given amount, the equated instalment increases when:
Select an option first.
Correct answer: B — The rate of interest rises, the tenure being unchanged
Explanation: A higher rate means more interest to recover over the same number of payments, so each instalment rises. Extending the tenure spreads the principal over more payments and LOWERS the instalment, though it raises the total interest paid - a distinction worth stating whenever a question contrasts instalment size with total cost.
Question 45
The arithmetic mean of 2 and 8 is x and their geometric mean is y. The value of x - y is:
Select an option first.
Correct answer: A — 1
Explanation: The arithmetic mean is 5 and the geometric mean is the square root of 16 = 4, so the difference is 1. The arithmetic mean always equals or exceeds the geometric mean, with equality only when the two numbers are identical - so a negative answer here would signal an error.
Question 46
The difference between compound and simple interest for TWO years depends on:
Select an option first.
Correct answer: D — The principal, the rate and whether compounding is annual
Explanation: For two years the difference is P(r/100) squared, so it turns on principal and rate - but only if compounding is annual. With half-yearly compounding the interest-on-interest starts within the first year and the formula no longer applies, which is why the compounding frequency belongs in the answer.
Question 47
The difference between compound interest and simple interest on Rs.10,000 for 2 years at 6% per annum is:
Select an option first.
Correct answer: C — Rs.36
Explanation: For two years the difference is P(r/100) squared = 10,000 x 0.0036 = Rs.36. It represents the interest earned in the second year on the first year's interest of Rs.600, that is 6% of 600 = Rs.36. Understanding it as interest-on-interest makes the formula unnecessary.
Question 48
The value of log 100 minus log 10, both to base 10, is:
Select an option first.
Correct answer: D — 1
Explanation: log 100 = 2 and log 10 = 1, so the difference is 1. Equivalently, by the quotient rule the expression is log(100/10) = log 10 = 1. Distractor B subtracts the NUMBERS rather than their logarithms - the whole point of logarithms is that division becomes subtraction, not that the values themselves are subtracted.
Question 49
If y = x^3 - 6x^2 + 9x + 4, the value of dy/dx at x = 2 is:
Select an option first.
Correct answer: B — -3
Explanation: Differentiating term by term, dy/dx = 3x^2 - 12x + 9. At x = 2 this is 12 - 24 + 9 = -3. The negative value tells us the function is DECREASING at that point. Note that the constant 4 differentiates to zero, which is why two curves differing only by a constant have identical slopes everywhere.
Question 50
The derivative of log x with respect to x is:
Select an option first.
Correct answer: B — 1/x
Explanation: The derivative of the natural logarithm of x is 1/x, valid for positive x. This is the standard result that also makes the integral of 1/x equal to log x plus a constant - the pair is worth knowing in both directions. Where the base is not e, the derivative becomes 1/(x log a), which the question would state explicitly.
Question 51
In discounting the cash flows of an investment proposal, the rate normally used is the:
Select an option first.
Correct answer: B — Firm's cost of capital
Explanation: The cost of capital is the minimum return the firm must earn to satisfy its providers of finance, so it is the correct hurdle for discounting. A positive NPV at that rate means the project earns more than the finance costs. This is why the same rate serves as both the discount rate and the accept-reject benchmark.
Question 52
In how many ways can 3 distinct prizes be awarded among 5 boys, if a boy may receive more than one prize?
Select an option first.
Correct answer: A — 125
Explanation: Each prize can go to any of the 5 boys independently, so the count is 5 x 5 x 5 = 125. Distractor C is the answer when no boy may receive more than one prize, that is 5 x 4 x 3. Ask first whether repetition is permitted - it changes the method entirely, from permutations to a simple power.
Question 53
A intersection (B union C) equals:
Select an option first.
Correct answer: B — (A intersection B) union (A intersection C)
Explanation: Intersection distributes over union just as multiplication distributes over addition, so the expression expands term by term. The dual law also holds: A union (B intersection C) equals (A union B) intersection (A union C). Sketching a three-circle Venn diagram confirms either identity in seconds.
Question 54
Rs.180 is divided among three persons in the ratio 2 : 3 : 4. The largest share is:
Select an option first.
Correct answer: D — Rs.80
Explanation: The ratio terms total 9, so the shares are 40, 60 and 80, the largest being Rs.80. Check that the three add back to Rs.180. Distractor A is the middle share, offered for anyone who computes the parts correctly but then picks the wrong one - read which share is wanted before answering.
Question 55
Rs.7,000 is divided among A, B and C in the ratio 2 : 3 : 5. C's share is:
Select an option first.
Correct answer: B — Rs.3,500
Explanation: The ratio terms total 10, so C receives 5/10 of Rs.7,000 = Rs.3,500. Convert each share to a FRACTION of the whole before multiplying; treating the ratio terms as rupees directly is the usual error. Check that the three shares - 1,400, 2,100 and 3,500 - add back to Rs.7,000.
Question 56
For a given nominal rate, the amount accumulated is greatest when interest is compounded:
Select an option first.
Correct answer: C — Monthly
Explanation: The more frequently interest is added to the principal, the sooner it starts earning interest itself, so the accumulated amount rises with the frequency of compounding. Monthly beats quarterly, which beats half-yearly, which beats annual - and the effective rate rises in the same order.
Question 57
If the discount rate rises, the present value of a given series of future receipts will:
Select an option first.
Correct answer: B — Fall
Explanation: A higher rate means each future rupee is worth less today, so every discounted term shrinks and the total present value falls. This inverse relationship is why bond prices fall when interest rates rise, and it is the reasoning a written answer should give rather than merely asserting the direction.
Question 58
The effective annual rate corresponding to a nominal 12% per annum compounded quarterly is:
Select an option first.
Correct answer: B — 12.55%
Explanation: Effective rate = (1 + 0.12/4)^4 - 1 = (1.03)^4 - 1 = 0.125509, or 12.55%. The effective rate always EXCEEDS the nominal rate when compounding is more frequent than annually, and the gap widens with frequency - 12.36% would be half-yearly and 12.68% continuous. It is the figure that makes two differently compounded offers comparable.
Question 59
A nominal rate of 10% per annum compounded half-yearly gives an effective annual rate of:
Select an option first.
Correct answer: B — 10.25%
Explanation: With half-yearly compounding the rate per period is 5% over 2 periods, so the effective rate is (1.05) squared - 1 = 0.1025, or 10.25%. Compare it with the 12.55% obtained earlier from a 12% nominal rate compounded quarterly: the more frequent the compounding, the wider the gap between nominal and effective.
Question 60
In economics, marginal cost, marginal revenue and marginal product are all obtained by:
Select an option first.
Correct answer: D — Differentiating the total function with respect to quantity
Explanation: Marginal always means the rate of change of a total, which is its derivative. Dividing the total by the quantity gives the AVERAGE instead - a different quantity that happens to coincide with the marginal only in special cases. Keeping total, average and marginal distinct is essential in this topic.
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