Quantitative Aptitude

Algebra — Practice MCQs for CCAT

20 Questions Section A: Fundamentals Quantitative Aptitude

Practice 20 Algebra multiple-choice questions designed for CDAC CCAT exam preparation. Click "Show Answer" to reveal the correct option with detailed explanation.

Q1.
Solve for x: 3x + 7 = 22
A3
B5
C7
D15
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Correct Answer: B — 5

3x = 22-7 = 15. x = 5.

Q2.
If x + y = 7 and xy = 10, find x² + y².
A25
B29
C35
D39
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Correct Answer: B — 29

x² + y² = (x+y)² - 2xy = 49 - 20 = 29.

Q3.
If a + 1/a = 4, find a² + 1/a².
A12
B14
C16
D18
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Correct Answer: B — 14

a² + 1/a² = (a + 1/a)² - 2 = 16 - 2 = 14.

Q4.
Find the value of 125^(1/3).
A3
B4
C5
D6
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Correct Answer: C — 5

125 = 5³, so 125^(1/3) = 5.

Q5.
If 2^x = 64, what is x?
A4
B5
C6
D7
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Correct Answer: C — 6

64 = 2⁶, so x = 6.

Q6.
Simplify: (x² - 9)/(x - 3)
Ax - 3
Bx + 3
Cx² - 3
D(x-3)²
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Correct Answer: B — x + 3

x² - 9 = (x+3)(x-3). Dividing by (x-3) gives x+3.

Q7.
If 3x - 2y = 11 and x + 2y = 5, find x.
A2
B3
C4
D5
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Correct Answer: C — 4

Adding equations: 4x = 16, x = 4.

Q8.
The sum of two numbers is 15 and their product is 56. Find the numbers.
A6 and 9
B7 and 8
C5 and 10
D4 and 11
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Correct Answer: B — 7 and 8

x + y = 15, xy = 56. Testing: 7 + 8 = 15, 7 × 8 = 56.

Q9.
Find the roots of x² - 5x + 6 = 0.
A1, 6
B2, 3
C-2, -3
D1, 5
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Correct Answer: B — 2, 3

x² - 5x + 6 = (x-2)(x-3) = 0. x = 2 or 3.

Q10.
If (a + b)² = 25 and ab = 6, find a² + b².
A11
B13
C15
D17
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Correct Answer: B — 13

a² + b² = (a+b)² - 2ab = 25 - 12 = 13.

Q11.
If x - 1/x = 3, find x² + 1/x².
A9
B11
C13
D15
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Correct Answer: B — 11

x² + 1/x² = (x - 1/x)² + 2 = 9 + 2 = 11.

Q12.
Find the value of (a + b + c)² - (a - b - c)².
A4a(b+c)
B4bc
C4ab
D4(ab+ac)
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Correct Answer: A — 4a(b+c)

Using a² - b² = (a+b)(a-b): = 2(b+c) × 2a = 4a(b+c).

Q13.
If x² + y² = 25 and xy = 12, find (x + y)².
A37
B49
C61
D64
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Correct Answer: B — 49

(x+y)² = x² + y² + 2xy = 25 + 24 = 49.

Q14.
Solve: √(x+5) = 3
A2
B4
C8
D14
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Correct Answer: B — 4

Squaring both sides: x + 5 = 9. x = 4.

Q15.
If log₁₀ 2 = 0.301, find log₁₀ 200.
A2.301
B2.602
C3.301
D0.602
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Correct Answer: A — 2.301

log 200 = log(2×100) = log 2 + log 100 = 0.301 + 2 = 2.301.

Q16.
Find the sum of first 20 terms of AP: 5, 8, 11, 14, ...
A670
B690
C710
D730
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Correct Answer: A — 670

a = 5, d = 3. S₂₀ = 20/2 × [2(5) + 19(3)] = 10 × 67 = 670.

Q17.
If 4ˣ - 4ˣ⁻¹ = 24, find x.
A2
B2.5
C3
D3.5
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Correct Answer: B — 2.5

4ˣ - 4ˣ/4 = 24. 4ˣ(1 - 1/4) = 24. 4ˣ × 3/4 = 24. 4ˣ = 32. x = 2.5.

Q18.
The 10th term of GP 3, 6, 12, 24, ... is:
A768
B1024
C1536
D3072
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Correct Answer: C — 1536

a = 3, r = 2. T₁₀ = 3 × 2⁹ = 3 × 512 = 1536.

Q19.
If α and β are roots of x² - 5x + 6 = 0, find 1/α + 1/β.
A5/6
B6/5
C5
D6
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Correct Answer: A — 5/6

1/α + 1/β = (α+β)/αβ = 5/6.

Q20.
Find the value of 5^(log₅ 7).
A5
B7
C35
D25
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Correct Answer: B — 7

a^(logₐ x) = x. So 5^(log₅ 7) = 7.