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Algebra - Practice MCQs for CCAT

60 Questions Section A: Fundamentals Quantitative Aptitude

Algebra Question Bank for C-CAT

Topic-wise Algebra MCQs for CDAC C-CAT preparation with answers and explanations.

Q1.
Solve for x: 3x + 7 = 22
A3
B7
C5
D15
Show Answer & Explanation

Correct Answer: C - 5

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

Q2.
If x + y = 7 and xy = 10, find x² + y².
A25
B29
C35
D39
Show Answer & Explanation

Correct Answer: B - 29

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

Q3.
If a + 1/a = 4, find a² + 1/a².
A12
B18
C16
D14
Show Answer & Explanation

Correct Answer: D - 14

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

Q4.
Find the value of 125(1/3).
A3
B5
C4
D6
Show Answer & Explanation

Correct Answer: B - 5

125 = 5³, so 125(1/3) = 5.

Q5.
If 2x = 64, what is x?
A4
B6
C5
D7
Show Answer & Explanation

Correct Answer: B - 6

64 = 26, so x = 6.

Q6.
Simplify: (x² - 9)/(x - 3)
Ax - 3
B(x-3)²
Cx² - 3
Dx + 3
Show Answer & Explanation

Correct Answer: D - 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
B4
C3
D5
Show Answer & Explanation

Correct Answer: B - 4

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

Q8.
The sum of two numbers is 15 and their product is 56. Find the numbers.
A7 and 8
B6 and 9
C5 and 10
D4 and 11
Show Answer & Explanation

Correct Answer: A - 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
Show Answer & Explanation

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
B15
C13
D17
Show Answer & Explanation

Correct Answer: C - 13

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

Q11.
If x - 1/x = 3, find x² + 1/x².
A9
B13
C11
D15
Show Answer & Explanation

Correct Answer: C - 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)
Show Answer & Explanation

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
Show Answer & Explanation

Correct Answer: B - 49

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

Q14.
Solve: √(x+5) = 3
A2
B14
C8
D4
Show Answer & Explanation

Correct Answer: D - 4

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

Q15.
If log₁₀ 2 = 0.301, find log₁₀ 200.
A0.602
B2.602
C3.301
D2.301
Show Answer & Explanation

Correct Answer: D - 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, ...
A690
B670
C710
D730
Show Answer & Explanation

Correct Answer: B - 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
Show Answer & Explanation

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
B1536
C1024
D3072
Show Answer & Explanation

Correct Answer: B - 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
Show Answer & Explanation

Correct Answer: A - 5/6

1/α + 1/β = (α+β)/αβ = 5/6.

Q20.
Find the value of 5(log₅ 7).
A5
B25
C35
D7
Show Answer & Explanation

Correct Answer: D - 7

a(logₐ x) = x. So 5(log₅ 7) = 7.

Q21.
If x + 1/x = 5, then x² + 1/x² =
A27
B25
C23
D21
Show Answer & Explanation

Correct Answer: C - 23

(x+1/x)²=x²+2+1/x²=25. So x²+1/x²=23.

Q22.
Solve: 3x - 7 = 2x + 5
A12
B10
C14
D8
Show Answer & Explanation

Correct Answer: A - 12

3x-2x=5+7. x=12.

Q23.
If a+b=10 and ab=21, then a²+b²=
A58
B52
C64
D48
Show Answer & Explanation

Correct Answer: A - 58

(a+b)²=a²+2ab+b². 100=a²+b²+42. a²+b²=58.

Q24.
If 2(x+3) = 32, then x =
A5
B3
C4
D2
Show Answer & Explanation

Correct Answer: D - 2

2(x+3)=25. x+3=5. x=2.

Q25.
The roots of x²-5x+6=0 are:
A3, -2
B1, 6
C-2, -3
D2, 3
Show Answer & Explanation

Correct Answer: D - 2, 3

x²-5x+6=(x-2)(x-3)=0. x=2 or x=3.

Q26.
If 3x = 81, then x =
A2
B3
C5
D4
Show Answer & Explanation

Correct Answer: D - 4

34=81. So x=4.

Q27.
Simplify: (a+b)² - (a-b)² =
A2a²+2b²
B2ab
C4ab
Da²+b²
Show Answer & Explanation

Correct Answer: C - 4ab

(a+b)²-(a-b)²=a²+2ab+b²-a²+2ab-b²=4ab.

Q28.
If x² - 3x - 10 = 0, the values of x are:
A5, 2
B-5, 2
C5, -2
D-5, -2
Show Answer & Explanation

Correct Answer: C - 5, -2

(x-5)(x+2)=0. x=5 or x=-2.

Q29.
Sum of roots of 2x² - 8x + 6 = 0:
A3
B4
C8
D6
Show Answer & Explanation

Correct Answer: B - 4

Sum = -(-8)/2 = 4.

Q30.
Product of roots of x² - 7x + 12 = 0:
A7
B12
C-12
D-7
Show Answer & Explanation

Correct Answer: B - 12

Product = 12/1 = 12.

Q31.
If log₂(x) = 5, then x =
A10
B25
C32
D64
Show Answer & Explanation

Correct Answer: C - 32

x = 25 = 32.

Q32.
Solve: |2x - 3| = 7
A3, -7
B5, 2
C-5, 2
D5, -2
Show Answer & Explanation

Correct Answer: D - 5, -2

2x-3=7 → x=5. 2x-3=-7 → x=-2.

Q33.
If x = 2+√3, then x + 1/x =
A2√3
B4
C4+2√3
D2+√3
Show Answer & Explanation

Correct Answer: B - 4

1/x=1/(2+√3)=2-√3. x+1/x=2+√3+2-√3=4.

Q34.
Simplify: (x³ - 8)/(x - 2) when x ≠ 2:
Ax²+4
Bx²-2x+4
Cx²+2x+4
Dx²-4
Show Answer & Explanation

Correct Answer: C - x²+2x+4

x³-8=(x-2)(x²+2x+4). Divided by (x-2) = x²+2x+4.

Q35.
If a/b = 3/5, then (a+b)/(a-b) =
A-4
B4
C-8/2
D8/2
Show Answer & Explanation

Correct Answer: A - -4

Let a=3k, b=5k. (3k+5k)/(3k-5k)=8k/-2k=-4.

Q36.
Solve the system: x + y = 10, x - y = 4:
Ax=7, y=3
Bx=8, y=2
Cx=6, y=4
Dx=5, y=5
Show Answer & Explanation

Correct Answer: A - x=7, y=3

Adding: 2x=14, x=7. y=10-7=3.

Q37.
The discriminant of 3x² + 2x + 1 = 0 is:
A-4
B8
C4
D-8
Show Answer & Explanation

Correct Answer: D - -8

D=b²-4ac=4-12=-8. Roots are imaginary.

Q38.
If a - b = 3 and a² - b² = 39, then a + b =
A13
B12
C10
D15
Show Answer & Explanation

Correct Answer: A - 13

a²-b²=(a+b)(a-b). 39=3(a+b). a+b=13.

Q39.
Find the value of x: 5(2x-1) = 125
A1
B3
C2
D4
Show Answer & Explanation

Correct Answer: C - 2

5(2x-1)=53. 2x-1=3. x=2.

Q40.
If f(x) = 2x² - 3x + 1, then f(2) =
A3
B5
C7
D1
Show Answer & Explanation

Correct Answer: A - 3

f(2)=2(4)-3(2)+1=8-6+1=3.

Q41.
If one root of x² - 5x + k = 0 is 2, find k:
A8
B4
C6
D10
Show Answer & Explanation

Correct Answer: C - 6

4-10+k=0. k=6.

Q42.
Solve: 2x × 4x = 64:
A4
B3
C2
D1
Show Answer & Explanation

Correct Answer: C - 2

2x × 2(2x) = 26. 2(3x)=26. 3x=6. x=2.

Q43.
If √(x+5) = 3, then x =
A2
B9
C14
D4
Show Answer & Explanation

Correct Answer: D - 4

x+5=9. x=4.

Q44.
The nth term of AP: 3, 7, 11, 15... is:
A4n-1
B4n+1
C3n+1
D4n-3
Show Answer & Explanation

Correct Answer: A - 4n-1

a=3, d=4. nth term=3+(n-1)4=4n-1.

Q45.
Sum of first 20 terms of AP: 5, 8, 11...
A670
B650
C700
D630
Show Answer & Explanation

Correct Answer: A - 670

a=5, d=3, n=20. S=20/2[10+19×3]=10[10+57]=670.

Q46.
If log₁₀(x) + log₁₀(x²) = 3:
Ax=1000
Bx=100
Cx=10
Dx=√10
Show Answer & Explanation

Correct Answer: C - x=10

log(x)+2log(x)=3. 3log(x)=3. log(x)=1. x=10.

Q47.
If (x-2) is a factor of x³ - kx + 4, find k:
A6
B4
C8
D2
Show Answer & Explanation

Correct Answer: A - 6

f(2)=0. 8-2k+4=0. 2k=12. k=6.

Q48.
Simplify: (27)(2/3):
A9
B18
C3
D6
Show Answer & Explanation

Correct Answer: A - 9

27(2/3) = (3³)(2/3) = 3² = 9.

Q49.
If x² + y² = 29 and xy = 10, then (x+y)² =
A29
B39
C59
D49
Show Answer & Explanation

Correct Answer: D - 49

(x+y)²=x²+2xy+y²=29+20=49.

Q50.
The GP 2, 6, 18, 54... has 10th term:
A2×3¹⁰
B2×3⁹
C3⁹
D6×3⁸
Show Answer & Explanation

Correct Answer: B - 2×3⁹

a=2, r=3. 10th term=2×39=39366.

Q51.
If x + 1/x = 5, then x2 + 1/x2 equals:
A21
B23
C25
D27
Show Answer & Explanation

Correct Answer: B - 23

(x+1/x)2 = x2 + 2 + 1/x2 = 25, so required value is 23.

Q52.
If a + b = 10 and ab = 21, then a2 + b2 is:
A52
B56
C58
D60
Show Answer & Explanation

Correct Answer: C - 58

a2+b2=(a+b)2-2ab=100-42=58.

Q53.
The roots of x2 - 7x + 12 = 0 are:
A2, 6
B3, 4
C1, 12
D5, 2
Show Answer & Explanation

Correct Answer: B - 3, 4

x2 - 7x + 12 = (x-3)(x-4), so roots are 3 and 4.

Q54.
If 2x - 3y = 7 and x + y = 6, then x is:
A4
B5
C6
D7
Show Answer & Explanation

Correct Answer: B - 5

y=6-x. 2x-3(6-x)=7 gives 5x=25, so x=5.

Q55.
If x:y = 2:3, then (3x+2y):(4x-y) is:
A12:5
B6:5
C5:6
D10:7
Show Answer & Explanation

Correct Answer: A - 12:5

Let x=2k, y=3k. Ratio=(6k+6k):(8k-3k)=12k:5k=12:5.

Q56.
Simplify: (x3 - y3)/(x - y), x != y.
Ax2 + xy + y2
Bx2 - xy + y2
Cx2 - y2
Dx+y
Show Answer & Explanation

Correct Answer: A - x2 + xy + y2

x3-y3=(x-y)(x2+xy+y2).

Q57.
If log10 x = 2.5, then x is:
A250
B316.23 approximately
C1000
D25
Show Answer & Explanation

Correct Answer: B - 316.23 approximately

x=102.5=100 x sqrt(10), approximately 316.23.

Q58.
For real x, the minimum value of x2 - 6x + 14 is:
A3
B5
C7
D9
Show Answer & Explanation

Correct Answer: B - 5

x2-6x+14=(x-3)2+5, minimum is 5.

Q59.
If x - 1/x = 4, then x2 + 1/x2 equals:
A14
B16
C18
D20
Show Answer & Explanation

Correct Answer: C - 18

(x-1/x)2 = x2 -2 +1/x2 =16, so required value=18.

Q60.
The coefficient of x2 in (x+2)4 is:
A12
B16
C24
D32
Show Answer & Explanation

Correct Answer: C - 24

Term with x2 is C(4,2)x2(2)2 = 6 x 4 = 24.

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