Islamabad High Court Assistant / Clerk Mathematics: Algebra MCQs

Practice Algebra MCQs for Islamabad High Court Assistant / Clerk Mathematics — topic-wise sets with solved answers.

Islamabad High Court Assistant / Clerk Mathematics: Algebra MCQs — sample questions

  1. Question 1

    Q1. Find the value of x in the series: x, 9, 25, 49, 81, 121, ... Number Series

    • A) 1
    • B) 3
    • C) 5
    • D) 7

    Answer: 1

    Explanation: The series consists of consecutive odd squares: 1², 3², 5², 7², 9², 11²; the missing first term is 1.

  2. Question 2

    Q2. If X% of 25/2 is 150, what is the value of X?

    • A) 1000
    • B) 1200
    • C) 1400
    • D) None of these

    Answer: 1200

    Explanation: The correct value is 1200. Apply the formula or arithmetic step shown in the question and

  3. Question 3

    Q3. If, x - y = 6 and x + y = 16, then Linear Equations

    • A) x=5 and y = 3
    • B) x=8 and y= 5
    • C) x=10 and y= 3
    • D) x=11 and y= 5

    Answer: x=11 and y= 5

    Explanation: Adding the two equations: 2x = 22 → x = 11; substituting back: y = 5.

  4. Question 4

    Q4. If 144 / 0.144 = 14.4 / x, what is the value of x?

    • A) 0.144
    • B) 144
    • C) 14.4
    • D) 0.0144

    Answer: 0.0144

    Explanation: 144/0.144 = 1000; therefore 14.4/x = 1000 → x = 14.4/1000 = 0.0144.

  5. Question 5

    Q5. If 0.009/x = 0.01, what is the value of x?

    • A) 0.09
    • B) 0.9
    • C) 0.009
    • D) None of these

    Answer: 0.9

    Explanation: The correct value is 0.9. Apply the formula or arithmetic step shown in the question and

  6. Question 6

    Q6. In the system of equations ax+2y=5 and 3x-6y=20, a is a constant. If the system has one solution, which of the following CANNOT be the value of a?

    • A) -1
    • B) 1
    • C) 2
    • D) -3

    Answer: -1

    Explanation: For a unique solution, lines must not be parallel; the system is parallel when a/3 = 2/(−6), i.e., a = −1, so a = −1 cannot be the value.

  7. Question 7

    Q7. Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x² + 8x + 4 = 0?

    • A) 15
    • B) 14
    • C) 24
    • D) 26

    Answer: 14

    Explanation: a/b+b/a = (a²+b²)/ab = ((a+b)²−2ab)/ab; a+b = −8, ab = 4; value = (64−8)/4 = 14.

  8. Question 8

    Q8. If 3 is a solution to the equation 3x² + (k − 1)x + 9 = 0, what is the value of k?

    • A) -9
    • B) -11
    • C) -13
    • D) -16

    Answer: -11

    Explanation: Substituting x=3: 3(9)+(k−1)(3)+9 = 0 → 27+3k−3+9 = 0 → k = −11.

  9. Question 9

    Q9. Solve: √64 + 3.

    • A) 8
    • B) 3
    • C) 4
    • D) 11

    Answer: 11

    Explanation: √64 = 8, and adding 3 gives 11. Show the calculation clearly when solving similar quantitative items.

  10. Question 10

    Q10. The sum and the product of the roots of the quadratic equation x^2 + 20x + 3 = 0 are?

    • A) 10, 3
    • B) -10, 3
    • C) -20, 3
    • D) -10, -3

    Answer: -20, 3

    Explanation: For x² + 20x + 3 = 0, sum of roots = −20 and product of roots = 3 (by Vieta's formulas).

  11. Question 11

    Q11. 3x + 3 / (4x - 4) = 5/4, the value of x is:

    • A) 3
    • B) 4
    • C) 5
    • D) 6

    Answer: 4

    Explanation: Rewriting as 3(x+1)/[4(x−1)] = 5/4, cross-multiplying gives 12(x+1) = 20(x−1), which simplifies to x = 4.

  12. Question 12

    Q12. Solve: 2^5 x 2^3 =?

    • A) 256
    • B) 128
    • C) 54
    • D) 60

    Answer: 256

    Explanation: When multiplying powers with the same base, exponents are added: 2^5 × 2^3 = 2^8 = 256.

  13. Question 13

    Q13. Solve: 6.334 × 10^3

    • A) 0.0006334
    • B) 0.06334
    • C) 6334
    • D) 63340

    Answer: 6334

    Explanation: Multiplying by 10³ shifts the decimal three places to the right: 6.334 × 10³ = 6334.

  14. Question 14

    Q14. Solve: 2^1 × 2^2 × 2^5. (Note: the symbol ^ indicates power)

    • A) 64
    • B) 250
    • C) 256
    • D) None of these

    Answer: 256

    Explanation: The correct value is 256. Apply the formula or arithmetic step shown in the question and

  15. Question 15

    Q15. What is the value of x that satisfies the equation 7x + 1 = 4x - 8?

    • A) 400
    • B) 380
    • C) -3
    • D) 340

    Answer: -3

    Explanation: Rearranging 7x + 1 = 4x − 8 gives 3x = −9, so x = −3.

  16. Question 16

    Q16. If 3x + 16 = 40, what is the value of x?

    • A) 5
    • B) 6
    • C) 7
    • D) 8

    Answer: 8

    Explanation: Subtracting 16 from both sides gives 3x = 24, so x = 8.

  17. Question 17

    Q17. Solve for x if (30x + 70) / x = 100. Linear Equations

    • A) 2
    • B) 4
    • C) 1
    • D) 3

    Answer: 1

    Explanation: Multiplying through by x: 30x + 70 = 100x, which gives 70x = 70 and x = 1.

  18. Question 18

    Q18. If A = (√5 + 1)/(√5 - 1) and B = (√5 - 1)/(√5 + 1), what is the value of A + B?

    • A) 3
    • B) 2
    • C) 1
    • D) 4√5

    Answer: 3

    Explanation: Rationalising each fraction: A = (√5+1)²/4 and B = (√5−1)²/4; A+B = [(6+2√5)+(6−2√5)]/4 = 12/4 = 3.

  19. Question 19

    Q19. If 3^(x^3) + 7 = 250, what is the value of x?

    • A) 5
    • B) 3.2
    • C) 1.71
    • D) None of these

    Answer: 1.71

    Explanation: The correct value is 1.71. Apply the formula or arithmetic step shown in the question and

  20. Question 20

    Q20. Which number can replace both the question marks in the equation 2/? = ?/50?

    • A) 5
    • B) 10
    • C) 25
    • D) 100

    Answer: 10

    Explanation: Cross-multiplying 2/x = x/50 gives x² = 100, so x = 10.

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