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Algebra MCQs 2026

45 questions with detailed answers · 17 from past papers · 5 quiz batches available

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Read each question, think about the answer, then click Show Answer to reveal the correct option and explanation. Load 10 at a time so it stays manageable — perfect for one-topic study sessions on the bus or during a break.

Page 1 of 1 Questions 1–10 of 45
  1. Q1 Past Paper · PPSC/FPSC/NTS easy

    Simplify: x^-2

    1. A -x^2
    2. B 1/x^2
    3. C x^2
    4. D -1/x^2
    💡 Explanation:

    A negative exponent gives the reciprocal: x^-2 = 1/x^2.

  2. Q2 medium

    Simplify: sqrt(2) * sqrt(8)

    1. A 2
    2. B 3
    3. C 4
    4. D 16
    💡 Explanation:

    sqrt(2) * sqrt(8) = sqrt(16) = 4.

  3. Q3 medium

    Rationalize: 1/sqrt(2)

    1. A sqrt(2)
    2. B 2
    3. C 1/2
    4. D sqrt(2)/2
    💡 Explanation:

    Multiply numerator and denominator by sqrt(2): 1/sqrt(2) = sqrt(2)/2.

  4. Q4 hard

    The discriminant of the quadratic equation ax^2 + bx + c = 0 is

    1. A b^2 + 4ac
    2. B b^2 - 2ac
    3. C b^2 - 4ac
    4. D 4ac - b^2
    💡 Explanation:

    The discriminant is defined as b^2 - 4ac.

  5. Q5 Past Paper · PPSC/FPSC/NTS easy

    Expand: (a+b)^2

    1. A a^2+b^2
    2. B a^2-b^2
    3. C a^2+2ab-b^2
    4. D a^2+2ab+b^2
    💡 Explanation:

    (a+b)^2 = a^2+2ab+b^2.

  6. Q6 easy

    Expand: (a-b)^2

    1. A a^2-2ab+b^2
    2. B a^2+2ab+b^2
    3. C a^2-b^2
    4. D a^2+b^2
    💡 Explanation:

    (a-b)^2 = a^2-2ab+b^2.

  7. Q7 Past Paper · PPSC/FPSC/NTS easy

    a^2 - b^2 is equal to

    1. A (a-b)^2
    2. B (a+b)(a-b)
    3. C (a+b)^2
    4. D (a-b)(a-b)
    💡 Explanation:

    a^2-b^2 factors as (a+b)(a-b).

  8. Q8 easy

    What is the value of x^0 for any nonzero x

    1. A 1
    2. B 0
    3. C x
    4. D undefined
    💡 Explanation:

    Any nonzero number raised to the power 0 equals 1.

  9. Q9 easy

    Simplify: (x^3)^2

    1. A x^5
    2. B x^9
    3. C x^8
    4. D x^6
    💡 Explanation:

    When raising a power to a power, multiply exponents: (x^3)^2 = x^6.

  10. Q10 easy

    Simplify: x^4 / x^2

    1. A x^8
    2. B x^6
    3. C x^2
    4. D x
    💡 Explanation:

    When dividing powers with the same base, subtract exponents: x^4/x^2 = x^2.

  11. Q11 hard

    Find k if (x - 2) is a factor of x^2 + kx - 10

    1. A 5
    2. B -3
    3. C -5
    4. D 3
    💡 Explanation:

    p(2) = 4 + 2k - 10 = 0 gives k = 3.

  12. Q12 medium

    The nth term of an arithmetic progression with first term a and common difference d is

    1. A a+(n-1)d
    2. B a+nd
    3. C a-(n-1)d
    4. D na+d
    💡 Explanation:

    The nth term of an AP is a + (n-1)d.

  13. Q13 Past Paper · PPSC/FPSC/NTS medium

    Find the 10th term of the AP: 3, 7, 11, 15, ...

    1. A 35
    2. B 39
    3. C 43
    4. D 41
    💡 Explanation:

    T10 = 3 + 9(4) = 39.

  14. Q14 medium

    The sum of the first n terms of an AP with first term a and last term l is

    1. A n(a+l)
    2. B n/2 (a-l)
    3. C n/2 (a+l)
    4. D 2n(a+l)
    💡 Explanation:

    Sum of first n terms of an AP = n/2 (a+l), where l is the last term.

  15. Q15 Past Paper · PPSC/FPSC/NTS hard

    Find the sum of the first 20 natural numbers

    1. A 190
    2. B 200
    3. C 205
    4. D 210
    💡 Explanation:

    Sum = n(n+1)/2 = 20(21)/2 = 210.

  16. Q16 medium

    The nth term of a geometric progression with first term a and common ratio r is

    1. A a*r^(n-1)
    2. B a*r^n
    3. C a+(n-1)r
    4. D a*n*r
    💡 Explanation:

    The nth term of a GP is a * r^(n-1).

  17. Q17 Past Paper · PPSC/FPSC/NTS medium

    Find the 5th term of the GP: 2, 6, 18, 54, ...

    1. A 154
    2. B 162
    3. C 148
    4. D 170
    💡 Explanation:

    T5 = 2 * 3^4 = 2 * 81 = 162.

  18. Q18 medium

    The sum of an infinite geometric progression with |r| < 1 is given by

    1. A a(1-r^n)/(1-r)
    2. B a*n/(1-r)
    3. C a/(1-r)
    4. D a/(1+r)
    💡 Explanation:

    For an infinite GP with |r|<1, the sum is a/(1-r).

  19. Q19 easy

    Solve the inequality: 2x - 3 > 7

    1. A x<5
    2. B x<=5
    3. C x>-5
    4. D x>5
    💡 Explanation:

    Adding 3 to both sides and dividing by 2: x > 5.

  20. Q20 medium

    Solve the inequality: 3 - x >= 1

    1. A x>=2
    2. B x<=-2
    3. C x>2
    4. D x<=2
    💡 Explanation:

    Dividing by -1 reverses the inequality direction: x <= 2.

  21. Q21 Past Paper · PPSC/FPSC/NTS hard

    By the Remainder Theorem, when a polynomial p(x) is divided by (x - a), the remainder equals

    1. A p(a)
    2. B p(-a)
    3. C p(0)
    4. D p(1)
    💡 Explanation:

    By the Remainder Theorem, dividing p(x) by (x-a) leaves remainder p(a).

  22. Q22 Past Paper · PPSC/FPSC/NTS hard

    By the Factor Theorem, (x - a) is a factor of p(x) if and only if

    1. A p(0)=0
    2. B p(a)=0
    3. C p(a)=1
    4. D p(-a)=0
    💡 Explanation:

    By the Factor Theorem, (x-a) is a factor of p(x) if and only if p(a) = 0.

  23. Q23 hard

    Find the remainder when p(x) = x^3 - 3x^2 + 2x - 5 is divided by (x - 1)

    1. A 5
    2. B 0
    3. C -5
    4. D -3
    💡 Explanation:

    p(1) = 1 - 3 + 2 - 5 = -5.

  24. Q24 medium

    a^3 + b^3 is equal to

    1. A (a+b)(a^2+ab+b^2)
    2. B (a-b)(a^2+ab+b^2)
    3. C (a+b)(a^2-2ab+b^2)
    4. D (a+b)(a^2-ab+b^2)
    💡 Explanation:

    a^3+b^3 = (a+b)(a^2-ab+b^2).

  25. Q25 medium

    a^3 - b^3 is equal to

    1. A (a-b)(a^2+ab+b^2)
    2. B (a+b)(a^2-ab+b^2)
    3. C (a-b)(a^2-ab+b^2)
    4. D (a-b)(a^2+2ab+b^2)
    💡 Explanation:

    a^3-b^3 = (a-b)(a^2+ab+b^2).

  26. Q26 Past Paper · PPSC/FPSC/NTS easy

    Simplify: x^2 * x^3

    1. A x^6
    2. B x^5
    3. C x^1
    4. D x^-1
    💡 Explanation:

    When multiplying powers with the same base, add exponents: x^2 * x^3 = x^5.

  27. Q27 Past Paper · PPSC/FPSC/NTS easy

    Factorize: x^2 + 7x + 12

    1. A (x+2)(x+6)
    2. B (x+3)(x+4)
    3. C (x+1)(x+12)
    4. D (x-3)(x-4)
    💡 Explanation:

    3 and 4 multiply to 12 and add to 7, so x^2+7x+12 = (x+3)(x+4).

  28. Q28 Past Paper · PPSC/FPSC/NTS easy

    Solve for x: 3x + 7 = 22

    1. A 5
    2. B 6
    3. C 7
    4. D 8
    💡 Explanation:

    Subtract 7 from both sides: 3x = 15, so x = 5.

  29. Q29 easy

    If x - 5 = 12, find the value of x

    1. A 15
    2. B 17
    3. C 19
    4. D 22
    💡 Explanation:

    Add 5 to both sides: x = 12 + 5 = 17.

  30. Q30 Past Paper · PPSC/FPSC/NTS easy

    Solve for x: 2(x + 3) = 16

    1. A 4
    2. B 6
    3. C 5
    4. D 3
    💡 Explanation:

    Divide by 2: x + 3 = 8, so x = 5.

  31. Q31 easy

    Solve for x: 5x - 3 = 3x + 9

    1. A 3
    2. B 4
    3. C 5
    4. D 6
    💡 Explanation:

    Bring like terms together: 2x = 12, so x = 6.

  32. Q32 medium

    If x + y = 10 and x - y = 4, find the value of x

    1. A 7
    2. B 6
    3. C 8
    4. D 5
    💡 Explanation:

    Adding the two equations gives 2x = 14, so x = 7.

  33. Q33 medium

    If 2x + y = 11 and x - y = 1, find the value of y

    1. A 2
    2. B 3
    3. C 4
    4. D 5
    💡 Explanation:

    Subtracting the equations gives x = 4, then y = 11 - 2(4) = 3.

  34. Q34 medium

    If x + 2y = 8 and 2x + y = 7, find the value of x + y

    1. A 3
    2. B 4
    3. C 5
    4. D 6
    💡 Explanation:

    Solving the system gives x = 2 and y = 3, so x + y = 5.

  35. Q35 medium

    Solve for x: x/3 + x/4 = 7

    1. A 9
    2. B 10
    3. C 11
    4. D 12
    💡 Explanation:

    Multiply through by 12: 4x + 3x = 84, so x = 12.

  36. Q36 Past Paper · PPSC/FPSC/NTS medium

    What is the sum of the roots of the equation x^2 - 5x + 6 = 0

    1. A 5
    2. B 6
    3. C -5
    4. D 1
    💡 Explanation:

    Sum of roots = -b/a = -(-5)/1 = 5.

  37. Q37 Past Paper · PPSC/FPSC/NTS medium

    What is the product of the roots of the equation x^2 - 5x + 6 = 0

    1. A 5
    2. B 6
    3. C -6
    4. D -5
    💡 Explanation:

    Product of roots = c/a = 6/1 = 6.

  38. Q38 Past Paper · PPSC/FPSC/NTS medium

    What are the roots of the equation x^2 - 9 = 0

    1. A 3 only
    2. B -3 only
    3. C 3 and -3
    4. D 9 and -9
    💡 Explanation:

    x^2 = 9 gives x = 3 or x = -3.

  39. Q39 Past Paper · PPSC/FPSC/NTS medium

    What is the larger root of the equation x^2 + x - 6 = 0

    1. A -2
    2. B -3
    3. C 3
    4. D 2
    💡 Explanation:

    Factoring gives (x+3)(x-2) = 0, so x = -3 or x = 2; the larger root is 2.

  40. Q40 medium

    For a quadratic equation ax^2 + bx + c = 0, the sum of the roots is

    1. A -b/a
    2. B b/a
    3. C c/a
    4. D -c/a
    💡 Explanation:

    For ax^2+bx+c=0, sum of roots = -b/a.

  41. Q41 medium

    For a quadratic equation ax^2 + bx + c = 0, the product of the roots is

    1. A -b/a
    2. B c/a
    3. C -c/a
    4. D b/a
    💡 Explanation:

    For ax^2+bx+c=0, product of roots = c/a.

  42. Q42 medium

    Factorize: 2x^2 + 5x + 3

    1. A (2x+1)(x+3)
    2. B (x+3)(2x-1)
    3. C (2x+3)(x+1)
    4. D (2x-3)(x-1)
    💡 Explanation:

    (2x+3)(x+1) expands to 2x^2+5x+3.

  43. Q43 hard

    If the discriminant b^2 - 4ac = 0, the roots of the quadratic equation are

    1. A imaginary
    2. B irrational
    3. C unequal real
    4. D real and equal
    💡 Explanation:

    When the discriminant equals zero, the roots are real and equal.

  44. Q44 Past Paper · PPSC/FPSC/NTS easy

    Factorize: x^2 - 16

    1. A (x-4)(x+4)
    2. B (x-8)(x+2)
    3. C (x-2)(x+8)
    4. D (x+4)^2
    💡 Explanation:

    This is the difference of squares: x^2 - 16 = (x-4)(x+4).

  45. Q45 medium

    Expand: (a+b)^3

    1. A a^3+b^3
    2. B a^3+3a^2b+3ab^2
    3. C a^3+3a^2b+3ab^2+b^3
    4. D a^3-3a^2b+3ab^2-b^3
    💡 Explanation:

    (a+b)^3 = a^3+3a^2b+3ab^2+b^3.

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