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 1Questions 1–10 of 45

Q1medium
Expand: (a+b)^3
1. Aa^3+b^3
2. Ba^3+3a^2b+3ab^2
3. Ca^3+3a^2b+3ab^2+b^3
4. Da^3-3a^2b+3ab^2-b^3
💡 Explanation:
(a+b)^3 = a^3+3a^2b+3ab^2+b^3.
Q2easy
If x - 5 = 12, find the value of x
1. A15
2. B17
3. C19
4. D22
💡 Explanation:
Add 5 to both sides: x = 12 + 5 = 17.
Q3Past Paper · PPSC/FPSC/NTSeasy
Solve for x: 3x + 7 = 22
1. A5
2. B6
3. C7
4. D8
💡 Explanation:
Subtract 7 from both sides: 3x = 15, so x = 5.
Q4Past Paper · PPSC/FPSC/NTSeasy
Solve for x: 2(x + 3) = 16
1. A4
2. B6
3. C5
4. D3
💡 Explanation:
Divide by 2: x + 3 = 8, so x = 5.
Q5easy
Solve for x: 5x - 3 = 3x + 9
1. A3
2. B4
3. C5
4. D6
💡 Explanation:
Bring like terms together: 2x = 12, so x = 6.
Q6medium
If x + y = 10 and x - y = 4, find the value of x
1. A7
2. B6
3. C8
4. D5
💡 Explanation:
Adding the two equations gives 2x = 14, so x = 7.
Q7medium
If 2x + y = 11 and x - y = 1, find the value of y
1. A2
2. B3
3. C4
4. D5
💡 Explanation:
Subtracting the equations gives x = 4, then y = 11 - 2(4) = 3.
Q8medium
If x + 2y = 8 and 2x + y = 7, find the value of x + y
1. A3
2. B4
3. C5
4. D6
💡 Explanation:
Solving the system gives x = 2 and y = 3, so x + y = 5.
Q9medium
Solve for x: x/3 + x/4 = 7
1. A9
2. B10
3. C11
4. D12
💡 Explanation:
Multiply through by 12: 4x + 3x = 84, so x = 12.
Q10Past Paper · PPSC/FPSC/NTSmedium
What is the sum of the roots of the equation x^2 - 5x + 6 = 0
1. A5
2. B6
3. C-5
4. D1
💡 Explanation:
Sum of roots = -b/a = -(-5)/1 = 5.
Q11Past Paper · PPSC/FPSC/NTSmedium
What is the product of the roots of the equation x^2 - 5x + 6 = 0
1. A5
2. B6
3. C-6
4. D-5
💡 Explanation:
Product of roots = c/a = 6/1 = 6.
Q12Past Paper · PPSC/FPSC/NTSmedium
What are the roots of the equation x^2 - 9 = 0
1. A3 only
2. B-3 only
3. C3 and -3
4. D9 and -9
💡 Explanation:
x^2 = 9 gives x = 3 or x = -3.
Q13Past Paper · PPSC/FPSC/NTSmedium
What is the larger root of the equation x^2 + x - 6 = 0
1. A-2
2. B-3
3. C3
4. D2
💡 Explanation:
Factoring gives (x+3)(x-2) = 0, so x = -3 or x = 2; the larger root is 2.
Q14medium
For a quadratic equation ax^2 + bx + c = 0, the sum of the roots is
1. A-b/a
2. Bb/a
3. Cc/a
4. D-c/a
💡 Explanation:
For ax^2+bx+c=0, sum of roots = -b/a.
Q15medium
For a quadratic equation ax^2 + bx + c = 0, the product of the roots is
1. A-b/a
2. Bc/a
3. C-c/a
4. Db/a
💡 Explanation:
For ax^2+bx+c=0, product of roots = c/a.
Q16hard
The discriminant of the quadratic equation ax^2 + bx + c = 0 is
1. Ab^2 + 4ac
2. Bb^2 - 2ac
3. Cb^2 - 4ac
4. D4ac - b^2
💡 Explanation:
The discriminant is defined as b^2 - 4ac.
Q17hard
If the discriminant b^2 - 4ac = 0, the roots of the quadratic equation are
1. Aimaginary
2. Birrational
3. Cunequal real
4. Dreal and equal
💡 Explanation:
When the discriminant equals zero, the roots are real and equal.
Q18easy
Simplify: x^4 / x^2
1. Ax^8
2. Bx^6
3. Cx^2
4. Dx
💡 Explanation:
When dividing powers with the same base, subtract exponents: x^4/x^2 = x^2.
Q19Past Paper · PPSC/FPSC/NTSeasy
Simplify: x^2 * x^3
1. Ax^6
2. Bx^5
3. Cx^1
4. Dx^-1
💡 Explanation:
When multiplying powers with the same base, add exponents: x^2 * x^3 = x^5.
Q20medium
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).
Q21medium
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).
Q22Past Paper · PPSC/FPSC/NTSeasy
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).
Q23easy
Expand: (a-b)^2
1. Aa^2-2ab+b^2
2. Ba^2+2ab+b^2
3. Ca^2-b^2
4. Da^2+b^2
💡 Explanation:
(a-b)^2 = a^2-2ab+b^2.
Q24Past Paper · PPSC/FPSC/NTSeasy
Expand: (a+b)^2
1. Aa^2+b^2
2. Ba^2-b^2
3. Ca^2+2ab-b^2
4. Da^2+2ab+b^2
💡 Explanation:
(a+b)^2 = a^2+2ab+b^2.
Q25medium
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.
Q26Past Paper · PPSC/FPSC/NTSeasy
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).
Q27Past Paper · PPSC/FPSC/NTSeasy
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).
Q28Past Paper · PPSC/FPSC/NTSeasy
Simplify: x^-2
1. A-x^2
2. B1/x^2
3. Cx^2
4. D-1/x^2
💡 Explanation:
A negative exponent gives the reciprocal: x^-2 = 1/x^2.
Q29medium
Simplify: sqrt(2) * sqrt(8)
1. A2
2. B3
3. C4
4. D16
💡 Explanation:
sqrt(2) * sqrt(8) = sqrt(16) = 4.
Q30medium
Rationalize: 1/sqrt(2)
1. Asqrt(2)
2. B2
3. C1/2
4. Dsqrt(2)/2
💡 Explanation:
Multiply numerator and denominator by sqrt(2): 1/sqrt(2) = sqrt(2)/2.
Q31Past Paper · PPSC/FPSC/NTShard
By the Remainder Theorem, when a polynomial p(x) is divided by (x - a), the remainder equals
1. Ap(a)
2. Bp(-a)
3. Cp(0)
4. Dp(1)
💡 Explanation:
By the Remainder Theorem, dividing p(x) by (x-a) leaves remainder p(a).
Q32Past Paper · PPSC/FPSC/NTShard
By the Factor Theorem, (x - a) is a factor of p(x) if and only if
1. Ap(0)=0
2. Bp(a)=0
3. Cp(a)=1
4. Dp(-a)=0
💡 Explanation:
By the Factor Theorem, (x-a) is a factor of p(x) if and only if p(a) = 0.
Q33hard
Find the remainder when p(x) = x^3 - 3x^2 + 2x - 5 is divided by (x - 1)
1. A5
2. B0
3. C-5
4. D-3
💡 Explanation:
p(1) = 1 - 3 + 2 - 5 = -5.
Q34hard
Find k if (x - 2) is a factor of x^2 + kx - 10
1. A5
2. B-3
3. C-5
4. D3
💡 Explanation:
p(2) = 4 + 2k - 10 = 0 gives k = 3.
Q35medium
The nth term of an arithmetic progression with first term a and common difference d is
1. Aa+(n-1)d
2. Ba+nd
3. Ca-(n-1)d
4. Dna+d
💡 Explanation:
The nth term of an AP is a + (n-1)d.
Q36Past Paper · PPSC/FPSC/NTSmedium
Find the 10th term of the AP: 3, 7, 11, 15, ...
1. A35
2. B39
3. C43
4. D41
💡 Explanation:
T10 = 3 + 9(4) = 39.
Q37medium
The sum of the first n terms of an AP with first term a and last term l is
1. An(a+l)
2. Bn/2 (a-l)
3. Cn/2 (a+l)
4. D2n(a+l)
💡 Explanation:
Sum of first n terms of an AP = n/2 (a+l), where l is the last term.
Q38Past Paper · PPSC/FPSC/NTShard
Find the sum of the first 20 natural numbers
1. A190
2. B200
3. C205
4. D210
💡 Explanation:
Sum = n(n+1)/2 = 20(21)/2 = 210.
Q39medium
The nth term of a geometric progression with first term a and common ratio r is
1. Aa*r^(n-1)
2. Ba*r^n
3. Ca+(n-1)r
4. Da*n*r
💡 Explanation:
The nth term of a GP is a * r^(n-1).
Q40Past Paper · PPSC/FPSC/NTSmedium
Find the 5th term of the GP: 2, 6, 18, 54, ...
1. A154
2. B162
3. C148
4. D170
💡 Explanation:
T5 = 2 * 3^4 = 2 * 81 = 162.
Q41medium
The sum of an infinite geometric progression with |r| < 1 is given by
1. Aa(1-r^n)/(1-r)
2. Ba*n/(1-r)
3. Ca/(1-r)
4. Da/(1+r)
💡 Explanation:
For an infinite GP with |r|<1, the sum is a/(1-r).
Q42easy
Solve the inequality: 2x - 3 > 7
1. Ax<5
2. Bx<=5
3. Cx>-5
4. Dx>5
💡 Explanation:
Adding 3 to both sides and dividing by 2: x > 5.
Q43medium
Solve the inequality: 3 - x >= 1
1. Ax>=2
2. Bx<=-2
3. Cx>2
4. Dx<=2
💡 Explanation:
Dividing by -1 reverses the inequality direction: x <= 2.
Q44easy
What is the value of x^0 for any nonzero x
1. A1
2. B0
3. Cx
4. Dundefined
💡 Explanation:
Any nonzero number raised to the power 0 equals 1.
Q45easy
Simplify: (x^3)^2
1. Ax^5
2. Bx^9
3. Cx^8
4. Dx^6
💡 Explanation:
When raising a power to a power, multiply exponents: (x^3)^2 = x^6.

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Algebra MCQs 2026

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