TestMaster MCQs

Algebra MCQs

About Mathematics MCQs

Mathematics is a compulsory subject in almost every competitive exam, including CSS, PMS, banking, and armed forces tests. It tests your ability to solve problems logically and accurately under time constraints. From basic arithmetic to advanced algebra and geometry, consistent practice is the only way to master this subject.

Topics Covered in This Category

  • Arithmetic: Percentages, ratios, averages, profit and loss, and interest.
  • Algebra: Equations, inequalities, polynomials, and functions.
  • Geometry & Mensuration: Area, volume, angles, and coordinate geometry.
  • Word Problems: Time, speed, distance, and work-related problems.

Study Tips for Mathematics

Do not just memorize formulas; understand how they are derived. Practice is the key to speed. When solving MCQs, try to solve the problem first before looking at the options, or use the options to work backward. Maintain an error log to track the types of questions you get wrong and review them weekly.

Practice 50 Algebra MCQs

Question 1: If 3x − 7 = 11, then x = ?

  • A 4
  • B 5
  • C 6
  • D 7

Explanation: 3x = 18, so x = 6. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 2: If x + y = 10 and x − y = 4, then x = ?

  • A 3
  • B 6
  • C 7
  • D 4

Explanation: Adding gives 2x = 14, so x = 7. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 3: (a + b)² equals:

  • A 2a + 2b
  • B a² + 2ab + b²
  • C a² + b²
  • D a² − 2ab + b²

Explanation: This is the standard square-of-a-sum identity. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 4: (a − b)(a + b) equals:

  • A 2a
  • B a² + b²
  • C a² − b²
  • D a² − 2ab + b²

Explanation: This is the difference of squares. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 5: If 2x + 3 = 15, then x = ?

  • A 7
  • B 9
  • C 5
  • D 6

Explanation: 2x = 12, so x = 6. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 6: What is the square root of 144?

  • A 14
  • B 16
  • C 11
  • D 12

Explanation: 12 × 12 = 144. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 7: What is the average of 10, 20, 30, 40 and 50?

  • A 25
  • B 30
  • C 35
  • D 40

Explanation: Sum = 150; 150 ÷ 5 = 30. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 8: The average of 5 numbers is 20. Their sum is:

  • A 120
  • B 100
  • C 4
  • D 25

Explanation: Sum = average × count = 20 × 5. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 9: What is the derivative of x² with respect to x?

  • A x
  • B 2x
  • C x²
  • D 2

Explanation: By the power rule, d/dx (x^n) = n·x^(n−1), so d/dx (x²) = 2x. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 10: The derivative of sin x is:

  • A tan x
  • B cos x
  • C −cos x
  • D −sin x

Explanation: d/dx(sin x) = cos x. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 11: ∫ 2x dx equals:

  • A x + C
  • B x² + C
  • C 2x² + C
  • D 2 + C

Explanation: Integrate 2x to get x² + C. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 12: The derivative of a constant is:

  • A 1
  • B The constant itself
  • C Undefined

Explanation: A constant does not change, so its derivative is zero. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 13: Area of a circle of radius 7 cm (take π = 22/7) is:

  • A 44 cm²
  • B 154 cm²
  • C 308 cm²
  • D 49 cm²

Explanation: Area = πr² = (22/7) × 7 × 7 = 154 cm². Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 14: What is the sum of the interior angles of a quadrilateral?

  • A 360°
  • B 540°
  • C 180°
  • D 270°

Explanation: Any quadrilateral's angles add up to 360°. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 15: In a right-angled triangle with legs 3 cm and 4 cm, the hypotenuse is:

  • A 5 cm
  • B 7 cm
  • C 6 cm
  • D 25 cm

Explanation: √(3² + 4²) = 5. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 16: Each interior angle of a regular hexagon measures:

  • A 135°
  • B 150°
  • C 120°
  • D 108°

Explanation: (6−2)×180°/6 = 120°. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 17: What is the LCM of 12 and 18?

  • A 54
  • B 72
  • C 6
  • D 36

Explanation: 12 = 2²×3 and 18 = 2×3², so LCM = 2²×3² = 36. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 18: What is the HCF of 24 and 36?

  • A 6
  • B 8
  • C 24
  • D 12

Explanation: Common factors give the highest = 12. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 19: What is log₁₀ 100?

  • A 2
  • B 100
  • C 10
  • D 1

Explanation: 10² = 100, so the log is 2. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 20: log a + log b equals:

  • A log(a/b)
  • B log(a + b)
  • C log(ab)
  • D a·b

Explanation: Product rule of logarithms. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 21: Area of a rectangle with length 12 cm and width 5 cm is:

  • A 34 cm²
  • B 120 cm²
  • C 60 cm²
  • D 17 cm²

Explanation: Area = 12 × 5 = 60. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 22: Perimeter of a square with side 9 cm is:

  • A 27 cm
  • B 81 cm
  • C 18 cm
  • D 36 cm

Explanation: 4 × 9 = 36. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 23: Volume of a cube with side 4 cm is:

  • A 64 cm³
  • B 16 cm³
  • C 96 cm³
  • D 48 cm³

Explanation: 4³ = 64. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 24: Circumference of a circle of radius 7 cm (π = 22/7) is:

  • A 44 cm
  • B 49 cm
  • C 22 cm
  • D 154 cm

Explanation: 2πr = 2 × 22/7 × 7 = 44. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 25: Area of a triangle with base 10 cm and height 6 cm is:

  • A 60 cm²
  • B 15 cm²
  • C 30 cm²
  • D 16 cm²

Explanation: ½ × 10 × 6 = 30. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 26: What is the smallest prime number?

  • A 3
  • B 2
  • C 1

Explanation: 2 is the smallest and only even prime. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 27: What is 20% of 250?

  • A 25
  • B 40
  • C 50
  • D 60

Explanation: 20% of 250 = (20/100) × 250 = 50. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 28: What is 15% of 200?

  • A 20
  • B 15
  • C 30
  • D 45

Explanation: (15/100) × 200 = 30. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 29: A student scored 360 out of 450. What is the percentage?

  • A 80%
  • B 90%
  • C 75%
  • D 85%

Explanation: 360/450 × 100 = 80%. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 30: A price rises from Rs 200 to Rs 250. What is the percentage increase?

  • A 20%
  • B 25%
  • C 10%
  • D 50%

Explanation: Increase 50 ÷ 200 = 25%. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 31: The probability of getting a head in one toss of a fair coin is:

  • A 1
  • B 1/2
  • C 1/4

Explanation: There are 2 equally likely outcomes. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 32: A die is rolled. The probability of an even number is:

  • A 1/2
  • B 1/3
  • C 1/6
  • D 2/3

Explanation: Even outcomes: 2, 4, 6 → 3/6 = 1/2. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 33: An article bought for Rs 400 is sold for Rs 500. What is the profit percentage?

  • A 20%
  • B 25%
  • C 30%
  • D 15%

Explanation: Profit = 100; (100/400) × 100 = 25%. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 34: The roots of x² − 5x + 6 = 0 are:

  • A 2 and 3
  • B 2 and −3
  • C −2 and −3
  • D 1 and 6

Explanation: Factorise: (x − 2)(x − 3) = 0. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 35: The sum of the roots of x² − 7x + 10 = 0 is:

  • A 10
  • B 7
  • C −7
  • D 3

Explanation: Sum of roots = −b/a = 7. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 36: Two numbers are in the ratio 3:5 and their sum is 40. What is the larger number?

  • A 15
  • B 20
  • C 25
  • D 30

Explanation: Total parts = 8; one part = 5; larger = 5 × 5 = 25. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 37: If a:b = 2:3 and b:c = 4:5, then a:b:c is:

  • A 8:12:15
  • B 8:6:5
  • C 6:12:15
  • D 2:3:5

Explanation: Make b equal: a:b = 8:12 and b:c = 12:15. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 38: If A = {1, 2, 3} and B = {3, 4}, then A ∪ B =

  • A {3}
  • B {1, 2, 4}
  • C {1, 2, 3, 4}
  • D {1, 2}

Explanation: Union contains all elements of both sets. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 39: Simple interest on Rs 5,000 at 10% per annum for 2 years is:

  • A Rs 1,500
  • B Rs 1,100
  • C Rs 1,000
  • D Rs 500

Explanation: SI = (P × R × T)/100 = 5000×10×2/100 = 1,000. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 40: Compound interest on Rs 1,000 at 10% p.a. for 2 years is:

  • A Rs 220
  • B Rs 100
  • C Rs 200
  • D Rs 210

Explanation: Amount = 1000 × 1.1² = 1,210, so CI = 210. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 41: A car covers 120 km in 2 hours. What is its average speed?

  • A 40 km/h
  • B 50 km/h
  • C 60 km/h
  • D 80 km/h

Explanation: Speed = distance ÷ time = 120 ÷ 2 = 60 km/h. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 42: A 100 m long train passes a pole in 10 seconds. Its speed is:

  • A 20 m/s
  • B 100 m/s
  • C 10 m/s
  • D 1 m/s

Explanation: Speed = 100 m ÷ 10 s = 10 m/s. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 43: The median of 3, 5, 7, 9, 11 is:

  • A 9
  • B 5
  • C 6
  • D 7

Explanation: The middle value of the ordered list is 7. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 44: The mode of 2, 3, 3, 4, 5, 3, 6 is:

  • A 6
  • B 4
  • C 2
  • D 3

Explanation: 3 occurs most often. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 45: A can finish a job in 10 days and B in 15 days. Working together, how many days will they take?

  • A 5
  • B 6
  • C 8
  • D 12

Explanation: Combined rate = 1/10 + 1/15 = 1/6 per day, so 6 days. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 46: A pipe fills a tank in 6 hours and another empties it in 12 hours. If both are open, the tank fills in:

  • A 8 hours
  • B 18 hours
  • C 6 hours
  • D 12 hours

Explanation: Net rate = 1/6 − 1/12 = 1/12 per hour. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 47: The value of sin 30° is:

  • A √2/2
  • B 1/2
  • C √3/2
  • D 1

Explanation: sin 30° = 1/2. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 48: The value of cos 60° is:

  • A 1
  • B √3/2
  • C 1/2

Explanation: cos 60° = 1/2. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 49: The value of tan 45° is:

  • A √3
  • B 1/2
  • C 1

Explanation: tan 45° = 1. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Question 50: sin²θ + cos²θ equals:

  • A 1
  • B 2
  • C sin 2θ

Explanation: This is the Pythagorean identity. Useful for: NTS, PPSC, FPSC, ECAT, ASF, Police (ASI, Constable).

Frequently Asked Questions

How many Algebra MCQs are available on TestMasterMCQs?

There are currently 50 Algebra MCQs on this page, each with four options, the correct answer and a short explanation to help you understand the concept — not just memorise the answer.

Are these Algebra MCQs useful for PPSC, FPSC, NTS, CSS and MDCAT?

Yes — our Algebra questions follow the syllabus of common Pakistani competitive exams including CSS, PMS, PPSC, FPSC, NTS, and university entry tests like MDCAT and ECAT.

How should I practice Algebra MCQs for better retention?

Attempt 15–20 questions at a time, read the explanation after every question (even the ones you get right), and revisit wrong answers after 24 hours to reinforce memory.