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Mathematics MCQs

MCQs on Algebra, Calculus, Statistics and Geometry

61 Questions
Subject Preparation Guide

Prepare Mathematics with confidence

Develop speed and accuracy in arithmetic, algebra, geometry, percentages, ratios and other quantitative concepts.

ArithmeticAlgebraGeometryPercentages and Ratios
Helpful for academic exams, aptitude tests, NTS and quantitative competitive papers.
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1
Medium css fpsc ppsc nts

What is the expansion of (a-b)²?

  • A a² + b²
  • B a² - b²
  • C a² + 2ab + b²
  • D a² - 2ab + b²
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Correct Answer: Option D — a² - 2ab + b²
Explanation: (a-b)² = a² - 2ab + b². Along with (a+b)² = a²+2ab+b² and (a+b)(a-b) = a²-b² these form the three core algebraic identities. Recognizing which identity applies enables rapid expansion and factoring of algebraic expressions in competitive exam algebra sections saving significant time.
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2
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What is the slope of a line perpendicular to y = 2x + 3?

  • A 2
  • B -2
  • C 1/2
  • D -1/2
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Correct Answer: Option D — -1/2
Explanation: Slope of y=2x+3 is 2. Perpendicular slope = negative reciprocal = -1/2. Two lines are perpendicular when product of slopes = -1: 2×(-1/2)=-1. This condition is used in problems involving altitudes normals to curves and orthogonal intersections in coordinate geometry questions.
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3
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What is the nth term of arithmetic sequence 3 7 11 15?

  • A 4n-1
  • B 4n+1
  • C 3n+1
  • D 2n+3
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Correct Answer: Option A — 4n-1
Explanation: First term a=3 common difference d=4. nth term = a+(n-1)d = 3+4(n-1) = 4n-1. Verification: n=1→3 n=2→7 n=3→11 confirms correctness. Finding nth term formulas for arithmetic sequences is essential for sequences and series questions in competitive exams and is also used in salary progression and installment problems.
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4
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The price after 20% discount is Rs 400. What was the original price?

  • A Rs 480
  • B Rs 500
  • C Rs 520
  • D Rs 540
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Correct Answer: Option B — Rs 500
Explanation: 0.8P = 400 → P = 500. Finding the original price before discount requires dividing by (1 - discount rate). Adding 20% to 400 gives the wrong answer. This is a common trap in competitive exams. Always divide by the remaining percentage fraction to find the original pre-discount price.
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5
Medium fpsc ppsc nts

What is the sum of interior angles of a hexagon?

  • A 540°
  • B 720°
  • C 900°
  • D 1080°
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Correct Answer: Option B — 720°
Explanation: Sum of interior angles = (n-2)×180°. For hexagon n=6: (6-2)×180° = 4×180° = 720°. This formula applies to all convex polygons. Each interior angle of a regular hexagon = 720°/6 = 120°. Polygon angle formulas are standard geometry topics in competitive exams at all levels.
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6
Medium fpsc ppsc nts

If the radius of a circle is doubled what happens to its area?

  • A Doubles
  • B Triples
  • C Quadruples
  • D Remains same
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Correct Answer: Option C — Quadruples
Explanation: Area = πr². If radius becomes 2r: new area = π(2r)² = 4πr² which is 4 times the original. When linear dimensions scale by factor k areas scale by k² and volumes by k³. This scaling relationship is tested in geometry problems involving similar figures and scale models in competitive exams.
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7
Medium fpsc ppsc nts

A sum doubles itself in 8 years at simple interest. What is the rate?

  • A 10%
  • B 12.5%
  • C 15%
  • D 20%
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Correct Answer: Option B — 12.5%
Explanation: If principal = P then SI = P (since it doubles). SI = P×R×8/100 → P = P×R×8/100 → R = 100/8 = 12.5%. When money doubles at simple interest Rate = 100/Time. This relationship is a frequently tested shortcut in competitive exam problems about doubling or tripling periods.
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8
Medium css fpsc ppsc nts

Find the roots of x² - 5x + 6 = 0

  • A x=1 and x=6
  • B x=2 and x=3
  • C x=3 and x=4
  • D x=2 and x=4
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Correct Answer: Option B — x=2 and x=3
Explanation: Factoring: find two numbers multiplying to 6 and adding to -5 which are -2 and -3. So (x-2)(x-3) = 0 giving x=2 and x=3. Factoring is the fastest method when roots are rational integers. When factoring fails the quadratic formula provides a reliable universal method for finding roots.
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9
Medium fpsc ppsc nts

A clock shows 3:00. What is the angle between the hour and minute hands?

  • A 45°
  • B 60°
  • C 90°
  • D 120°
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Correct Answer: Option C — 90°
Explanation: At 3:00 the minute hand is at 12 (0°) and the hour hand is at 3 (3×30°=90°). Angle = 90°. Each hour mark represents 30° and each minute represents 6°. Clock angle problems are popular in competitive aptitude tests requiring knowledge of how both hands move relative to each other.
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10
Medium fpsc ppsc nts

If 2 to the power x equals 64 what is x?

  • A 5
  • B 6
  • C 7
  • D 8
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Correct Answer: Option B — 6
Explanation: 64 = 2⁶ so x = 6. When bases are equal the exponents must be equal. Recognizing powers of common bases (2 3 5 10) enables quick solutions. Such exponential equations appear in algebra sections of competitive exams requiring rapid mental identification of the correct power.
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11
Medium fpsc ppsc nts

What is 30% of 40% of 500?

  • A 50
  • B 60
  • C 70
  • D 80
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Correct Answer: Option B — 60
Explanation: 40% of 500 = 200. 30% of 200 = 60. Successive percentages require applying one percentage to the result of another. This type appears in successive discount problems population growth and data interpretation. Never add the percentages directly as 70% of 500 gives the wrong answer of 350.
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12
Medium fpsc ppsc nts

The average of 5 consecutive even numbers is 20. What is the largest number?

  • A 22
  • B 24
  • C 26
  • D 28
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Correct Answer: Option B — 24
Explanation: Consecutive even numbers: n n+2 n+4 n+6 n+8. Average = n+4 = 20 so n=16. Largest = 16+8 = 24. Consecutive number problems are common in competitive exams. Setting up the correct algebraic representation and using the average formula is the standard approach for solving such sequence problems efficiently.
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13
Medium fpsc ppsc nts

What is the surface area of a sphere with radius 7 cm using π = 22/7?

  • A 616 cm²
  • B 600 cm²
  • C 588 cm²
  • D 624 cm²
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Correct Answer: Option A — 616 cm²
Explanation: Surface area = 4πr² = 4 × (22/7) × 49 = 4 × 22 × 7 = 616 cm². Sphere formulas for both surface area and volume (4/3)πr³ are standard geometry questions. Understanding which formula to apply and correctly substituting values including the radius is the key challenge in competitive exam geometry problems.
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14
Medium fpsc ppsc nts

Two dice are rolled. What is the probability of getting a sum of 7?

  • A 1/6
  • B 5/36
  • C 6/36
  • D 7/36
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Correct Answer: Option C — 6/36
Explanation: Total outcomes = 36. Pairs giving sum 7: (1+6 2+5 3+4 4+3 5+2 6+1) = 6 pairs. Probability = 6/36 = 1/6. Dice probability requires careful enumeration of favorable outcomes from the total sample space. Such problems test systematic counting skills and are extremely common in competitive exam probability sections.
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15
Medium css fpsc ppsc nts

If sin θ = 3/5 what is cos θ for an acute angle?

  • A 3/4
  • B 4/5
  • C 5/3
  • D 3/5
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Correct Answer: Option B — 4/5
Explanation: Using Pythagorean theorem: opposite=3 hypotenuse=5 so adjacent = √(25-9) = 4. cos θ = 4/5. The 3-4-5 triple is the most used in trigonometry problems. Finding one trigonometric ratio from another using the Pythagorean identity is a standard and frequently tested competitive exam skill.
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16
Medium fpsc ppsc nts

What is 40% of three-quarters of 200?

  • A 45
  • B 50
  • C 55
  • D 60
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Correct Answer: Option D — 60
Explanation: 3/4 of 200 = 150. 40% of 150 = 0.4×150 = 60. Multi-step percentage problems require sequential operations. Always complete the inner fraction first then apply the percentage. These chained calculations appear throughout competitive exams in discount problems population calculations and data interpretation questions.
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17
Medium fpsc ppsc nts

A and B together do a job in 12 days. A alone takes 18 days. How long does B take alone?

  • A 36 days
  • B 30 days
  • C 28 days
  • D 24 days
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Correct Answer: Option A — 36 days
Explanation: B's rate = 1/12 - 1/18 = 3/36 - 2/36 = 1/36. B alone takes 36 days. This work problem requires subtracting individual rates from combined rates. Mastery of work-rate subtraction is essential as such problems appear in almost every competitive exam quantitative aptitude section often in more complex multi-worker forms.
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18
Medium fpsc ppsc nts

What is the sum of arithmetic series: first term 1 last term 100 with 100 terms?

  • A 5050
  • B 4950
  • C 5000
  • D 5100
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Correct Answer: Option A — 5050
Explanation: Sum = n/2 × (first + last) = 100/2 × (1+100) = 50×101 = 5050. This famous result was demonstrated by Gauss. Arithmetic series formulas are fundamental for sequences and series questions and appear in problems involving salary increments equal installments and staircase patterns in competitive exams.
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19
Medium css fpsc ppsc nts

What is the discriminant of x² - 5x + 6 = 0?

  • A 1
  • B 4
  • C 5
  • D 6
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Correct Answer: Option A — 1
Explanation: Discriminant D = b²-4ac = (-5)²-4(1)(6) = 25-24 = 1. Since D > 0 there are two distinct real roots. The discriminant determines nature of roots: D>0 (two real roots) D=0 (one repeated root) D<0 (complex roots). This concept is fundamental in quadratic equations tested across all competitive exam levels.
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20
Medium css fpsc ppsc nts

The slope of a line through points (2 3) and (4 7) is?

  • A 1
  • B 2
  • C 3
  • D 4
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Correct Answer: Option B — 2
Explanation: Slope = (y₂-y₁)/(x₂-x₁) = (7-3)/(4-2) = 4/2 = 2. The slope formula measures the steepness and direction of a line. Positive slope rises left to right. Slope is fundamental in coordinate geometry forming the basis for line equations parallel lines perpendicular lines and linear modeling.
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