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Mathematics MCQs

MCQs on Algebra, Calculus, Statistics and Geometry

50 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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21
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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22
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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23
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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24
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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25
Medium css fpsc ppsc

In how many ways can the letters of MATHS be arranged?

  • A 60
  • B 100
  • C 120
  • D 150
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Correct Answer: Option C — 120
Explanation: MATHS has 5 distinct letters. Arrangements = 5! = 5×4×3×2×1 = 120. When all letters are distinct the answer is simply n!. When letters repeat divide by the factorial of each repeating letter frequency. Permutations of word letters is a classic competitive exam topic appearing in combinatorics and probability sections.
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26
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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27
Medium css fpsc ppsc

Rationalize the denominator: 1 divided by √2

  • A √2/2
  • B √2
  • C 1/2
  • D 2/√2
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Correct Answer: Option A — √2/2
Explanation: Multiply numerator and denominator by √2: (1×√2)/(√2×√2) = √2/2. Rationalizing denominators removes irrational numbers from the denominator which is the conventional simplified form. This technique is a standard algebraic skill for simplifying surds and frequently appears in competitive exam algebra questions.
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28
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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29
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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30
Medium css fpsc ppsc

What is the equation of a line with slope 3 and y-intercept negative 2?

  • A y = 3x + 2
  • B y = -3x + 2
  • C y = 3x - 2
  • D y = -3x - 2
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Correct Answer: Option C — y = 3x - 2
Explanation: Slope-intercept form: y = mx + c where m = slope and c = y-intercept. With m=3 and c=-2 the equation is y = 3x - 2. Coordinate geometry including line equations slopes intercepts distances and midpoints is consistently tested at all competitive exam levels from NTS to CSS.
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31
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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32
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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33
Medium css fpsc ppsc

If log base 2 of x equals 5 what is x?

  • A 10
  • B 25
  • C 32
  • D 64
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Correct Answer: Option C — 32
Explanation: log₂(x) = 5 means x = 2⁵ = 32. Logarithms and exponentials are inverse operations. Converting from logarithmic to exponential form is the key skill. Recognizing powers of common bases enables quick solutions. Such equations appear in algebra sections of competitive exams requiring rapid identification of the correct exponent.
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34
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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35
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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36
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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37
Medium css fpsc ppsc

How many ways can 4 people be arranged in a line?

  • A 16
  • B 24
  • C 32
  • D 48
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Correct Answer: Option B — 24
Explanation: Arrangements of 4 distinct objects in a line = 4! = 4×3×2×1 = 24. Permutations apply when order matters while combinations apply when it does not. This fundamental counting principle appears in probability seating arrangement and scheduling problems throughout competitive exam quantitative aptitude sections.
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38
Medium css fpsc ppsc nts

What is the value of (1/2) raised to the power of negative 2?

  • A 1/4
  • B 1/2
  • C 2
  • D 4
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Correct Answer: Option D — 4
Explanation: (1/2)^(-2) = 2² = 4. A negative exponent means taking the reciprocal: (a/b)^(-n) = (b/a)^n. Negative and fractional exponents frequently appear in competitive exam algebra. Understanding this rule prevents errors and enables simplification of complex exponential expressions in higher-level mathematics questions.
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39
Medium css fpsc ppsc

If P(A)=0.4 and P(B)=0.3 and events are mutually exclusive what is P(A or B)?

  • A 0.12
  • B 0.58
  • C 0.70
  • D 0.82
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Correct Answer: Option C — 0.70
Explanation: For mutually exclusive events P(A or B) = P(A)+P(B) = 0.4+0.3 = 0.7. Mutually exclusive events cannot occur simultaneously. The addition rule for mutually exclusive events simply adds probabilities. For non-mutually exclusive events we must subtract P(A and B) to avoid double counting.
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40
Medium fpsc ppsc nts

A pipe fills a tank in 6 hours another empties it in 8 hours. Both open: how long to fill?

  • A 24 hours
  • B 20 hours
  • C 18 hours
  • D 16 hours
Permalink
Correct Answer: Option A — 24 hours
Explanation: Net fill rate = 1/6 - 1/8 = 4/24 - 3/24 = 1/24 per hour. Time = 24 hours. Pipes and cisterns problems use the same framework as work problems where filling pipes add rates and draining pipes subtract rates. Combining rates correctly is the key skill tested in these extremely common aptitude questions.
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