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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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21
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
Permalink
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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22
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
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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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23
Medium fpsc ppsc nts

The product of two numbers is 48 and their HCF is 4. What is their LCM?

  • A 12
  • B 16
  • C 24
  • D 48
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Correct Answer: Option A — 12
Explanation: LCM × HCF = Product of the two numbers. LCM = 48 ÷ 4 = 12. This important formula is frequently tested in competitive exams. It allows rapid calculation of LCM or HCF when the product and one factor are known making it a key shortcut for number theory problems in timed exam conditions.
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24
Medium fpsc ppsc nts

If 5 workers finish a job in 8 days how many days will 10 workers take?

  • A 2 days
  • B 4 days
  • C 6 days
  • D 8 days
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Correct Answer: Option B — 4 days
Explanation: Total work = 5×8 = 40 worker-days. With 10 workers: days = 40÷10 = 4 days. Work and time problems rely on the inverse relationship between number of workers and time. They are among the most common question types in competitive exams requiring understanding of work rate as a fundamental concept.
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25
Medium fpsc ppsc nts

A man walks 4 km North then 3 km East. How far is he from the start?

  • A 5 km
  • B 6 km
  • C 7 km
  • D 8 km
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Correct Answer: Option A — 5 km
Explanation: This forms a right triangle with legs 4 and 3. Distance = √(4²+3²) = √(16+9) = √25 = 5 km. The 3-4-5 Pythagorean triple is the most commonly used in competitive exams. The Pythagorean theorem a²+b²=c² is applied in distance navigation construction and coordinate geometry problems.
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26
Medium fpsc ppsc nts

In a right triangle if one angle is 30° what is the other acute angle?

  • A 45°
  • B 50°
  • C 60°
  • D 70°
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Correct Answer: Option C — 60°
Explanation: Sum of angles = 180°. With 90° and 30° the third angle = 180°-90°-30° = 60°. The 30-60-90 triangle has side ratios 1:√3:2 and is one of the most important special triangles in mathematics. It appears extensively in trigonometry geometry and physics problems in all levels of competitive examinations.
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27
Medium fpsc ppsc nts

If 3x - 7 = 2x + 5 what is x?

  • A 10
  • B 12
  • C 14
  • D 16
Permalink
Correct Answer: Option B — 12
Explanation: Subtract 2x: x - 7 = 5. Add 7: x = 12. Solving linear equations with variables on both sides is a core algebraic skill. Such equations frequently appear in word problems about ages work rates and number relationships in competitive exams. The key step is collecting like terms on each side methodically.
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28
Medium fpsc ppsc nts

What is the compound interest on Rs 1000 for 2 years at 10% per annum?

  • A Rs 200
  • B Rs 210
  • C Rs 220
  • D Rs 100
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Correct Answer: Option B — Rs 210
Explanation: CI = P(1+r/100)ⁿ - P = 1000(1.1)² - 1000 = 1210 - 1000 = Rs 210. Compound interest exceeds simple interest because interest is earned on previously accumulated interest. CI problems appear in banking and finance sections of competitive exams and require correct application of the compound interest formula.
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29
Medium fpsc ppsc nts

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

  • A 20
  • B 25
  • C 30
  • D 35
Permalink
Correct Answer: Option B — 25
Explanation: Let numbers be 5x and 3x. Sum = 8x = 40 so x = 5. Larger = 5×5 = 25. Ratio problems requiring algebraic substitution are consistent in competitive exams. Using a common multiplier x to represent ratio parts then solving with the given total sum or difference is the most reliable standard method.
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30
Medium fpsc ppsc nts

If the simple interest on Rs 1000 for 2 years is Rs 100 what is the rate?

  • A 4%
  • B 5%
  • C 6%
  • D 8%
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Correct Answer: Option B — 5%
Explanation: SI = (P×R×T)/100 → 100 = (1000×R×2)/100 → 100 = 20R → R = 5%. Simple interest problems are standard in competitive exams. The ability to rearrange the SI formula to find principal rate or time is a key skill. Always identify which variable is unknown and rearrange accordingly before substituting values.
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31
Medium css fpsc ppsc nts

Simplify: (a² - b²) divided by (a - b)

  • A a + b
  • B a - b
  • C a² + b²
  • D ab
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Correct Answer: Option A — a + b
Explanation: a² - b² factors as (a+b)(a-b) using the difference of squares identity. Dividing by (a-b) cancels that factor leaving (a+b). Recognizing algebraic identities including difference of squares perfect square trinomials and sum or difference of cubes is essential for quickly simplifying expressions in competitive exam algebra sections.
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32
Easy fpsc ppsc nts

What is the value of 3 factorial?

  • A 3
  • B 6
  • C 9
  • D 12
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Correct Answer: Option B — 6
Explanation: 3! = 3 × 2 × 1 = 6. Factorial of n is the product of all positive integers from 1 to n. Factorials appear in permutations combinations probability and the binomial theorem. Key values to memorize are: 0!=1 1!=1 2!=2 3!=6 4!=24 5!=120 6!=720 for competitive exam speed and accuracy.
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33
Easy 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 C — a² + 2ab + b²
Explanation: (a+b)² = a² + 2ab + b². This is one of the most fundamental algebraic identities alongside (a-b)² = a²-2ab+b² and (a+b)(a-b) = a²-b². These three identities are the foundation of algebra and appear constantly in competitive exam questions. Memorizing and recognizing them is essential for quick problem solving.
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34
Easy fpsc ppsc nts

What is the value of (3² + 4²)?

  • A 5
  • B 25
  • C 7
  • D 49
Permalink
Correct Answer: Option B — 25
Explanation: 3² = 9 and 4² = 16. Sum = 9 + 16 = 25. Notably √25 = 5 illustrating the 3-4-5 Pythagorean triple where 3² + 4² = 5². Recognizing Pythagorean triples such as 3-4-5 and 5-12-13 saves significant calculation time in competitive exam geometry distance and right triangle problems.
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35
Easy fpsc ppsc nts

What is the perimeter of a square with side 9 cm?

  • A 27 cm
  • B 32 cm
  • C 36 cm
  • D 40 cm
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Correct Answer: Option C — 36 cm
Explanation: Perimeter of square = 4 × side = 4 × 9 = 36 cm. For a square all four sides are equal so perimeter is simply four times the side length. Knowing the relationship between side length perimeter area and diagonal of a square is a basic geometry requirement for all competitive exam mathematics sections.
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36
Easy fpsc ppsc nts

What is the median of data: 3 7 5 9 1?

  • A 5
  • B 6
  • C 7
  • D 4
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Correct Answer: Option A — 5
Explanation: Arranging in order: 1 3 5 7 9. The middle value (3rd of 5) is 5. Median divides data into two equal halves and is unaffected by extreme outliers unlike the mean. Mean median and mode are the three measures of central tendency frequently tested in the statistics portion of competitive exam quantitative sections.
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37
Easy fpsc ppsc nts

What is the probability of getting a head when a fair coin is tossed?

  • A 1/4
  • B 1/3
  • C 1/2
  • D 3/4
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Correct Answer: Option C — 1/2
Explanation: A fair coin has two equally likely outcomes: head and tail. Probability = favorable outcomes / total outcomes = 1/2. This foundational concept establishes equally likely outcomes. Classical probability assumes equal likelihood and forms the basis of all probability calculations from simple coin tosses to complex combinatorial problems.
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38
Easy fpsc ppsc nts

What is the mode of data: 4 7 4 9 7 4 3?

  • A 3
  • B 4
  • C 7
  • D 9
Permalink
Correct Answer: Option B — 4
Explanation: Mode is the value appearing most frequently. In this set 4 appears three times more than any other making 4 the mode. A data set can be unimodal bimodal or multimodal. Mode is especially useful for categorical data and is one of the three measures of central tendency alongside mean and median.
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39
Easy fpsc ppsc nts

The volume of a cube with side 5 cm is?

  • A 100 cm³
  • B 115 cm³
  • C 125 cm³
  • D 130 cm³
Permalink
Correct Answer: Option C — 125 cm³
Explanation: Volume of cube = side³ = 5×5×5 = 125 cm³. Volume formulas for cube cuboid cylinder cone and sphere are standard in competitive exam geometry. These problems often combine volume with surface area calculations or require unit conversions making accurate formula recall a critical competitive exam skill.
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40
Easy fpsc ppsc nts

What is the area of a triangle with base 10 cm and height 6 cm?

  • A 25 cm²
  • B 30 cm²
  • C 35 cm²
  • D 40 cm²
Permalink
Correct Answer: Option B — 30 cm²
Explanation: Area of triangle = (1/2) × base × height = (1/2) × 10 × 6 = 30 cm². This formula applies to all triangles when the perpendicular height is known. For triangles where only sides are given Heron's formula is used. Triangle area calculations are fundamental and appear across all competitive exam geometry sections.
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