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Mathematics MCQs

MCQs on Algebra, Calculus, Statistics and Geometry

9 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
Hard css fpsc ppsc

A bag has 5 red and 3 blue balls. What is the probability of drawing 2 red balls?

  • A 5/14
  • B 10/28
  • C 10/56
  • D 5/28
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Correct Answer: Option A — 5/14
Explanation: P = C(5,2)/C(8,2) = 10/28 = 5/14. C(5,2)=10 favorable outcomes from C(8,2)=28 total. This is a combination-based probability problem. When drawing without replacement order does not matter so combinations are used. Such problems appear in probability sections of CSS FPSC and higher competitive examinations.
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2
Hard css pms fpsc ppsc

What is the value of log base 2 of 32 plus log base 2 of 4?

  • A 7
  • B 8
  • C 9
  • D 6
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Correct Answer: Option A — 7
Explanation: log₂(32) + log₂(4) = 5 + 2 = 7 using the property logb(x)+logb(y)=logb(xy) = log₂(128) = 7. Alternatively compute directly: 2⁵=32 so log₂(32)=5 and 2²=4 so log₂(4)=2. Logarithm addition and the change-of-base formula are frequently tested in competitive exam algebra sections.
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3
Hard css pms fpsc ppsc

Solve: x² + 4x + 4 = 0 and identify the nature of roots

  • A Two distinct real roots
  • B One repeated real root
  • C Two complex roots
  • D No roots
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Correct Answer: Option B — One repeated real root
Explanation: Discriminant = b²-4ac = 16-16 = 0. When D=0 there is exactly one repeated root: x = -b/2a = -4/2 = -2. This is a perfect square trinomial (x+2)² = 0. Recognizing perfect square quadratics allows instant factoring and reveals repeated roots without computing the full quadratic formula.
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4
Hard css pms fpsc ppsc

In a class 60% passed math 70% passed English and 20% failed both. What % passed both?

  • A 50%
  • B 40%
  • C 30%
  • D 60%
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Correct Answer: Option A — 50%
Explanation: Eccentricity of a circle is 0. Eccentricity measures how much a conic deviates from being circular: circle e=0 ellipse 0<e<1 parabola e=1 and hyperbola e>1. Understanding all four conic sections and their properties including eccentricity foci directrix and standard equations is required for CSS PMS and engineering entrance examinations.
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5
Hard css pms fpsc ppsc

A mixture of 40 liters has milk:water ratio 3:1. How much water to add for ratio 3:2?

  • A 5 liters
  • B 8 liters
  • C 10 liters
  • D 12 liters
Permalink
Correct Answer: Option C — 10 liters
Explanation: Milk = 30L water = 10L. New ratio 3:2 means water = (2/3)×30 = 20L. Add 20-10 = 10 liters. Mixture problems require identifying the invariant component (milk) and solving for the new amount of the variable component. Such alligation problems are extremely common in competitive exam quantitative aptitude.
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6
Hard css pms fpsc ppsc

What is the sum of squares formula: a² + b² equals?

  • A (a+b)² - 2ab
  • B (a-b)² + 2ab
  • C (a+b)(a-b)
  • D Both A and B
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Correct Answer: Option D — Both A and B
Explanation: a² + b² = (a+b)² - 2ab = (a-b)² + 2ab. Both identities are correct and equivalent. This means if sum (a+b) and product (ab) are known we can find sum of squares without knowing individual values. Such algebraic manipulation problems are frequently tested in competitive exams to assess algebraic fluency.
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7
Hard css pms fpsc ppsc

What is the number of diagonals in a polygon with n sides?

  • A n(n-1)/2
  • B n(n-3)/2
  • C n(n+1)/2
  • D n²/2
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Correct Answer: Option B — n(n-3)/2
Explanation: Diagonals = n(n-3)/2. A pentagon (n=5) has 5×2/2 = 5 diagonals. This formula comes from selecting 2 vertices from n vertices (C(n 2)) then subtracting n sides. Polygon formulas for diagonals interior angles and exterior angles are standard geometry topics tested in higher competitive exam papers.
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8
Hard css fpsc ppsc

The sum of a geometric series with a=2 r=3 and 4 terms is?

  • A 80
  • B 90
  • C 100
  • D 110
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Correct Answer: Option A — 80
Explanation: Sum = a(rⁿ-1)/(r-1) = 2(3⁴-1)/(3-1) = 2(80)/2 = 80. The finite geometric series formula applies when r≠1. For infinite series with |r|<1 sum = a/(1-r). Geometric series appear in competitive exam sequences and progressions sections and in financial problems involving compound growth scenarios.
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9
Hard css pms fpsc ppsc

How many prime numbers are between 1 and 50?

  • A 14
  • B 15
  • C 16
  • D 17
Permalink
Correct Answer: Option B — 15
Explanation: Primes: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 = 15 primes. The Sieve of Eratosthenes systematically eliminates multiples to identify primes. Counting and identifying primes within a range is a number theory skill tested in competitive exams and is useful for quick factorization and divisibility checks.
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