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PPSC MCQs

Punjab Public Service Commission — Complete MCQ Bank

86 Questions
Exam Preparation Guide

How to prepare for PPSC

PPSC examinations recruit candidates for Punjab government departments and commonly test general knowledge, current affairs, English and post-related subjects.

Punjab AffairsGeneral KnowledgeCurrent AffairsEnglish
Give special attention to Punjab geography, history and administration alongside the advertised post’s specialist syllabus.
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All Subjects Biology Chemistry Computer Science Current Affairs English Everyday Science General Knowledge Islamic Studies Mathematics Pakistan Studies Physics
1
Mathematics Hard

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

  • A5/14
  • B10/28
  • C10/56
  • D5/28
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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
Mathematics Hard

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

  • A7
  • B8
  • C9
  • D6
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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
Mathematics Hard

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

  • ATwo distinct real roots
  • BOne repeated real root
  • CTwo complex roots
  • DNo 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
Mathematics Hard

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

  • A50%
  • B40%
  • C30%
  • D60%
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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
Mathematics Hard

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

  • A5 liters
  • B8 liters
  • C10 liters
  • D12 liters
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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
Mathematics Hard

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)
  • DBoth 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
Mathematics Medium

What is the expansion of (a-b)²?

  • Aa² + b²
  • Ba² - b²
  • Ca² + 2ab + b²
  • Da² - 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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8
Mathematics Medium

What is the slope of a line perpendicular to y = 2x + 3?

  • A2
  • B-2
  • C1/2
  • 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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9
Mathematics Medium

The sum of an infinite geometric series with first term 1 and ratio 1/2 is?

  • A1
  • B2
  • C3
  • D4
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Correct Answer: Option B — 2
Explanation: Sum = a/(1-r) = 1/(1-0.5) = 1/0.5 = 2. The series 1+1/2+1/4+1/8+... converges to 2. The condition |r|<1 must hold for convergence. Infinite geometric series appear in competitive exam algebra and also model real-world phenomena like bouncing balls and repeating decimal conversions.
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10
Mathematics Medium

If f(x) = x² - 4 what are the zeros of f(x)?

  • Ax = ±1
  • Bx = ±2
  • Cx = ±3
  • Dx = ±4
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Correct Answer: Option B — x = ±2
Explanation: Set f(x) = 0: x²-4 = 0 → x² = 4 → x = ±2. Zeros are x-values where the function crosses the x-axis. For quadratics zeros can be found by factoring completing the square or the quadratic formula. Finding zeros is fundamental for graphing analyzing and applying polynomial functions in competitive mathematics.
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