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CSS MCQs

Civil Superior Services — Complete MCQ Bank

899 Questions
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How to prepare for CSS

CSS is Pakistan’s premier federal competitive examination. Strong preparation requires conceptual clarity, broad general knowledge and consistent practice across compulsory and optional areas.

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511
Mathematics Hard

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

  • An(n-1)/2
  • Bn(n-3)/2
  • Cn(n+1)/2
  • Dn²/2
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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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512
Mathematics Medium

If variance of a data set is 25 what is the standard deviation?

  • A5
  • B10
  • C15
  • D25
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Correct Answer: Option A — 5
Explanation: Standard deviation = √variance = √25 = 5. Variance is the average of squared deviations from the mean. Standard deviation being the square root is expressed in the same units as the original data making it more interpretable. Both quantify data spread and appear in statistics-based competitive exam questions.
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513
Mathematics Hard

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

  • A80
  • B90
  • C100
  • D110
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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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514
Mathematics Hard

How many prime numbers are between 1 and 50?

  • A14
  • B15
  • C16
  • D17
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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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515
Mathematics Medium

What is the equation of a circle centered at origin with radius r?

  • Ax² + y² = r
  • Bx² - y² = r²
  • Cx² + y² = r²
  • Dx + y = r²
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Correct Answer: Option C — x² + y² = r²
Explanation: Standard equation of circle at origin: x²+y² = r². For center (h k): (x-h)²+(y-k)² = r². Circle equations including finding center and radius from general form and tangent line conditions are standard coordinate geometry topics in higher competitive exam papers including CSS and PMS.
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516
Mathematics Medium

Solve the absolute value equation: |2x - 3| = 7

  • Ax=5 or x=-2
  • Bx=5 or x=2
  • Cx=-5 or x=2
  • Dx=4 or x=-2
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Correct Answer: Option A — x=5 or x=-2
Explanation: Two cases: 2x-3=7 → x=5 or 2x-3=-7 → x=-2. Absolute value equations always yield two cases. This concept appears in both equation and inequality forms in competitive exams. Always solve both cases and verify each solution satisfies the original equation to avoid extraneous solutions.
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517
Mathematics Medium

What is the value of log(ab) in terms of log a and log b?

  • Alog a - log b
  • Blog a × log b
  • Clog a + log b
  • Dlog a / log b
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Correct Answer: Option C — log a + log b
Explanation: log(ab) = log a + log b is the product rule of logarithms. The three fundamental log rules: log(ab)=log a+log b (product) log(a/b)=log a-log b (quotient) log(aⁿ)=n×log a (power). These rules simplify complex logarithmic expressions and are heavily tested in competitive exam algebra.
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518
Mathematics Medium

If f(x) = 2x² + 3x - 5 what is f(2)?

  • A9
  • B10
  • C11
  • D13
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Correct Answer: Option A — 9
Explanation: f(2) = 2(4) + 3(2) - 5 = 8 + 6 - 5 = 9. Function evaluation requires substituting the given value and simplifying carefully following order of operations. This skill is fundamental for calculus topics and appears in algebra sections of competitive exams testing polynomial function evaluation.
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519
Mathematics Medium

What is the value of C(5 2)?

  • A5
  • B10
  • C15
  • D20
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Correct Answer: Option B — 10
Explanation: f(2) = 2(2²) + 3(2) - 5 = 8 + 6 - 5 = 9. Function evaluation requires substituting the given input value and carefully following order of operations. This skill is essential for polynomial and composite functions and appears in algebra and pre-calculus sections of competitive exams testing structured algebraic manipulation.
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520
Mathematics Medium

What is the derivative of x³ with respect to x?

  • Ax²
  • B3x
  • C3x²
  • D2x³
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Correct Answer: Option C — 3x²
Explanation: Derivative of xⁿ = nxⁿ⁻¹ (power rule). For x³: derivative = 3x². Differentiation measures the instantaneous rate of change of a function. The power rule is the most fundamental differentiation rule forming the starting point for all calculus problems in CSS PMS and higher competitive examinations.
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