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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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521
Mathematics Medium

What is the geometric mean of 4 and 16?

  • A6
  • B8
  • C10
  • D12
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Correct Answer: Option B — 8
Explanation: Geometric mean = √(a×b) = √(4×16) = √64 = 8. Geometric mean is appropriate for data involving ratios or multiplicative growth unlike arithmetic mean for additive data. The geometric mean always lies between the arithmetic mean (10) and harmonic mean of the same two numbers.
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522
Mathematics Medium

Evaluate the integral of x dx from 0 to 4

  • A8
  • B10
  • C12
  • D16
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Correct Answer: Option A — 8
Explanation: ∫x dx = x²/2. Evaluated from 0 to 4: (4²/2) - (0²/2) = 8 - 0 = 8. Definite integration computes the area under a curve between two limits. The power rule for integration states ∫xⁿdx = xⁿ⁺¹/(n+1). Basic integration is tested in CSS PMS and higher-level competitive exams.
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523
Mathematics Medium

Find the roots of x² - 5x + 6 = 0

  • Ax=1 and x=6
  • Bx=2 and x=3
  • Cx=3 and x=4
  • Dx=2 and x=4
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Correct Answer: Option B — x=2 and x=3
Explanation: Factoring: find two numbers multiplying to 6 and adding to -5 which are -2 and -3. So (x-2)(x-3) = 0 giving x=2 and x=3. Factoring is the fastest method when roots are rational integers. When factoring fails the quadratic formula provides a reliable universal method for finding roots.
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524
Mathematics Medium

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

  • A60
  • B100
  • C120
  • D150
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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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525
Mathematics Medium

Rationalize the denominator: 1 divided by √2

  • A√2/2
  • B√2
  • C1/2
  • D2/√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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526
Mathematics Medium

If sin θ = 3/5 what is cos θ for an acute angle?

  • A3/4
  • B4/5
  • C5/3
  • D3/5
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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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527
Mathematics Medium

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

  • Ay = 3x + 2
  • By = -3x + 2
  • Cy = 3x - 2
  • Dy = -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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528
Mathematics Medium

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

  • A10
  • B25
  • C32
  • D64
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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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529
Mathematics Medium

What is the discriminant of x² - 5x + 6 = 0?

  • A1
  • B4
  • C5
  • D6
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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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530
Mathematics Medium

The slope of a line through points (2 3) and (4 7) is?

  • A1
  • B2
  • C3
  • D4
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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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