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CSS MCQs

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44 Questions
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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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31
Mathematics Medium

Find the roots of xΒ² - 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 β€” 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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32
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 β€” 120
Explanation: MATHS has 5 distinct letters. Arrangements = 5! = 5Γ—4Γ—3Γ—2Γ—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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33
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 β€” √2/2
Explanation: Multiply numerator and denominator by √2: (1Γ—βˆš2)/(√2Γ—βˆš2) = √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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34
Mathematics Medium

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

  • A3/4
  • B4/5
  • C5/3
  • D3/5
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Correct Answer: Option B β€” 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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35
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 β€” 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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36
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 β€” 32
Explanation: logβ‚‚(x) = 5 means x = 2⁡ = 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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37
Mathematics Medium

What is the discriminant of xΒ² - 5x + 6 = 0?

  • A1
  • B4
  • C5
  • D6
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Correct Answer: Option A β€” 1
Explanation: Discriminant D = bΒ²-4ac = (-5)Β²-4(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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38
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 β€” 2
Explanation: Slope = (yβ‚‚-y₁)/(xβ‚‚-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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39
Mathematics Medium

How many ways can 4 people be arranged in a line?

  • A16
  • B24
  • C32
  • D48
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Correct Answer: Option B β€” 24
Explanation: Arrangements of 4 distinct objects in a line = 4! = 4Γ—3Γ—2Γ—1 = 24. Permutations apply when order matters while combinations apply when it does not. This fundamental counting principle appears in probability seating arrangement and scheduling problems throughout competitive exam quantitative aptitude sections.
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40
Mathematics Medium

What is the value of (1/2) raised to the power of negative 2?

  • A1/4
  • B1/2
  • C2
  • D4
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Correct Answer: Option D β€” 4
Explanation: (1/2)^(-2) = 2Β² = 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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