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FPSC MCQs

Federal Public Service Commission — Complete MCQ Bank

94 Questions
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How to prepare for FPSC

FPSC recruitment tests assess subject knowledge, general ability and job-related competence for federal government positions across Pakistan.

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Read the official syllabus first, then combine subject-specific revision with timed mixed-question practice.
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41
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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42
Mathematics Medium

What is the surface area of a sphere with radius 7 cm using π = 22/7?

  • A616 cm²
  • B600 cm²
  • C588 cm²
  • D624 cm²
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Correct Answer: Option A — 616 cm²
Explanation: Surface area = 4πr² = 4 × (22/7) × 49 = 4 × 22 × 7 = 616 cm². Sphere formulas for both surface area and volume (4/3)πr³ are standard geometry questions. Understanding which formula to apply and correctly substituting values including the radius is the key challenge in competitive exam geometry problems.
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43
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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44
Mathematics Medium

Two dice are rolled. What is the probability of getting a sum of 7?

  • A1/6
  • B5/36
  • C6/36
  • D7/36
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Correct Answer: Option C — 6/36
Explanation: Total outcomes = 36. Pairs giving sum 7: (1+6 2+5 3+4 4+3 5+2 6+1) = 6 pairs. Probability = 6/36 = 1/6. Dice probability requires careful enumeration of favorable outcomes from the total sample space. Such problems test systematic counting skills and are extremely common in competitive exam probability sections.
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45
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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46
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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47
Mathematics Medium

What is 40% of three-quarters of 200?

  • A45
  • B50
  • C55
  • D60
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Correct Answer: Option D — 60
Explanation: 3/4 of 200 = 150. 40% of 150 = 0.4×150 = 60. Multi-step percentage problems require sequential operations. Always complete the inner fraction first then apply the percentage. These chained calculations appear throughout competitive exams in discount problems population calculations and data interpretation questions.
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48
Mathematics Medium

A and B together do a job in 12 days. A alone takes 18 days. How long does B take alone?

  • A36 days
  • B30 days
  • C28 days
  • D24 days
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Correct Answer: Option A — 36 days
Explanation: B's rate = 1/12 - 1/18 = 3/36 - 2/36 = 1/36. B alone takes 36 days. This work problem requires subtracting individual rates from combined rates. Mastery of work-rate subtraction is essential as such problems appear in almost every competitive exam quantitative aptitude section often in more complex multi-worker forms.
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49
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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50
Mathematics Medium

What is the sum of arithmetic series: first term 1 last term 100 with 100 terms?

  • A5050
  • B4950
  • C5000
  • D5100
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Correct Answer: Option A — 5050
Explanation: Sum = n/2 × (first + last) = 100/2 × (1+100) = 50×101 = 5050. This famous result was demonstrated by Gauss. Arithmetic series formulas are fundamental for sequences and series questions and appear in problems involving salary increments equal installments and staircase patterns in competitive exams.
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