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FPSC MCQs

Federal Public Service Commission — Complete MCQ Bank

1,458 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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1071
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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1072
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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1073
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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1074
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 — 24
Explanation: Arrangements of 4 distinct objects in a line = 4! = 4×3×2×1 = 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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1075
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 — 4
Explanation: (1/2)^(-2) = 2² = 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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1076
Mathematics Medium

If P(A)=0.4 and P(B)=0.3 and events are mutually exclusive what is P(A or B)?

  • A0.12
  • B0.58
  • C0.70
  • D0.82
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Correct Answer: Option C — 0.70
Explanation: For mutually exclusive events P(A or B) = P(A)+P(B) = 0.4+0.3 = 0.7. Mutually exclusive events cannot occur simultaneously. The addition rule for mutually exclusive events simply adds probabilities. For non-mutually exclusive events we must subtract P(A and B) to avoid double counting.
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1077
Mathematics Medium

A pipe fills a tank in 6 hours another empties it in 8 hours. Both open: how long to fill?

  • A24 hours
  • B20 hours
  • C18 hours
  • D16 hours
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Correct Answer: Option A — 24 hours
Explanation: Net fill rate = 1/6 - 1/8 = 4/24 - 3/24 = 1/24 per hour. Time = 24 hours. Pipes and cisterns problems use the same framework as work problems where filling pipes add rates and draining pipes subtract rates. Combining rates correctly is the key skill tested in these extremely common aptitude questions.
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1078
Mathematics Medium

The product of two numbers is 48 and their HCF is 4. What is their LCM?

  • A12
  • B16
  • C24
  • D48
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Correct Answer: Option A — 12
Explanation: LCM × HCF = Product of the two numbers. LCM = 48 ÷ 4 = 12. This important formula is frequently tested in competitive exams. It allows rapid calculation of LCM or HCF when the product and one factor are known making it a key shortcut for number theory problems in timed exam conditions.
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1079
Mathematics Medium

If 5 workers finish a job in 8 days how many days will 10 workers take?

  • A2 days
  • B4 days
  • C6 days
  • D8 days
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Correct Answer: Option B — 4 days
Explanation: Total work = 5×8 = 40 worker-days. With 10 workers: days = 40÷10 = 4 days. Work and time problems rely on the inverse relationship between number of workers and time. They are among the most common question types in competitive exams requiring understanding of work rate as a fundamental concept.
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1080
Mathematics Medium

A man walks 4 km North then 3 km East. How far is he from the start?

  • A5 km
  • B6 km
  • C7 km
  • D8 km
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Correct Answer: Option A — 5 km
Explanation: This forms a right triangle with legs 4 and 3. Distance = √(4²+3²) = √(16+9) = √25 = 5 km. The 3-4-5 Pythagorean triple is the most commonly used in competitive exams. The Pythagorean theorem a²+b²=c² is applied in distance navigation construction and coordinate geometry problems.
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