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PMS MCQs

Provincial Management Service — Complete MCQ Bank

17 Questions
Exam Preparation Guide

How to prepare for PMS

The Provincial Management Service examination tests candidates for administrative roles through general knowledge, language and province-focused compulsory papers.

General KnowledgePakistan StudiesEnglishProvincial Affairs
Focus on your province’s history and administration while maintaining strong preparation in current affairs and compulsory subjects.
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All Subjects Computer Science Current Affairs English General Knowledge Islamic Studies Mathematics Pakistan Studies
11
Mathematics Hard

What does a radian measure?

  • Aπ/2 degrees
  • B57.3 degrees
  • C90 degrees
  • D180 degrees
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Correct Answer: Option B — 57.3 degrees
Explanation: One radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius. 1 radian ≈ 57.3°. There are 2π radians in a full circle. Radian measure simplifies calculus and physics formulas and is essential for differentiation of trigonometric functions.
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12
Mathematics Hard

What is the determinant of the 2x2 matrix with rows [2 3] and [1 4]?

  • A5
  • B8
  • C11
  • D14
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Correct Answer: Option A — 5
Explanation: Det = ad-bc = (2×4)-(3×1) = 8-3 = 5. Determinants are used to solve linear systems find matrix inverses and identify singular matrices. A matrix with zero determinant is singular and uninvertible. Matrix algebra including determinants inverses and systems of equations is tested in CSS PMS and higher competitive exams.
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13
Mathematics Medium

What is the value of i² where i is the imaginary unit?

  • A1
  • B-1
  • Ci
  • D-i
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Correct Answer: Option B — -1
Explanation: The imaginary unit i is defined as √(-1) so i² = -1. Powers of i cycle every four: i¹=i i²=-1 i³=-i i⁴=1. Complex numbers extend the real number system to solve equations like x²+1=0. They appear in higher mathematics physics and engineering topics tested in advanced competitive exams.
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14
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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15
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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16
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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17
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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