Join WhatsApp ChannelDaily MCQs & Exam Updates

PMS MCQs

Provincial Management Service — Complete MCQ Bank

271 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.
Start PracticingTake a Mock Test
PMS preparation illustration
All Subjects Computer Science Current Affairs English General Knowledge Islamic Studies Mathematics Pakistan Studies
111
Mathematics Hard

What is the sum of squares formula: a² + b² equals?

  • A(a+b)² - 2ab
  • B(a-b)² + 2ab
  • C(a+b)(a-b)
  • DBoth A and B
Permalink
Correct Answer: Option D — Both A and B
Explanation: a² + b² = (a+b)² - 2ab = (a-b)² + 2ab. Both identities are correct and equivalent. This means if sum (a+b) and product (ab) are known we can find sum of squares without knowing individual values. Such algebraic manipulation problems are frequently tested in competitive exams to assess algebraic fluency.
Submitted by: PaperMCQs
112
Mathematics Hard

What does a radian measure?

  • Aπ/2 degrees
  • B57.3 degrees
  • C90 degrees
  • D180 degrees
Permalink
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.
Submitted by: PaperMCQs
113
Mathematics Hard

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

  • A5
  • B8
  • C11
  • D14
Permalink
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.
Submitted by: PaperMCQs
114
Mathematics Medium

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

  • A1
  • B-1
  • Ci
  • D-i
Permalink
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.
Submitted by: PaperMCQs
115
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
Permalink
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.
Submitted by: PaperMCQs
116
Mathematics Hard

How many prime numbers are between 1 and 50?

  • A14
  • B15
  • C16
  • D17
Permalink
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.
Submitted by: PaperMCQs
117
Mathematics Medium

What is the derivative of x³ with respect to x?

  • Ax²
  • B3x
  • C3x²
  • D2x³
Permalink
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.
Submitted by: PaperMCQs
118
Mathematics Medium

Evaluate the integral of x dx from 0 to 4

  • A8
  • B10
  • C12
  • D16
Permalink
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.
Submitted by: PaperMCQs
119
English Hard

Choose the correct sentence using the correct form of 'lie' or 'lay'.

  • AShe lay down on the bed and slept.
  • BShe laid down on the bed and slept.
  • CShe lain down on the bed and slept.
  • DShe lying down on the bed and slept.
Permalink
Correct Answer: Option A — She lay down on the bed and slept.
Explanation: 'Lie' (meaning to recline) has the past tense form 'lay', making 'She lay down on the bed' the grammatically correct usage, distinct from 'lay' meaning to place something.
Submitted by: PaperMCQs
120
English Hard

Choose the correct sentence: 'By the time we arrived, the movie ___.'

  • Ahad already started
  • Bhas already started
  • Calready started
  • Dstarts already
Permalink
Correct Answer: Option A — had already started
Explanation: The past perfect tense 'had already started' correctly indicates an action that was completed before another past action, 'arrived', making option A correct.
Submitted by: PaperMCQs
Other Exams
CSS MCQs PMS MCQs FPSC MCQs PPSC MCQs NTS MCQs
Mock Tests
Quick Test (20 Q) Full Mock (60 Q)