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Mathematics MCQs

MCQs on Algebra, Calculus, Statistics and Geometry

44 Questions
Subject Preparation Guide

Prepare Mathematics with confidence

Develop speed and accuracy in arithmetic, algebra, geometry, percentages, ratios and other quantitative concepts.

ArithmeticAlgebraGeometryPercentages and Ratios
Helpful for academic exams, aptitude tests, NTS and quantitative competitive papers.
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21
Hard css fpsc ppsc

The sum of a geometric series with a=2 r=3 and 4 terms is?

  • A 80
  • B 90
  • C 100
  • D 110
Permalink
Correct Answer: Option A — 80
Explanation: Sum = a(rⁿ-1)/(r-1) = 2(3⁴-1)/(3-1) = 2(80)/2 = 80. The finite geometric series formula applies when r≠1. For infinite series with |r|<1 sum = a/(1-r). Geometric series appear in competitive exam sequences and progressions sections and in financial problems involving compound growth scenarios.
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22
Hard css pms fpsc ppsc

How many prime numbers are between 1 and 50?

  • A 14
  • B 15
  • C 16
  • D 17
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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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23
Medium css fpsc ppsc

What is the equation of a circle centered at origin with radius r?

  • A x² + y² = r
  • B x² - y² = r²
  • C x² + y² = r²
  • D x + y = r²
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Correct Answer: Option C — x² + y² = r²
Explanation: Standard equation of circle at origin: x²+y² = r². For center (h k): (x-h)²+(y-k)² = r². Circle equations including finding center and radius from general form and tangent line conditions are standard coordinate geometry topics in higher competitive exam papers including CSS and PMS.
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24
Medium css fpsc ppsc

Solve the absolute value equation: |2x - 3| = 7

  • A x=5 or x=-2
  • B x=5 or x=2
  • C x=-5 or x=2
  • D x=4 or x=-2
Permalink
Correct Answer: Option A — x=5 or x=-2
Explanation: Two cases: 2x-3=7 → x=5 or 2x-3=-7 → x=-2. Absolute value equations always yield two cases. This concept appears in both equation and inequality forms in competitive exams. Always solve both cases and verify each solution satisfies the original equation to avoid extraneous solutions.
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25
Medium css fpsc ppsc

What is the value of log(ab) in terms of log a and log b?

  • A log a - log b
  • B log a × log b
  • C log a + log b
  • D log a / log b
Permalink
Correct Answer: Option C — log a + log b
Explanation: log(ab) = log a + log b is the product rule of logarithms. The three fundamental log rules: log(ab)=log a+log b (product) log(a/b)=log a-log b (quotient) log(aⁿ)=n×log a (power). These rules simplify complex logarithmic expressions and are heavily tested in competitive exam algebra.
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26
Medium css fpsc ppsc

If f(x) = 2x² + 3x - 5 what is f(2)?

  • A 9
  • B 10
  • C 11
  • D 13
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Correct Answer: Option A — 9
Explanation: f(2) = 2(4) + 3(2) - 5 = 8 + 6 - 5 = 9. Function evaluation requires substituting the given value and simplifying carefully following order of operations. This skill is fundamental for calculus topics and appears in algebra sections of competitive exams testing polynomial function evaluation.
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27
Medium css fpsc ppsc

What is the value of C(5 2)?

  • A 5
  • B 10
  • C 15
  • D 20
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Correct Answer: Option B — 10
Explanation: f(2) = 2(2²) + 3(2) - 5 = 8 + 6 - 5 = 9. Function evaluation requires substituting the given input value and carefully following order of operations. This skill is essential for polynomial and composite functions and appears in algebra and pre-calculus sections of competitive exams testing structured algebraic manipulation.
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28
Medium css pms fpsc

What is the derivative of x³ with respect to x?

  • A x²
  • B 3x
  • C 3x²
  • D 2x³
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.
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29
Medium css fpsc ppsc

What is the geometric mean of 4 and 16?

  • A 6
  • B 8
  • C 10
  • D 12
Permalink
Correct Answer: Option B — 8
Explanation: Geometric mean = √(a×b) = √(4×16) = √64 = 8. Geometric mean is appropriate for data involving ratios or multiplicative growth unlike arithmetic mean for additive data. The geometric mean always lies between the arithmetic mean (10) and harmonic mean of the same two numbers.
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30
Medium css pms fpsc

Evaluate the integral of x dx from 0 to 4

  • A 8
  • B 10
  • C 12
  • D 16
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.
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31
Medium css fpsc ppsc nts

Find the roots of x² - 5x + 6 = 0

  • A x=1 and x=6
  • B x=2 and x=3
  • C x=3 and x=4
  • D x=2 and x=4
Permalink
Correct Answer: Option B — 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
Medium css fpsc ppsc

In how many ways can the letters of MATHS be arranged?

  • A 60
  • B 100
  • C 120
  • D 150
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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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33
Medium css fpsc ppsc

Rationalize the denominator: 1 divided by √2

  • A √2/2
  • B √2
  • C 1/2
  • D 2/√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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34
Medium css fpsc ppsc nts

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

  • A 3/4
  • B 4/5
  • C 5/3
  • D 3/5
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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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35
Medium css fpsc ppsc

What is the equation of a line with slope 3 and y-intercept negative 2?

  • A y = 3x + 2
  • B y = -3x + 2
  • C y = 3x - 2
  • D y = -3x - 2
Permalink
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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36
Medium css fpsc ppsc

If log base 2 of x equals 5 what is x?

  • A 10
  • B 25
  • C 32
  • D 64
Permalink
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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37
Medium css fpsc ppsc nts

What is the discriminant of x² - 5x + 6 = 0?

  • A 1
  • B 4
  • C 5
  • D 6
Permalink
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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38
Medium css fpsc ppsc nts

The slope of a line through points (2 3) and (4 7) is?

  • A 1
  • B 2
  • C 3
  • D 4
Permalink
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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39
Medium css fpsc ppsc

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

  • A 16
  • B 24
  • C 32
  • D 48
Permalink
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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40
Medium css fpsc ppsc nts

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

  • A 1/4
  • B 1/2
  • C 2
  • D 4
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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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