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Mathematics MCQs

MCQs on Algebra, Calculus, Statistics and Geometry

50 Questions
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Prepare Mathematics with confidence

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

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Filter: All Exams css pms fpsc ppsc nts | All Easy Medium Hard
1
Medium css fpsc ppsc nts

What is the expansion of (a-b)²?

  • A a² + b²
  • B a² - b²
  • C a² + 2ab + b²
  • D a² - 2ab + b²
Permalink
Correct Answer: Option D — a² - 2ab + b²
Explanation: (a-b)² = a² - 2ab + b². Along with (a+b)² = a²+2ab+b² and (a+b)(a-b) = a²-b² these form the three core algebraic identities. Recognizing which identity applies enables rapid expansion and factoring of algebraic expressions in competitive exam algebra sections saving significant time.
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2
Medium css fpsc ppsc nts

What is the slope of a line perpendicular to y = 2x + 3?

  • A 2
  • B -2
  • C 1/2
  • D -1/2
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Correct Answer: Option D — -1/2
Explanation: Slope of y=2x+3 is 2. Perpendicular slope = negative reciprocal = -1/2. Two lines are perpendicular when product of slopes = -1: 2×(-1/2)=-1. This condition is used in problems involving altitudes normals to curves and orthogonal intersections in coordinate geometry questions.
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3
Medium css fpsc ppsc

The sum of an infinite geometric series with first term 1 and ratio 1/2 is?

  • A 1
  • B 2
  • C 3
  • D 4
Permalink
Correct Answer: Option B — 2
Explanation: Sum = a/(1-r) = 1/(1-0.5) = 1/0.5 = 2. The series 1+1/2+1/4+1/8+... converges to 2. The condition |r|<1 must hold for convergence. Infinite geometric series appear in competitive exam algebra and also model real-world phenomena like bouncing balls and repeating decimal conversions.
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4
Medium css fpsc ppsc

If f(x) = x² - 4 what are the zeros of f(x)?

  • A x = ±1
  • B x = ±2
  • C x = ±3
  • D x = ±4
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Correct Answer: Option B — x = ±2
Explanation: Set f(x) = 0: x²-4 = 0 → x² = 4 → x = ±2. Zeros are x-values where the function crosses the x-axis. For quadratics zeros can be found by factoring completing the square or the quadratic formula. Finding zeros is fundamental for graphing analyzing and applying polynomial functions in competitive mathematics.
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5
Medium css pms fpsc

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

  • A 1
  • B -1
  • C i
  • 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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6
Medium css fpsc ppsc

If variance of a data set is 25 what is the standard deviation?

  • A 5
  • B 10
  • C 15
  • D 25
Permalink
Correct Answer: Option A — 5
Explanation: Standard deviation = √variance = √25 = 5. Variance is the average of squared deviations from the mean. Standard deviation being the square root is expressed in the same units as the original data making it more interpretable. Both quantify data spread and appear in statistics-based competitive exam questions.
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7
Medium fpsc ppsc nts

What is the nth term of arithmetic sequence 3 7 11 15?

  • A 4n-1
  • B 4n+1
  • C 3n+1
  • D 2n+3
Permalink
Correct Answer: Option A — 4n-1
Explanation: First term a=3 common difference d=4. nth term = a+(n-1)d = 3+4(n-1) = 4n-1. Verification: n=1→3 n=2→7 n=3→11 confirms correctness. Finding nth term formulas for arithmetic sequences is essential for sequences and series questions in competitive exams and is also used in salary progression and installment problems.
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8
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
Permalink
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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9
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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10
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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11
Medium css fpsc ppsc

If f(x) = 2x² + 3x - 5 what is f(2)?

  • A 9
  • B 10
  • C 11
  • D 13
Permalink
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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12
Medium css fpsc ppsc

What is the value of C(5 2)?

  • A 5
  • B 10
  • C 15
  • D 20
Permalink
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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13
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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14
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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15
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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16
Medium fpsc ppsc nts

The price after 20% discount is Rs 400. What was the original price?

  • A Rs 480
  • B Rs 500
  • C Rs 520
  • D Rs 540
Permalink
Correct Answer: Option B — Rs 500
Explanation: 0.8P = 400 → P = 500. Finding the original price before discount requires dividing by (1 - discount rate). Adding 20% to 400 gives the wrong answer. This is a common trap in competitive exams. Always divide by the remaining percentage fraction to find the original pre-discount price.
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17
Medium fpsc ppsc nts

What is the sum of interior angles of a hexagon?

  • A 540°
  • B 720°
  • C 900°
  • D 1080°
Permalink
Correct Answer: Option B — 720°
Explanation: Sum of interior angles = (n-2)×180°. For hexagon n=6: (6-2)×180° = 4×180° = 720°. This formula applies to all convex polygons. Each interior angle of a regular hexagon = 720°/6 = 120°. Polygon angle formulas are standard geometry topics in competitive exams at all levels.
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18
Medium fpsc ppsc nts

If the radius of a circle is doubled what happens to its area?

  • A Doubles
  • B Triples
  • C Quadruples
  • D Remains same
Permalink
Correct Answer: Option C — Quadruples
Explanation: Area = πr². If radius becomes 2r: new area = π(2r)² = 4πr² which is 4 times the original. When linear dimensions scale by factor k areas scale by k² and volumes by k³. This scaling relationship is tested in geometry problems involving similar figures and scale models in competitive exams.
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19
Medium fpsc ppsc nts

A sum doubles itself in 8 years at simple interest. What is the rate?

  • A 10%
  • B 12.5%
  • C 15%
  • D 20%
Permalink
Correct Answer: Option B — 12.5%
Explanation: If principal = P then SI = P (since it doubles). SI = P×R×8/100 → P = P×R×8/100 → R = 100/8 = 12.5%. When money doubles at simple interest Rate = 100/Time. This relationship is a frequently tested shortcut in competitive exam problems about doubling or tripling periods.
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20
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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