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NTS MCQs

National Testing Service — Complete MCQ Bank

61 Questions
Exam Preparation Guide

How to prepare for NTS

NTS tests evaluate aptitude, analytical reasoning, quantitative ability, English and subject knowledge for admissions, scholarships and recruitment.

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1
Mathematics Medium

What is the expansion of (a-b)²?

  • Aa² + b²
  • Ba² - b²
  • Ca² + 2ab + b²
  • Da² - 2ab + b²
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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
Mathematics Medium

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

  • A2
  • B-2
  • C1/2
  • 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
Mathematics Medium

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

  • A4n-1
  • B4n+1
  • C3n+1
  • D2n+3
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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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4
Mathematics Medium

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

  • ARs 480
  • BRs 500
  • CRs 520
  • DRs 540
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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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5
Mathematics Medium

What is the sum of interior angles of a hexagon?

  • A540°
  • B720°
  • C900°
  • D1080°
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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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6
Mathematics Medium

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

  • ADoubles
  • BTriples
  • CQuadruples
  • DRemains same
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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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7
Mathematics Medium

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

  • A10%
  • B12.5%
  • C15%
  • D20%
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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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8
Mathematics Medium

Find the roots of x² - 5x + 6 = 0

  • Ax=1 and x=6
  • Bx=2 and x=3
  • Cx=3 and x=4
  • Dx=2 and x=4
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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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9
Mathematics Medium

A clock shows 3:00. What is the angle between the hour and minute hands?

  • A45°
  • B60°
  • C90°
  • D120°
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Correct Answer: Option C — 90°
Explanation: At 3:00 the minute hand is at 12 (0°) and the hour hand is at 3 (3×30°=90°). Angle = 90°. Each hour mark represents 30° and each minute represents 6°. Clock angle problems are popular in competitive aptitude tests requiring knowledge of how both hands move relative to each other.
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10
Mathematics Medium

If 2 to the power x equals 64 what is x?

  • A5
  • B6
  • C7
  • D8
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Correct Answer: Option B — 6
Explanation: 64 = 2⁶ so x = 6. When bases are equal the exponents must be equal. Recognizing powers of common bases (2 3 5 10) enables quick solutions. Such exponential equations appear in algebra sections of competitive exams requiring rapid mental identification of the correct power.
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