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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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31
Mathematics Medium

Simplify: (a² - b²) divided by (a - b)

  • Aa + b
  • Ba - b
  • Ca² + b²
  • Dab
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Correct Answer: Option A — a + b
Explanation: a² - b² factors as (a+b)(a-b) using the difference of squares identity. Dividing by (a-b) cancels that factor leaving (a+b). Recognizing algebraic identities including difference of squares perfect square trinomials and sum or difference of cubes is essential for quickly simplifying expressions in competitive exam algebra sections.
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32
Mathematics Easy

What is the value of 3 factorial?

  • A3
  • B6
  • C9
  • D12
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Correct Answer: Option B — 6
Explanation: 3! = 3 × 2 × 1 = 6. Factorial of n is the product of all positive integers from 1 to n. Factorials appear in permutations combinations probability and the binomial theorem. Key values to memorize are: 0!=1 1!=1 2!=2 3!=6 4!=24 5!=120 6!=720 for competitive exam speed and accuracy.
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33
Mathematics Easy

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 C — a² + 2ab + b²
Explanation: (a+b)² = a² + 2ab + b². This is one of the most fundamental algebraic identities alongside (a-b)² = a²-2ab+b² and (a+b)(a-b) = a²-b². These three identities are the foundation of algebra and appear constantly in competitive exam questions. Memorizing and recognizing them is essential for quick problem solving.
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34
Mathematics Easy

What is the value of (3² + 4²)?

  • A5
  • B25
  • C7
  • D49
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Correct Answer: Option B — 25
Explanation: 3² = 9 and 4² = 16. Sum = 9 + 16 = 25. Notably √25 = 5 illustrating the 3-4-5 Pythagorean triple where 3² + 4² = 5². Recognizing Pythagorean triples such as 3-4-5 and 5-12-13 saves significant calculation time in competitive exam geometry distance and right triangle problems.
Submitted by: PaperMCQs
35
Mathematics Easy

What is the perimeter of a square with side 9 cm?

  • A27 cm
  • B32 cm
  • C36 cm
  • D40 cm
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Correct Answer: Option C — 36 cm
Explanation: Perimeter of square = 4 × side = 4 × 9 = 36 cm. For a square all four sides are equal so perimeter is simply four times the side length. Knowing the relationship between side length perimeter area and diagonal of a square is a basic geometry requirement for all competitive exam mathematics sections.
Submitted by: PaperMCQs
36
Mathematics Easy

What is the median of data: 3 7 5 9 1?

  • A5
  • B6
  • C7
  • D4
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Correct Answer: Option A — 5
Explanation: Arranging in order: 1 3 5 7 9. The middle value (3rd of 5) is 5. Median divides data into two equal halves and is unaffected by extreme outliers unlike the mean. Mean median and mode are the three measures of central tendency frequently tested in the statistics portion of competitive exam quantitative sections.
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37
Mathematics Easy

What is the probability of getting a head when a fair coin is tossed?

  • A1/4
  • B1/3
  • C1/2
  • D3/4
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Correct Answer: Option C — 1/2
Explanation: A fair coin has two equally likely outcomes: head and tail. Probability = favorable outcomes / total outcomes = 1/2. This foundational concept establishes equally likely outcomes. Classical probability assumes equal likelihood and forms the basis of all probability calculations from simple coin tosses to complex combinatorial problems.
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38
Mathematics Easy

What is the mode of data: 4 7 4 9 7 4 3?

  • A3
  • B4
  • C7
  • D9
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Correct Answer: Option B — 4
Explanation: Mode is the value appearing most frequently. In this set 4 appears three times more than any other making 4 the mode. A data set can be unimodal bimodal or multimodal. Mode is especially useful for categorical data and is one of the three measures of central tendency alongside mean and median.
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39
Mathematics Easy

The volume of a cube with side 5 cm is?

  • A100 cm³
  • B115 cm³
  • C125 cm³
  • D130 cm³
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Correct Answer: Option C — 125 cm³
Explanation: Volume of cube = side³ = 5×5×5 = 125 cm³. Volume formulas for cube cuboid cylinder cone and sphere are standard in competitive exam geometry. These problems often combine volume with surface area calculations or require unit conversions making accurate formula recall a critical competitive exam skill.
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40
Mathematics Easy

What is the area of a triangle with base 10 cm and height 6 cm?

  • A25 cm²
  • B30 cm²
  • C35 cm²
  • D40 cm²
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Correct Answer: Option B — 30 cm²
Explanation: Area of triangle = (1/2) × base × height = (1/2) × 10 × 6 = 30 cm². This formula applies to all triangles when the perpendicular height is known. For triangles where only sides are given Heron's formula is used. Triangle area calculations are fundamental and appear across all competitive exam geometry sections.
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