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NUST NET Maths MCQs with answers

Practise NUST NET Maths (Engineering) with 219 exam-style MCQs, each with the answer and a short explanation. Every test is marked the moment you finish and shows your score chapter by chapter, so you know what to revise next. It is free and needs no sign-up.

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NUST NET Maths MCQs with answers

Practise NUST NET Maths (Engineering) with 219 exam-style MCQs, each with the answer and a short explanation. Every test is marked the moment you finish and shows your score chapter by chapter, so you know what to revise next. It is free and needs no sign-up.

219 questions · 11 chapters

What each chapter covers 11 chapters

The questions follow the syllabus chapter by chapter. You can test the whole subject or one chapter at a time.

  1. Maths · Numbers, sets and functions 21 questionsComplex numbers, Sets and functions
  2. Maths · Matrices and determinants 14 questionsMatrices and determinants
  3. Maths · Quadratic equations 14 questionsQuadratic equations
  4. Maths · Sequences, series and the binomial theorem 23 questionsSequences and series, Binomial theorem and partial fractions
  5. Maths · Permutations, combinations and probability 16 questionsPermutations and combinations, Probability
  6. Maths · Trigonometry 24 questionsTrigonometric ratios and identities, Trigonometric graphs, triangles and equations
  7. Maths · Functions and limits 11 questionsLimits and continuity
  8. Maths · Differentiation 26 questionsRules of differentiation, Applications of derivatives
  9. Maths · Integration 26 questionsMethods of integration, Definite integrals and areas
  10. Maths · Analytic geometry 30 questionsStraight lines, Circles and conic sections, Linear inequalities and linear programming
  11. Maths · Vectors 14 questionsVectors in space
Sample NUST NET Maths MCQs with answers 12 questions

12 questions from the test, one or two from each chapter. Try each one, then open the answer.

1. A set A has 128 subsets. The number of elements in A is

  1. A
    64
  2. B
    7
  3. C
    8
  4. D
    6
Show answer

Answer: B. A set with n elements has 2n subsets, and 27 = 128, so n = 7. Halving 128 to get 64 confuses subsets with elements.

2. The value of the determinant with rows [1 2 3], [4 5 6] and [2 4 6] is

  1. A
    0
  2. B
    6
  3. C
    −6
  4. D
    12
Show answer

Answer: A. The third row is 2 times the first row. A determinant with two proportional rows is 0, so no expansion is needed.

3. α and β are the roots of 2x2 + 5x − 3 = 0. The equation whose roots are 1/α and 1/β is

  1. A
    3x2 + 5x − 2 = 0
  2. B
    3x2 − 5x − 2 = 0
  3. C
    2x2 − 5x + 3 = 0
  4. D
    3x2 − 5x + 2 = 0
Show answer

Answer: B. Replace x by 1/x and clear fractions: 2 + 5x − 3x2 = 0, i.e. 3x2 − 5x − 2 = 0. Check: the original roots are 1/2 and −3, and (3x + 1)(x − 2) = 0 gives 2 and −1/3.

4. The sum of the coefficients in the expansion of (3x − 2)5 is

  1. A
    −1
  2. B
    243
  3. C
    3125
  4. D
    1
Show answer

Answer: D. Put x = 1: the sum of the coefficients is (3 − 2)5 = 1. Adding 3 and 2 instead gives 55 = 3125.

5. In how many ways can 8 people sit at a round table if two particular people must sit together?

  1. A
    1440
  2. B
    720
  3. C
    10080
  4. D
    5040
Show answer

Answer: A. Treat the pair as one unit: 7 units round a table in (7 − 1)! = 720 ways, and the pair can swap seats in 2 ways, giving 1440. Forgetting the swap gives 720.

6. sin4θ − cos4θ is equal to

  1. A
    cos 2θ
  2. B
    1
  3. C
    −cos 2θ
  4. D
    sin 2θ
Show answer

Answer: C. Factorise: (sin2θ − cos2θ)(sin2θ + cos2θ) = sin2θ − cos2θ = −(cos2θ − sin2θ) = −cos 2θ.

7. f(x) = x/|x| for x ≠ 0, and f(0) = 0. At x = 0, f is

  1. A
    continuous, because f(0) is defined
  2. B
    discontinuous, because f(0) is not defined
  3. C
    continuous, because the limit is 0
  4. D
    discontinuous, because the left and right limits are −1 and 1
Show answer

Answer: D. f(x) = −1 for x < 0 and f(x) = 1 for x > 0, so the limit at 0 does not exist. f(0) = 0 is defined, but that alone does not make f continuous.

8. If y = xx (x > 0), then dy/dx equals

  1. A
    x · xx − 1
  2. B
    xx ln x
  3. C
    xx(1 + ln x)
  4. D
    xx(1 − ln x)
Show answer

Answer: C. Take logs: ln y = x ln x, so (1/y) dy/dx = ln x + 1 and dy/dx = xx(1 + ln x). The power rule and the ax rule each give only part of this.

9. ∫ dx/(2x + 1) equals

  1. A
    (1/2) ln|2x + 1| + c
  2. B
    ln|2x + 1| + c
  3. C
    2 ln|2x + 1| + c
  4. D
    −2/(2x + 1)2 + c
Show answer

Answer: A. d/dx ln|2x + 1| = 2/(2x + 1), so divide by 2: the integral is (1/2) ln|2x + 1| + c.

10. The distance between the points (−1, 2) and (5, −6) is

  1. A
    10
  2. B
    14
  3. C
    4√2
  4. D
    100
Show answer

Answer: A. √[(5 + 1)2 + (−6 − 2)2] = √(36 + 64) = √100 = 10. Adding the coordinates instead of subtracting them gives 4√2.

11. A vector makes an angle of 60° with the x-axis and 60° with the y-axis. The acute angle it makes with the z-axis is

  1. A
    60°
  2. B
    30°
  3. C
    90°
  4. D
    45°
Show answer

Answer: D. cos2 α + cos2 β + cos2 γ = 1 gives 1/4 + 1/4 + cos2 γ = 1, so cos γ = 1/√2 and γ = 45°.

12. The conjugate of (2 − i)2 is

  1. A
    3 − 4i
  2. B
    3 + 4i
  3. C
    5 + 4i
  4. D
    −3 + 4i
Show answer

Answer: B. (2 − i)2 = 4 − 4i + i2 = 3 − 4i, and the conjugate changes only the sign of the imaginary part: 3 + 4i. The option 3 − 4i is the square itself, not its conjugate.

Try 207 more questions

Ways to practise 5 ways

When you get a question wrong, a short note called "The idea behind this" explains the topic it belongs to, with the rules to remember and a worked example.

Common questions

Is this NUST NET Maths test free?

Yes. Every test and every explanation is free, and you do not need an account. If you sign in, your results are kept across your devices.

Are these past paper questions?

The 219 MCQs are our own, written to the syllabus in the style of the exam.

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Instantly. You get your score, the right answer and an explanation for every question, and a list of the topics to work on.

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