NUST NET Maths chapter 1: Maths · Numbers, sets and functions MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

21 exam-style questions on Maths · Numbers, sets and functions, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

21 questions · 2 topics · 10 per test

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What chapter 1 covers

Ten Maths · Numbers, sets and functions questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

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 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.

3. f is an odd function defined for all real x, and f(3) = −5. The value of f(−3) + f(0) is

  1. A
    −5
  2. B
    5
  3. C
    0
  4. D
    10
Show answer

Answer: B. For an odd function f(−x) = −f(x), so f(−3) = 5, and f(0) = −f(0) forces f(0) = 0. The total is 5 + 0 = 5.

4. The value of i−35 is

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

Answer: D. i−35 = i−35 × i36 = i, because i36 = (i4)9 = 1. Finding i35 = −i and ignoring the negative power gives the slip −i.

5. The range of f(x) = x2 − 4x + 7, x ∈ ℝ, is

  1. A
    y ≥ 7
  2. B
    y ≥ 3
  3. C
    y ≥ 2
  4. D
    all real y
Show answer

Answer: B. Complete the square: x2 − 4x + 7 = (x − 2)2 + 3 ≥ 3, with minimum 3 at x = 2. 7 is only the value at x = 0, and 2 is where the minimum occurs, not its value.

6. A complex number z satisfies z + z̄ = 6 and z − z̄ = 8i. The value of |z| is

  1. A
    5
  2. B
    10
  3. C
    7
  4. D
    25
Show answer

Answer: A. If z = x + iy, then z + z̄ = 2x = 6 and z − z̄ = 2iy = 8i, so z = 3 + 4i and |z| = √(9 + 16) = 5. Forgetting the factor 2 gives z = 6 + 8i and |z| = 10.

7. U = {1, 2, 3, ..., 10}, A is the set of primes in U and B is the set of odd numbers in U. Then A ∩ B′ is

  1. A
    {3, 5, 7}
  2. B
    {1, 9}
  3. C
    {2}
  4. D
    {1, 2, 9}
Show answer

Answer: C. A = {2, 3, 5, 7} and B′ is the set of even numbers {2, 4, 6, 8, 10}. The only even prime is 2. {3, 5, 7} is A ∩ B and {1, 9} is B − A.

8. The principal argument of −1 + √3 i is

  1. A
    −π/3
  2. B
    π/3
  3. C
    2π/3
  4. D
    −2π/3
Show answer

Answer: C. The point (−1, √3) is in the second quadrant with reference angle tan−1√3 = π/3, so the argument is π − π/3 = 2π/3. Writing tan−1(−√3) = −π/3 directly ignores the quadrant.

9. If f(x) = 3x − 1 and g(x) = x2 + 2, then (f∘g)(1) is

  1. A
    8
  2. B
    6
  3. C
    5
  4. D
    3
Show answer

Answer: A. (f∘g)(1) = f(g(1)) = f(3) = 3(3) − 1 = 8. Working out g(f(1)) = g(2) = 6 uses the wrong order.

10. If f(x) = (2x + 1)/(x − 3), x ≠ 3, then f−1(x) is

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

Answer: C. Put y = (2x + 1)/(x − 3): xy − 3y = 2x + 1, so x(y − 2) = 3y + 1 and x = (3y + 1)/(y − 2). The reciprocal 1/f(x) is not the inverse function.

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Ways to practise this chapter

Maths · Numbers, sets and functions: questions students ask

How many Maths · Numbers, sets and functions MCQs are there?

21, each with the answer and a short explanation, across 2 topics: Complex numbers, Sets and functions. Every chapter test draws ten of them, so you can take it many times.

Is the NUST NET Maths chapter 1 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

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