NUST NET Maths chapter 7: Maths · Functions and limits MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

11 exam-style questions on Maths · Functions and limits, 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.

11 questions · 1 topics · 10 per test

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What chapter 7 covers

Ten Maths · Functions and limits questions with answers

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

1. 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.

2. limx→0 (3x − 1)/x equals

  1. A
    ln 3
  2. B
    3
  3. C
    1
  4. D
    3 ln 3
Show answer

Answer: A. Standard result: limx→0 (ax − 1)/x = ln a, so the answer is ln 3. The limit equals 1 only when a = e.

3. limx→0 (1 − cos 2x)/x2 equals

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

Answer: C. 1 − cos 2x = 2 sin2 x, so the expression is 2(sin x / x)2 → 2 × 1 = 2. The value 1/2 is the limit of (1 − cos x)/x2, a different expression.

4. If x° means x degrees, then limx→0 (sin x°)/x equals

  1. A
    1
  2. B
    180/π
  3. C
    π/180
  4. D
    0
Show answer

Answer: C. x° = πx/180 radians, so (sin x°)/x = (π/180) × sin(πx/180)/(πx/180) → π/180. The result (sin x)/x → 1 holds only when x is in radians.

5. limx→2 (x3 − 8)/(x − 2) equals

  1. A
    12
  2. B
    4
  3. C
    0
  4. D
    8
Show answer

Answer: A. x3 − 8 = (x − 2)(x2 + 2x + 4), so the limit is 4 + 4 + 4 = 12. Direct substitution gives 0/0, which only tells you to simplify first.

6. limx→0 (√(x + 4) − 2)/x equals

  1. A
    1/4
  2. B
    1/2
  3. C
    4
  4. D
    0
Show answer

Answer: A. Multiply top and bottom by √(x + 4) + 2. The expression becomes 1/(√(x + 4) + 2), which tends to 1/(2 + 2) = 1/4.

7. f(x) = (x2 − 9)/(x − 3) for x ≠ 3, and f(3) = k. f is continuous at x = 3 when k equals

  1. A
    6
  2. B
    0
  3. C
    3
  4. D
    9
Show answer

Answer: A. For x ≠ 3, f(x) = x + 3, so the limit at x = 3 is 6. Continuity needs f(3) to equal this limit, so k = 6.

8. f(x) = (sin 3x)/x for x ≠ 0, and f(0) = k. The value of k that makes f continuous at x = 0 is

  1. A
    1/3
  2. B
    3
  3. C
    1
  4. D
    0
Show answer

Answer: B. (sin 3x)/x = 3 × (sin 3x)/(3x) → 3 as x → 0, so k = 3 makes f(0) equal to the limit.

9. limx→0 (sin 5x)/(2x) equals

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

Answer: B. Write it as (5/2) × (sin 5x)/(5x). Since (sin θ)/θ → 1 as θ → 0, the limit is 5/2. Writing 2/5 turns the ratio upside down.

10. limn→∞ (1 + 2/n)n equals

  1. A
    e
  2. B
    1
  3. C
    2e
  4. D
    e2
Show answer

Answer: D. Put n = 2m: (1 + 1/m)2m = [(1 + 1/m)m]2 → e2. In general (1 + a/n)n → ea. The answer is not 1: a base tending to 1 raised to a power tending to ∞ needs care.

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Ways to practise this chapter

Maths · Functions and limits: questions students ask

How many Maths · Functions and limits MCQs are there?

11, each with the answer and a short explanation, across 1 topics: Limits and continuity. Every chapter test draws ten of them, so you can take it many times.

Is the NUST NET Maths chapter 7 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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