NUST NET Maths chapter 4: Maths · Sequences, series and the binomial theorem MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

23 exam-style questions on Maths · Sequences, series and the binomial theorem, 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.

23 questions · 2 topics · 10 per test

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What chapter 4 covers

Ten Maths · Sequences, series and the binomial theorem questions with answers

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

1. 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.

2. If 1/((x − 1)2(x + 2)) = A/(x − 1) + B/(x − 1)2 + C/(x + 2), then B is

  1. A
    1/3
  2. B
    −1/9
  3. C
    1/9
  4. D
    3
Show answer

Answer: A. Multiply through by (x − 1)2(x + 2) and put x = 1: 1 = 3B, so B = 1/3. (The other constants are A = −1/9 and C = 1/9.)

3. Using the binomial series, the value of ∛65 correct to 3 decimal places is

  1. A
    4.063
  2. B
    4.005
  3. C
    4.021
  4. D
    4.042
Show answer

Answer: C. ∛65 = 4(1 + 1/64)1/3 ≈ 4(1 + 1/192) = 4 + 1/48 ≈ 4.021. Leaving out the power 1/3 gives 4 + 4/64 ≈ 4.063, and not multiplying the 1/192 by 4 gives 4 + 1/192 ≈ 4.005.

4. The nth term of an arithmetic sequence is Tn = 7 − 3n. Its common difference is

  1. A
    −3
  2. B
    3
  3. C
    4
  4. D
    7
Show answer

Answer: A. d = Tn+1 − Tn = −3. Check: T1 = 4, T2 = 1, T3 = −2; 4 is the first term, not the difference.

5. The harmonic mean between 1/2 and 1/5 is

  1. A
    2/7
  2. B
    7/20
  3. C
    1/√10
  4. D
    7/2
Show answer

Answer: A. H = 2ab/(a + b) = 2(1/10)/(7/10) = 2/7. 7/20 is the arithmetic mean and 1/√10 the geometric mean.

6. The coefficient of x5 in the expansion of (1 − x)8 is

  1. A
    56
  2. B
    −70
  3. C
    −56
  4. D
    28
Show answer

Answer: C. The term is 8C5(−x)5 = −56x5, since 8C5 = 56 and an odd power of −x is negative.

7. The sum of the first n terms of a series is Sn = 3n2 + 2n. Its 10th term is

  1. A
    320
  2. B
    62
  3. C
    59
  4. D
    261
Show answer

Answer: C. T10 = S10 − S9 = 320 − 261 = 59. 320 is the sum of the first ten terms, not the tenth term.

8. An infinite geometric series has sum 4, and the series formed by the squares of its terms has sum 16/3. The first term is

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

Answer: B. a/(1 − r) = 4 and a2/(1 − r2) = 16/3. Dividing the second by the first gives a/(1 + r) = 4/3; with a = 4(1 − r) this gives r = 1/2 and a = 2.

9. Three real geometric means are inserted between 1/3 and 27. Their product is

  1. A
    9
  2. B
    27
  3. C
    81
  4. D
    729
Show answer

Answer: B. 1/3, G1, G2, G3, 27 are in G.P. with r4 = 81, so the means are 1, 3, 9 (or −1, 3, −9). Either way the product is 27; 9 is only the middle mean.

10. The 3rd term of a geometric sequence is 12 and its 6th term is 96. Its first term is

  1. A
    6
  2. B
    1.5
  3. C
    2
  4. D
    3
Show answer

Answer: D. ar5 ÷ ar2 = r3 = 96/12 = 8, so r = 2 and a = 12/r2 = 3. Using ar3 for the 3rd term gives 1.5, and 2 is the common ratio, not the first term.

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Ways to practise this chapter

Maths · Sequences, series and the binomial theorem: questions students ask

How many Maths · Sequences, series and the binomial theorem MCQs are there?

23, each with the answer and a short explanation, across 2 topics: Sequences and series, Binomial theorem and partial fractions. Every chapter test draws ten of them, so you can take it many times.

Is the NUST NET Maths chapter 4 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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