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MCQ practice · SSC Higher Mathematics Board questions · Chapter 10: Binomial Expansion

Chattogram Board 2023

In the expansion of (1 − x/2)⁶, which is correct?

  1. i. the number of terms = 7
  2. ii. the coefficient of x⁴ = −15/16
  3. iii. the coefficient of x³ = −5/2

Think it through first, then pick an option.

  1. a i and ii
  2. b i and iii
  3. c ii and iii
  4. d i, ii and iii
Answer and explanation

Correct answer: b i and iii

i true: for n = 6 the number of terms is 6 + 1 = 7; ii false: the coefficient of x⁴ is (6 4)(−1/2)⁴ = 15/16, positive because the power is even; iii true: the coefficient of x³ is (6 3)(−1/2)³ = 20 × (−1/8) = −5/2

Why the other options are wrong

  • a i and ii: ii is false: the coefficient of x⁴ is (6 4)(−1/2)⁴ = 15/16, positive because the power is even; so it cannot be included.
  • c ii and iii: i is true: for n = 6 the number of terms is 6 + 1 = 7; so it cannot be left out.
  • d i, ii and iii: ii is false: the coefficient of x⁴ is (6 4)(−1/2)⁴ = 15/16, positive because the power is even; so it cannot be included.