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Maths Binomial Theorem & Mathematical Induction Properties of Binomial Coefficients Single Correct MCQ

Published on: August 14, 2026

The coefficient of x r (0 ≤ r ≤ (n – 1)) in the expansion of (x + 2) n–1 + (x + 2) n–2 (x + 1) + (x + 2) n–3 (x + 1) 2 + …. + (x + 1) n–1

is equal to -

(2 n+r + 1) n C r

(2 n–r + 1) n C r

(2 n–r –1) n C r

(2 n+r –1) n C r

Text Solution

Verified by Experts

The correct answer is:

We have,

(x + 2) n–1 + (x + 2) n–2 (x + 1) + (x + 2) n–3 (x + 1)

2 + ….. + (x + 1) n–1

= (x + 2) n – 1

= (x + 2) n – (x + 1) n

∴ Coefficient of x r in the given expression

= Coefficient of x r in (x + 2) n – Coefficient of x r in (x + 1) n

= n C r 2 n–r – n C r

= (2 n–r – 1) n C r

Hence is correct answer.

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