Question

Given positive integers r > 1, n > 2 and the coefficient of (3r)th and (r + 2)th terms in the binomial expansion of (1 + x)²ⁿ are equal. Then-

• A. n = 2r
• B. n = 2r + 1
• C. n = 3r
• D. None of these

Answer 1

Answer: (A)

n = 2r

Answer 2

Here t_3r = ²ⁿC_{3r – 1}(x)^3r–1

and t_r+2 = ²ⁿC_r+1(x)^r+1

Given binomial coefficients of t_3r and t_r+2 are equal

Ž ²ⁿC_3r–1^{= 2n}C_r+1

Or 2n = (3r – 1) + (r + 1)

Ž 2r = 2 or 2n = 4r

Ž r = 1 or n = 2r

But r > 1

\n = 2r.