Question

If middle term in the expansion of (2 - x³/3)⁷ is a/27 x⁹ then a = ........

(a) 560 

(b) -560

(c) 280/3

(d) - 280/3

Answer 1

Correct option: (b) -560

Explanation:

n = 7 = odd hence middle term

[(n + 1) / 2] and [(n + 3) / 2] i.e. 4^th and 5^th term.

∴ T_r+1 = ⁿc_r a^n–r b^r 

hence

T₄ = ⁷c₃ a⁴ b³ and T₅ = ⁷c₄ a³ b⁴ 

∴ T₄ = ⁷c₃ (2)⁴ [– (x³ / 3)]³ and T₅ = ⁷c₄ ∙ (2)³ [– (x³ / 3)]⁴ 

given: middle term is (a / 27) x⁹ 

∴ [(25 × 16) / (27)] (– x⁹) = (a / 27) x⁹ ------- equating T₄ 

∴ a = 35 × 16

∴ a = – 560