Question

Co-efficient of x^-3 in expansion of (x - a/x)¹¹ is ......

(a) -792 a⁵ 

(b) -923 a⁷ 

(c) -792 a⁶ 

(d) -330 a⁷

Answer 1

Correct option: (d) -330 a⁷ 

Explanation:

given: [x – (a/x)]¹¹ 

we know,

T_r+1 = ⁿc_r a^n–r b^r 

∴ T_r+1 = ⁿc_r (x)^n–r [– (a/x)]^r 

= ⁿc_r (– a)^r ∙ (x)^n–2r 

= ¹¹c_r (– a)^r ∙ (x)^11–2r 

To find coefficient of x^–3 i.e. 11 – 2r = – 3

∴  r = 7

∴   T_r+1 = ¹¹c₇ (– a)⁷ x^–3 

∴  coefficient of x^–3 is = ¹¹c₇ a⁷ (– 1) = – 330 a⁷