Question

The term not containing x in expansion of (1 - x)² (x + 1/x)¹⁰ is

(A) ¹¹C₅

(B)¹⁰C₅

(C) ¹⁰C₄

(D) ¹⁰C₇

Answer 1

(A) ¹¹C₅

Term not containing x = A + B,

Where A = ¹⁰C_r x^10-r(1/x)^r for r such that

10 - r - r = 0, i.e., r = 5

A = ¹⁰C₅

and B = ¹⁰C_r x^10-r(1/x)^r

for r such that 10 - r - r = -2

i.e., r = 6

B = ¹⁰C₆

Required coefficient = A + B = ¹⁰C₅ + ¹⁰C₆

 = ¹⁰C₅ + ¹⁰C₄ = ¹¹C₅