The term independent of x in the expansion of ( 1 - x ) 2 ( x + 1 x ) 10 is

Question

The term independent of x in the expansion of ( 1 - x ) 2 ( x + 1 x ) 10 is, 10 C 5, 10 C 6, 11 C 5, 17 C 7

MARKS App · Accepted Answer

We have, ( 1 - x ) 2 ( x + 1 x ) 10 = 1 − 2 x + x 2 x 10 + C 10 1 x 9 · 1 x + C 10 2 x 8 × 1 x 2 + ... + 1 x 10 = 1 − 2 x + x 2 x 10 + C 10 1 x 8 + C 10 2 x 6 + ... + 10 C 9 × 1 x 8 + 1 x 10 So, the term independent of x is C 10 5 + − 2 × 0 + C 10 6 = C 10 5 + C 10 6 = 11 C 5

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