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If the number of terms in the expansion ...

If the number of terms in the expansion of `(1-2/x+4/(x^2))^n , x!=0,` is 28, then the sum of the coefficients of all the terms in this expansion, is : (1) 64 (2) 2187 (3) 243 (4) 729

A

2187

B

243

C

729

D

64

Text Solution

Verified by Experts

The correct Answer is:
C
Theroectically the number of terms are `2n+1`(i.e, odd)
But given that number of term is `28`.
So considering number of term `= .^(n+2)C_(2) = 28`. (Here we are ignoring clubbing of terms)
`:. N = 6`
`:.` Sum of coefficient `= 3^(n) = 3^(6) = 729` (Putting `x = 1`)
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