If the number of terms in the expansion of $${\left( {1 - {2 \over x} + {4 \over {{x^2}}}} \right)^n},\,x \ne 0,$$ is 28, then the sum of the coefficients of all the terms in this expansion, is :
JEE · Math · previous-year question
- A.243
- B.729correct
- C.64
- D.2187
Answer
B. 729
Explanation
Total no of terms in $${\left( {1 - {2 \over x} + {4 \over {{x^2}}}} \right)^n}$$ = $${}^{n + 2}{C_2}$$ = 28 (n+2)(n+1) = 56 $$ \Rightarrow n = 6$$ Sum of coefficient = (1 - 2 + 4)6 = 36 = 729
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