Question

If the sum of the coefficient in the expansion of $(x+y{)}^n$ is $1024$ , then the value of the greatest coefficient in the expansion is

• A. 356
• B. 252
• C. 210
• D. 120

Answer 1

Answer: (B)

Given that the sum of the coefficient in the expansion of $(x+y{)}^n=1024$ i.e.,
$2^n=1024$
$2^n=2^{10}\Rightarrow n=10$
Since, $n$ is even, hence greatest coefficient
$={}^n{C}_{n/2}={}^{10}{C}_5$
$=\frac{10!}{5!\times 5!}=\frac{10\times 9\times 8\times 7\times 6}{5\times 4\times 3\times 2\times 1}=252$