Question

The sum of the coefficients in the expansion of $(x+y{)}^n$ is 4096. The greatest coefficient in the expansion is

• A. 1024
• B. 924
• C. 824
• D. 724

Answer 1

The correct option is B 924

By hypothesis, $2^n=4096=2^{12}\Rightarrow n=12$
Since n is even, hence greatest coefficient
${}^n{C}_{\frac{n}{2}}{=}^{12}{C}_6=\frac{\mathrm{12.11.10.9.8.7}}{\mathrm{1.2.3.4.5.6}}=924$