Question

The sum of the coefficient 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 $924$

${\left(x+y\right)}^n,Sumofcoefficient=4096$

$Whenx=y=1,ifn=12\Rightarrow {\left(1+1\right)}^{12}=2^{12}=4096$

$\Rightarrow Hence,greatestcoefficient{}^n{C}_{n/2}{=}^{12}{C}_6=\frac{12!}{6!6!}=924$

Hence, this is the answer.