Question

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

• A. ${}^{11}{C}_5$
• B. ${}^{12}{C}_5$
• C. ${}^{12}{C}_6$
• D. ${}^{14}{C}_7$

Answer 1

The correct option is C ${}^{12}{C}_6$

Substituting $x=1$ and $y=1$
we get some of the coefficients as
$1+{}^n{C}_1+{}^n{C}_2+...+{}^n{C}_n$
$=2^n$
It is given that the sum of the coefficients is $4096$
$2^n=4096$
$n=12$
Hence the greatest coefficient will be the coefficient of the middle term
Middle term$=\frac{n}{2}+1$ th term
Hence middle term is the $7$th term
Hence the greatest coefficient is ${}^{12}{C}_6$