Browse Questions

# If the sum of coefficients in the expansion of $(a+b)^n$ is $4096$ then the greatest coefficient in the expansion is

$\begin{array}{1 1}(A)\;1594\\(B)\;792\\(C)\;924\\(D)\;2924\end{array}$

Sum of coefficients =4096
$\therefore (a+b)^n$ when a,b are each 1=4096
$\Rightarrow (1+1)^n=4096=2^{12}$
$\Rightarrow n=12$
Hence n is even
$\Rightarrow$ Greatest coefficient
$\Rightarrow nC_{n/2}=12C_6$
$\Rightarrow \large\frac{12!}{6!6!}$
$\Rightarrow 924$
Hence (C) is the correct answer.
Why 'a' and 'b' should reach '1' in order to determine 'n'?