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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} $

1 Answer

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.
answered Jun 26, 2014 by sreemathi.v
Why 'a' and 'b' should reach '1' in order to determine 'n'?
why did you assume that values of a and b are randomly equal to 1?

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