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Home  >>  CBSE XI  >>  Math  >>  Binomial Theorem
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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} $

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1 Answer

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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'?
 

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