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

$\begin{array}{1 1} 924 \\ 792 \\ 1594 \\ 942 \end{array} $

1 Answer

Toolbox:
  • sum of the coefficients in the expansion $(x+y)^n$ = $2^n$
  • If $n$ is even, then the greatest coefficient of $^nC_r$ for $r=1,2,.......n$ is $^nC_{\large\frac{n}{2}}$
Given : $2^n=4096$
$\Rightarrow\:n=12$
$\therefore, $ The greatest coefficient is $^{12}C_{\large\frac{12}{2}}$$=^{12}C_6=924$
answered Oct 12, 2013 by rvidyagovindarajan_1
 

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