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# If the sum of the coefficients in the expansion of $(x+y)^n$ is $1024$,then the value of the greatest coefficient in the expansion is

$\begin{array}{1 1}(A)\;356\\(B)\;252\\(C)\;210\\(D)\;120\end{array}$

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## 1 Answer

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Toolbox:
• Sum of the coefficient =$2^n$
• If $n$ is even middle term =$\large\frac{n+2}{2}$
Sum of the coefficient =$2^n$
$\Rightarrow 2^n=1024$
$\Rightarrow 2^{10}=1024$
$2^n=2^{10}$
$n=10$
Middle term =$\large\frac{T_{10+2}}{2}$
$\Rightarrow T_6$
$T_{5+1}=10C_5x^5y^5$
$\qquad=252x^5y^5$
$\therefore$ Greatest coefficient =252
Hence (B) is the correct answer.
answered Jun 26, 2014

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