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Find the value of r if the coefficient of $(2r+4)^{th}$ and $(r-2)^{th}$ terms in the expansion of $(1+x)^{18}$ are equal.

$\begin{array}{1 1}(A)\;4\\(B)\;5\\(C)\;6\\(D)\;7\end{array} $

1 Answer

  • General term in the expansion of $(a+b)^n$ are $T_{r+1}=nC_ra^{n-r}b^r$
$\Rightarrow 10C_r (1) ^{18-r}(x)^r$
The coefficient of $(2r+4)^{th}$ term in $(1+x)^{18}=18C_{2r+3}$
The coefficient of $(r-2)^{th}$ term $=18C_{r-3}$
Given :
Coefficient of $(2r+4)^{th}=(r-2)^{th}$ term
Or $2r+3+r-3=18$
Hence (C) is the correct answer.
answered Jun 24, 2014 by sreemathi.v

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