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Home  >>  CBSE XI  >>  Math  >>  Binomial Theorem

If the third term in the binomial expansion if $(1+x)^m$ is $-\large\frac{1}{8}$$x^2$ then the rational value of m is

$\begin{array}{1 1}(A)\;2\\(B)\;\large\frac{1}{2}\\(C)\;3\\(D)\;4\end{array} $

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1 Answer

$(1+x)^m=1+mx+\large\frac{m(m-1)}{1.2}+.......$
$\therefore \large\frac{m(m-1)}{2}$$x^2=\large\frac{1}{8}$$x^2$
$\Rightarrow 4m(m-1)=-1$
$\Rightarrow 4m^2-4m+1=0$
$\Rightarrow (2m-1)^2=0$
$\Rightarrow m=\large\frac{1}{2}$
Hence (B) is the correct answer.
answered Jun 25, 2014 by sreemathi.v
 

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