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

Find a positive value of m for which the coefficient of $x^2$ in the expansion of $(1+x)^m$ is $6$

$\begin{array}{1 1}(A)\;3\\(B)\;4\\(C)\;5\\(D)\;6\end{array} $

1 Answer

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  • Coefficient of $x^2$ in the expansion of $(1+x)^m$ is $C(m,2)$ .
According to the problem
$C(m,2)=6$
Or $\large\frac{m(m-1)}{2!}$$=6$
$m^2-m=12$
$m^2-m-12=0$
$m^2-4m+3m-12=0$
$m(m-4)+3(m-4)=0$
$(m-4)(m+3)=0$
$m=4$ since $m\neq -3$
Hence (B) is the correct answer.
answered Jun 23, 2014 by sreemathi.v
 
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