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

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Solution

The correct option is D 4
We know that the coefficient of $x^{r}$ in $(1 + x)^{n}$ is $n_{C_{r}}$ . Therefore, Coefficient of $x^{2}$ in $(1 + x)^{m}$ is $m_{C_{2}}$ .
It is given that the coefficient of $x^{2}$ in $(1 + x)^{m}$ is $6$ .
Therefore,
$m_{C_{2}} = 6$
$\frac{m (m - 1)}{2!} = 6$

$m^{2} - m = 12$
$m^{2} - m - 12 = 0$
$(m - 4) (m + 3) = 0$
$m - 4 = 0$
$m = 4$

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