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

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Solution

The correct option is B 4
We know that the coefficient of $x^{r}$ in $(1 + x)^{n}$ is $n_{C_{r}}$ .

Therefore, the 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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