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

Open in App

Solution

$(x + a)^{n} = \sum_{r = 0}^{n}^{n} C_{r} x^{r} a^{n - r}$
$(1 + x)^{m} = 1 +^{m} C_{1} x +^{m} C_{2} x^{2} + . . . . . .$
Here given $^{m} C_{2} = 6 \Rightarrow \frac{m!}{(m - 2)! 2!} = 6$
$\Rightarrow \frac{m (m - 1)}{2} = 6 \Rightarrow m (m - 1) = 12 \Rightarrow m = 4$

Suggest Corrections

Similar questions

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

x^{2}

(1 + x)^{m}

6

x^{2}

(1 + x)^{m}

x^{2}

(1 + x)^{m}

6

m =

x^{2}

{(1 + x)}^{m}

6

Join BYJU'S Learning Program