Question

If the coefficent of $x^2$ in the expansion of $(1+x{)}^m$ is $6$ then $m=..........$

• A. $4$
• B. $-4$
• C. $0$
• D. $none$

Answer 1

The correct option is A $4$

the coefficient of $x^r$ in $(1+x{)}^n$ is ${}^n{C}_r$

$⟹$ the coefficient of $x^2$ in $(1+x{)}^m$ is ${}^m{C}_2=6⟹\frac{m(m-1)}{2}=6⟹m^2-m-12=0$

$⟹m=4,-3$

$\because m$ is a positive number ,so $m=4$