Question

If $6^{th}$ terms in the expansion of $(x+\ast {)}^n$ is equal to ${}^n{C}_5{x}^{n-10}$, find $\ast$

Answer 1

$T_6=T_{r+1}$

so, $r=5$

$T_6{=}^n{C}_5\left(x{)}^{n-5}\right(\ast {)}^5$

Since $T_6{=}^n{C}_5{x}^{n-10}$

$\left(x^{n-5}\right)(\ast {)}^5=x^{n-10}$

$⟹(\ast {)}^5=x^{-5}$

$⟹\ast =x^{-1}$