Question

The term independent of $x$ in ${(x^9-\frac{1}{x^{}})}^9$ is

• A. $84$
• B. $96$
• C. $112$
• D. $Noneofthese$

Answer 1

The correct option is D $Noneofthese$

${(x^9-\frac{1}{x})}^9$

$T_{2+1}{=}^9{C}_r(x^9{)}^{9-2}{\left(\frac{-1}{x}\right)}^r$

${}^9{C}_r{x}^{81-9r}(-1{)}^r{x}^{-r}$

${}^9{C}_r(-1{)}^r{x}^{81-10r}$

$\therefore$ no term independent of $x$