Question

The term independent of $x$ in the expansion of
${(x^2+\frac{1}{x})}^9$ is

• A. 1
• B. -1
• C. 48
• D. 84

Answer 1

The correct option is D 84

$T_{r+1}={}^n{C}_r{a}^{n-r}{b}^r$
Applying to the above question, we get
$T_{r+1}={}^9{C}_r{x}^{18-2r}{x}^{-r}$
$={}^9{C}_r{x}^{18-3r}$ ...(i)
For term independent of $x$
$\Rightarrow 18-3r=0$
$\Rightarrow r=6$
Substituting in (i), we get
$T_7={}^9{C}_6$
$=84$