Question

The term independent of $x$ in ${(\frac{3}{2}{x}^2-\frac{1}{3x})}^9$ is

• A. ${{}^{8}C}_3.\frac{1}{3^3{.2}^3}$
• B. ${{}^{9}C}_3.\frac{1}{3^3{.2}^3}$
• C. ${{}^{9}C}_2.\frac{1}{3^3{.2}^3}$
• D. ${{}^{8}C}_2.\frac{1}{3^3{.2}^3}$

Answer 1

The correct option is B ${{}^{9}C}_3.\frac{1}{3^3{.2}^3}$

In the above question
$T_{r+1}=(-1{)}^r{}^9{C}_r{x}^{18-3r}{3}^{9-2r}{2}^{r-9}$
Hence the term independent of x will be
$18-3r=0$
$r=6$
$T_7={}^9{C}_6{3}^{-3}{2}^{-3}$
$={}^9{C}_3{3}^{-3}{2}^{-3}$