Question

The term independent of x in the expansion of $(1+x+2x^4)(\frac{3}{2}{x}^2-\frac{1}{3x}{)}^9$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$T_{r+1}$ in the expansion of $(\frac{3}{2}{x}^2-\frac{1}{3x}{)}^9$
${}^9{C}_r\left(\frac{3}{2}{)}^{9-r}\right)x^{18-2r}(-1{)}^r.\frac{1}{3^r}{x}^{-r}$
${}^9{C}_r(-1{)}^r(\frac{3}{2}{)}^{9-r}\left)\right(-1).\frac{1}{3^r}{x}^{18-3r}$
Term indepent of x in $(1+x+2x^4).(\frac{3}{2}{x}^2-\frac{1}{3x}{)}^9$
=(coeff. of $x^0$+ coeff. of $x^{-1}$+2. coeff. of $x^{-4}$ in the expansion of $\frac{3}{2}{x}^2-\frac{1}{3x}{)}^9$
For coeff. of $x^0,18-3r=0\Rightarrow r=6$.