The absolute term (that is, term independent of x) in the expansion of 32x2−13x9is:

A
$\frac{1}{9}$
B
$\frac{2}{17}$
C
$\frac{7}{18}$
D
$\frac{11}{18}$

Solution:

$\begin{aligned} T_{r + 1} =^{9} C_{r} {(\frac{3}{2} x^{2})}^{9 - r} {(- \frac{1}{3 x})}^{r} \\ =^{9} C_{r} {(\frac{3}{2})}^{9 - r} {(- \frac{1}{3})}^{r} x^{18 - 3 r} \end{aligned}$
For term independent of $x$ , we set $18 - 3 r = 0$ or $r = 6 .$ Thus
term independent of $x$ in the expansion of ${(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{9}$ is $^{9} C_{6} {(\frac{3}{2})}^{9 - 6} {(- \frac{1}{3})}^{6} = \frac{7}{18}$

The absolute term (that is, term independent of $x$ ) in the expansion of ${(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{9}$ is:

Solution:

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