First slide

Binomial theorem for positive integral Index

Question

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

Moderate

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 $^{9} C_{6} {(\frac{3}{2})}^{9 - 6} {(- \frac{1}{3})}^{6} = \frac{7}{18}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App