The term independent of x in the expansion of ( 3 2 x 2 - 1 3 x ) 6 is

Question

The term independent of $x$ in the expansion of ${(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{6}$ is

Smart Achievers · Accepted Answer

(1)

${(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{6}$

$T_{r + 1} = {}^{6}C_{r} {(\frac{3}{2} x^{2})}^{6 - r} {(\frac{- 1}{3 x})}^{r} = {}^{6}C_{r} {(\frac{3}{2})}^{6 - r} {(\frac{- 1}{3})}^{r} x^{12 - 3 r}$

$Put 12 - 3 r = 0 \Rightarrow r = 4$

$∴$ $Term independent of x is T_{5} = {}^{6}C_{4} {(\frac{3}{2})}^{2} {(\frac{- 1}{3})}^{4} = \frac{5}{12}$

Solution

Q.
The term independent of $x$ in the expansion of ${(\frac{3}{2} x^{2} - \frac{1}{3 x})}^{6}$ is

1 $\frac{5}{12}$

2 $\frac{12}{5}$

3 $\frac{5}{6}$

4 none of these

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Solution

Q. The term independent of x in the expansion of (32x2-13x)6 is

1 512

2 125

3 56