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Question: The term independent of x in \(\left( x^{2} - \frac{1}{x} \right)^{9}\) is...

The term independent of x in (x2−1x)9\left( x^{2} - \frac{1}{x} \right)^{9} is

A

1

B

–1

C

48

D

84

Answer

84

Explanation

Solution

General term in the expansion is $9C_{r}\left( x^{2} \right)\begin{matrix} \

\end{matrix}^{r}\left( \frac{- 1}{x} \right)^{9 - r}$

= 9Crx3r−9(−1)9−r9C_{r}x^{3r - 9}( - 1)^{9 - r}

For constant term, put r= 3