Find the term independent of $x$ in the expansion of ${(x^{2} + \frac{1}{x})}^{9}$ :

3

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4

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7

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8

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Solution

The correct option is C $7$
$T_{r + 1} =^{9} C_{r} (x^{2})^{9 - r} (x^{- 1})^{r}$
$=^{9} C_{r} x^{18 - 2 r} x^{- r}$
$18 - 3 r = 0$
$18 = 3 r$
$r = 6$
Hnece the required term is $7$ .

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