The coefficient of the term independent of $x$ in the expansion of ${[x^{2} + \frac{1}{x}]}^{15}$ is

3003

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3009

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4003

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4009

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Solution

The correct option is A 3003
The general term is
$T_{r + 1}$
$=^{15} C_{r} x^{30 - 3 r}$
Hence for term independent of x,
$30 - 3 r = 0$
$r = 10$
Substituting in the general term,we get the coefficient/term as
$^{15} C_{10}$
$=^{15} C_{5}$
$= \frac{15.14.13.12.11}{5!}$
$= 3003$ .

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