Find the term independent of $x$ in the expansion of ${(2 x - \frac{1}{x})}^{10}$ :

4

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5

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6

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7

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Solution

The correct option is D $6$
$T_{r + 1} =^{10} C_{r} (2 x)^{10 - r} (- x^{- 1})^{r}$
$=^{10} C_{r} 2^{10 - r} x^{10 - r} (- x)^{- r}$
$⟹ 10 - 2 r = 0$
$⟹ r = 5$
Term is $6$ th term

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