The term independent of x in the expansion of ( 2 x 5 - 1 2 x x ) 11 is

Question

The term independent of $x$ in the expansion of ${(\frac{2 \sqrt{x}}{5} - \frac{1}{2 x \sqrt{x}})}^{11}$ is

Smart Achievers · Accepted Answer

(4)

$Let T_{r + 1} be general term of given expansion$

$∴$ $T_{r + 1} = {}^{11}C_{r} {(\frac{2 \sqrt{x}}{5})}^{11 - r} {(\frac{- 1}{2 x \sqrt{x}})}^{r}$

$= {}^{11}C_{r} {(\frac{2}{5})}^{11 - r} \times {(\frac{- 1}{2})}^{r} x^{\frac{11 - r}{2} - \frac{3 r}{2}}$

$∴$ $T_{r + 1} = {}^{11}C_{r} {(\frac{2}{5})}^{11 - r} {(\frac{- 1}{2})}^{r} x^{(11 - 4 r) / 2}$

$For a term independent of x, put \frac{11 - 4 r}{2} = 0 or r = \frac{11}{4}$

$But r can not be in fraction.$

$∴$ $There is no term independent of x .$

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