The coefficient of the term independent of x in the expansion of ( x + 1 x ) 10 is equal to

Question

The coefficient of the term independent of $x$ in the expansion of ${(\sqrt{x} + \frac{1}{\sqrt{x}})}^{10}$ is equal to

Smart Achievers · Accepted Answer

(2)

$General term of expansion {(\sqrt{x} + \frac{1}{\sqrt{x}})}^{10} is$

$T_{r + 1} = {}^{10}C_{r} {(\sqrt{x})}^{10 - r} {(\frac{1}{\sqrt{x}})}^{r} = {}^{10}C_{r} x^{5 - r}$

$Term independent of x, means power of x is 0$

$\Rightarrow 5 - r = 0 \Rightarrow r = 5$

$Hence, T_{5 + 1} = {}^{10}C_{5} = 252$

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