A) \[10\]
B) \[252\]
C) \[20\]
D) \[256\]
Correct Answer: B
Solution :
\[\therefore \] The general term in the expansion of \[\left( \sqrt{x}+\frac{1}{\sqrt{x}} \right)\] is \[{{T}_{r+1}}{{=}^{10}}{{C}_{r}}{{(\sqrt{x})}^{10-r}}{{\left( \frac{1}{\sqrt{x}} \right)}^{r}}\] \[{{=}^{10}}{{C}_{r}}{{x}^{\frac{10-r}{2}}}\left( {{x}^{-\frac{r}{2}}} \right)\] \[{{=}^{10}}{{C}_{r}}{{x}^{\frac{10-2r}{2}}}\] For independent of x, Put \[\frac{10-2r}{2}=0,\] we get \[r=5\]s \[\therefore \] Required coefficient \[{{=}^{10}}{{C}_{5}}\] \[=\frac{10\times 9\times 8\times 7\times 6}{5\times 4\times 3\times 2\times 1}\] \[=252\]
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