A) \[1\]
B) \[^{10}{{C}_{1}}\]
C) \[\frac{5}{12}\]
D) None of these
Correct Answer: D
Solution :
The general term is \[{{T}_{r+1}}{{=}^{10}}{{C}_{r}}{{\left( \sqrt{\frac{x}{3}} \right)}^{10-r}}{{\left( \sqrt{\frac{3}{2{{x}^{2}}}} \right)}^{r}}\] \[{{=}^{10}}{{C}_{r}}{{\left( \frac{1}{3} \right)}^{5-(r/2)}}{{\left( \frac{3}{2} \right)}^{r/2}}\cdot {{x}^{5-(3r/2)}}\] for term independent of\[x\]. \[5-\frac{3r}{2}=0\Rightarrow \,\,r=\frac{10}{3}\], which is not a positive integer. Hence, there is no term independent of\[x\].
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