A) \[{{\,}^{10}}{{C}_{1}}\]
B) \[5/12\]
C) 1
D) None of these
Correct Answer: D
Solution :
\[{{T}_{r+1}}={{\,}^{10}}{{C}_{r}}{{\left( \sqrt{\frac{x}{3}} \right)}^{10-r}}{{\left( \sqrt{\frac{3}{2{{x}^{2}}}} \right)}^{r}}\] \[={{\,}^{10}}{{C}_{r}}{{\left( \frac{1}{\sqrt{3}} \right)}^{10-r}}{{\left( \sqrt{\frac{3}{2}} \right)}^{r}}{{x}^{\left( 5-\frac{r}{2}-r \right)}}\] Let \[{{\text{T}}_{\text{r+1}}}\]be the term independent of \[x.\] \[\therefore \] \[5-\frac{r}{2}-r=0\]\[\Rightarrow \]\[\frac{3r}{2}=5\Rightarrow r=\frac{10}{3}\] \[\therefore \] r is not a whole number. \[\therefore \]Given expression does not have any term independent of \[x.\]
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