A) \[^{18}{{C}_{6}}{{2}^{6}}\]
B) \[^{18}{{C}_{6}}{{2}^{12}}\]
C) \[^{18}{{C}_{18}}{{2}^{18}}\]
D) None of these
Correct Answer: A
Solution :
\[{{T}_{r+1}}={{\,}^{18}}{{C}_{r}}{{(\sqrt{x})}^{18-r}}{{\left( -\frac{2}{x} \right)}^{r}}={{\,}^{18}}{{C}_{r}}{{x}^{9-r/2-r}}{{(-2)}^{r}}\] If \[{{T}_{r+1}}\] is independent of x, then\[9-\frac{r}{2}-r=0\Rightarrow r=6\]. So term independent of \[x={{T}_{7}}={{\,}^{18}}{{C}_{6}}{{2}^{6}}\]
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