A) \[~-\,2916\]
B) 4860
C) 2160
D) none of these
Correct Answer: C
Solution :
The general term in the expansion of\[{{\left( 2x-\frac{3}{{{x}^{2}}} \right)}^{6}}\]is \[{{T}_{r+1}}={{\,}^{6}}{{C}_{r}}{{(2x)}^{6-r}}{{\left( -\frac{3}{{{x}^{2}}} \right)}^{r}}\] \[={{(-1)}^{r}}{{\,}^{6}}{{C}_{r}}{{2}^{6-r}}{{.3}^{r}}{{x}^{6-3r}}\] \[\therefore \]The term independent of \[x,\] if \[6-3r=0\]\[\Rightarrow \] \[r=2\] \[\therefore \]\[{{T}_{3}}={{\,}^{6}}{{C}_{2}}{{.2}^{4}}{{.3}^{2}}=2160\]
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