A) \[\frac{4580}{17}\]
B) \[-\frac{896}{27}\]
C) \[\frac{5580}{17}\]
D) none of these
Correct Answer: B
Solution :
Key Idea : The general term in the expansion of \[{{(x+a)}^{n}}\]is \[{{T}_{r+1}}{{=}^{n}}{{C}_{r}}{{x}^{n-r}}{{d}^{r}}\] Given expansion is\[{{\left( 2{{x}^{2}}-\frac{1}{3{{x}^{2}}} \right)}^{10}}\] \[\therefore \] \[{{T}_{r+1}}{{=}^{10}}{{C}_{r}}{{(2{{x}^{2}})}^{10-r}}{{\left( -\frac{1}{3{{x}^{2}}} \right)}^{r}}\] \[\Rightarrow \] \[{{T}_{6}}{{=}^{10}}{{C}_{5}}{{(2{{x}^{2}})}^{5}}{{\left( -\frac{1}{3{{x}^{2}}} \right)}^{5}}\] \[=-\frac{10!\times 32}{5!5!}\times \frac{1}{243}\] \[=-\frac{896}{27}\]
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