A) \[\frac{4580}{17}\]
B) \[-\frac{896}{27}\]
C) \[\frac{5580}{17}\]
D) none of these
Correct Answer: B
Solution :
The general term in the expansion of \[{{\left( 2{{x}^{2}}-\frac{1}{3{{x}^{2}}} \right)}^{10}}\]is \[{{T}_{r+1}}={{\,}^{n}}{{C}_{r}}{{(2{{x}^{2}})}^{n-r}}{{\left( -\frac{1}{3{{x}^{2}}} \right)}^{r}}\] \[\therefore \]6th term is \[{{T}_{5+1}}={{\,}^{10}}{{C}_{5}}{{(2{{x}^{2}})}^{10-5}}{{\left( -\frac{1}{3{{x}^{2}}} \right)}^{5}}\] \[=-\frac{10!}{5!5!}{{\left( \frac{2}{3} \right)}^{5}}\] \[=-\frac{10\times 9\times 8\times 7\times 6}{5\times 4\times 3\times 2\times 1}\times \frac{{{2}^{5}}}{{{3}^{5}}}\] \[=-\frac{896}{27}\]
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