In the expansion of (x + frac{2}{x^2})^{15},t | vedclass

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(B) The general term in the expansion of $(x + \frac{2}{x^2})^{15}$ is given by $T_{r+1} = ^{15}C_r (x)^{15-r} (\frac{2}{x^2})^r$. This simplifies to

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$^{15}C_5 	imes 2^5$

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(B) The general term in the expansion of $(x + \frac{2}{x^2})^{15}$ is given by $T_{r+1} = ^{15}C_r (x)^{15-r} (\frac{2}{x^2})^r$. This simplifies to $T_{r+1} = ^{15}C_r 	imes 2^r 	imes x^{15-r} 	imes x^{-2r} = ^{15}C_r 	imes 2^r 	imes x^{15-3r}$. For the term to be independent of $x$,the exponent of $x$ must be $0$. So,$15 - 3r = 0$,which gives $r = 5$. Substituting $r = 5$ into the general term expression,we get the term independent of $x$ as $^{15}C_5 	imes 2^5$.

In the expansion of $(x + \frac{2}{x^2})^{15}$,the term independent of $x$ is

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