(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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(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 $T_{r+1} = ^{15}C_r \times 2^r \times x^{15-r} \times x^{-2r} = ^{15}C_r \times 2^r \times x^{15-3r}$. 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 $^{15}C_5 \times 2^5$.

Class 11 Mathematics Binomial Theorem General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

Easy

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

A
$^{15}C_6 \times 2^6$
B
$^{15}C_5 \times 2^5$
C
$^{15}C_4 \times 2^4$
D
$^{15}C_8 \times 2^8$

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Binomial Theorem

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General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

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DifficultAIEEE 2012

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

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The coefficient of $x^2$ in the expansion of $(2x^2 + \frac{1}{x})^{10}, x \neq 0$,is:

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