(C) The general term $T_{r+1}$ in the expansion of $(x^4 - x^{-3})^{15}$ is given by:$T_{r+1} = ^{15}C_r (x^4)^{15-r} (-x^{-3})^r$$T_{r+1} = ^{15}C_r

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(C) The general term $T_{r+1}$ in the expansion of $(x^4 - x^{-3})^{15}$ is given by:$T_{r+1} = ^{15}C_r (x^4)^{15-r} (-x^{-3})^r$$T_{r+1} = ^{15}C_r (-1)^r x^{60-4r} x^{-3r}$$T_{r+1} = ^{15}C_r (-1)^r x^{60-7r}$To find the coefficient of $x^{32}$,we set the exponent of $x$ equal to $32$:$60 - 7r = 32$$7r = 28$$r = 4$Substituting $r = 4$ into the expression,the coefficient is $^{15}C_4 (-1)^4 = ^{15}C_4$.

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

Easy

The coefficient of $x^{32}$ in the expansion of $(x^4 - \frac{1}{x^3})^{15}$ is

A
$^{15}C_5$
B
$^{15}C_6$
C
$^{15}C_4$
D
$^{15}C_7$

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Chapter

Binomial Theorem

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

The greatest term in the expansion of $(1+x)^{15}$,when $x=\frac{1}{2}$ is

MediumAP EAMCET 2023

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If the constant term in the binomial expansion of $\left(\sqrt{x}-\frac{k}{x^{2}}\right)^{10}$ is $405$,then $|k|$ equals

MediumJEE MAIN 2020

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The coefficients of three consecutive terms in the expansion of $(1+a)^{n}$ are in the ratio $1:7:42$. Find $n$.

Difficult

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The $6^{th}$ term in the expansion of $\left( 2x^2 - \frac{1}{3x^2} \right)^{10}$ is

Medium

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In the expansion of $(1+x)^n$,the coefficients of the $p^{th}$ and $(p+1)^{th}$ terms are respectively $p$ and $q$. Then $p+q$ is equal to:

MediumTS EAMCET 2002

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The coefficient of $x^{32}$ in the expansion of $(x^4 - \frac{1}{x^3})^{15}$ is

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The greatest term in the expansion of $(1+x)^{15}$,when $x=\frac{1}{2}$ is

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