(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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(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
$^{15}C_7$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Binomial Theorem

Subtopic

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

The positive value of $a$ such that the coefficient of $x^5$ is equal to that of $x^{15}$ in the expansion of $(x^2 + \frac{a}{x^3})^{10}$ is

View Solution

If coefficients of $2^{nd}$,$3^{rd}$ and $4^{th}$ terms in the binomial expansion of $(1 + x)^n$ are in $A.P.$,then $n^2 - 9n$ is equal to

Medium

View Solution

If $t_r$ is the $r^{\text{th}}$ term in the expansion of $(2^x + 4^{-x})^8$ and if $t_3 = 7t_2$,then $x =$

EasyAP EAMCET 2017

View Solution

If the $4^{\text{th}}$ term in the expansion of $\left(\frac{x}{2}-\frac{2y}{3}\right)^6$ is $-20$,then $xy=$

EasyTS EAMCET 2022

View Solution

If $A$ and $B$ are the coefficients of $x^n$ in the expansions of $(1 + x)^{2n}$ and $(1 + x)^{2n - 1}$ respectively,then

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

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

Similar Questions

The positive value of $a$ such that the coefficient of $x^5$ is equal to that of $x^{15}$ in the expansion of $(x^2 + \frac{a}{x^3})^{10}$ is

If coefficients of $2^{nd}$,$3^{rd}$ and $4^{th}$ terms in the binomial expansion of $(1 + x)^n$ are in $A.P.$,then $n^2 - 9n$ is equal to

If $t_r$ is the $r^{\text{th}}$ term in the expansion of $(2^x + 4^{-x})^8$ and if $t_3 = 7t_2$,then $x =$

If the $4^{\text{th}}$ term in the expansion of $\left(\frac{x}{2}-\frac{2y}{3}\right)^6$ is $-20$,then $xy=$

If $A$ and $B$ are the coefficients of $x^n$ in the expansions of $(1 + x)^{2n}$ and $(1 + x)^{2n - 1}$ respectively,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module