(A) The general term in the expansion of $(x + a)^n$ is given by $T_{r+1} = {}^nC_r x^{n-r} a^r$.For the expansion of $(x + 3)^6$,the general term is

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

(A) The general term in the expansion of $(x + a)^n$ is given by $T_{r+1} = {}^nC_r x^{n-r} a^r$.For the expansion of $(x + 3)^6$,the general term is $T_{r+1} = {}^6C_r x^{6-r} 3^r$.To find the coefficient of $x^5$,we set the exponent of $x$ equal to $5$:$6 - r = 5 \Rightarrow r = 1$.Substituting $r = 1$ into the expression for the coefficient:Coefficient $= {}^6C_1 \times 3^1 = 6 \times 3 = 18$.

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 $x^5$ in the expansion of $(x + 3)^6$ is

A
$18$
B
$6$
C
$12$
D
$10$

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

If the coefficients of the $r^{th}$ term and the $(r + 4)^{th}$ term are equal in the expansion of $(1 + x)^{20}$,then the value of $r$ is:

Medium

View Solution

If the coefficients of $(r-5)^{th}$ and $(2r-1)^{th}$ terms in the expansion of $(1+x)^{34}$ are equal,find $r$.

Medium

View Solution

If ${\left( {2 + \frac{x}{3}} \right)^{55}}$ is expanded in the ascending powers of $x$ and the coefficients of powers of $x$ in two consecutive terms of the expansion are equal,then these terms are

DifficultJEE MAIN 2014

View Solution

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

Easy

View Solution

If $n$ is a positive integer and $C_k = {^nC_k}$,then the value of $\sum\limits_{k = 1}^n {k^3\left( {\frac{C_k}{C_{k - 1}}} \right)^2}$ is:

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 $x^5$ in the expansion of $(x + 3)^6$ is

Similar Questions

If the coefficients of the $r^{th}$ term and the $(r + 4)^{th}$ term are equal in the expansion of $(1 + x)^{20}$,then the value of $r$ is:

If the coefficients of $(r-5)^{th}$ and $(2r-1)^{th}$ terms in the expansion of $(1+x)^{34}$ are equal,find $r$.

If ${\left( {2 + \frac{x}{3}} \right)^{55}}$ is expanded in the ascending powers of $x$ and the coefficients of powers of $x$ in two consecutive terms of the expansion are equal,then these terms are

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

If $n$ is a positive integer and $C_k = {^nC_k}$,then the value of $\sum\limits_{k = 1}^n {k^3\left( {\frac{C_k}{C_{k - 1}}} \right)^2}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module