(C) The general term in the expansion of $(a + b)^n$ is given by $T_{r+1} = {}^nC_r a^{n-r} b^r$.For the $4^{th}$ term,$r = 3$,so $T_4 = {}^nC_3 a^{n-

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

(C) The general term in the expansion of $(a + b)^n$ is given by $T_{r+1} = {}^nC_r a^{n-r} b^r$.For the $4^{th}$ term,$r = 3$,so $T_4 = {}^nC_3 a^{n-3} b^3$.The coefficient of the $4^{th}$ term is ${}^nC_3 = 56$.Using the formula ${}^nC_3 = \frac{n(n-1)(n-2)}{3 \times 2 \times 1} = 56$.$n(n-1)(n-2) = 56 \times 6$.$n(n-1)(n-2) = 336$.We look for three consecutive integers whose product is $336$.$8 \times 7 \times 6 = 336$.Therefore,$n = 8$.

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

Easy

If the coefficient of the $4^{th}$ term in the expansion of $(a + b)^n$ is $56$,then $n$ is

A
$12$
B
$10$
C
$8$
D
$6$

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 sum of all rational terms in the expansion of $(2^{\frac{1}{5}} + 5^{\frac{1}{3}})^{15}$ is equal to :

DifficultJEE MAIN 2024

View Solution

The coefficient of the term independent of $x$ in the expansion of $(1 + x + 2x^3) \left( \frac{3}{2}x^2 - \frac{1}{3x} \right)^9$ is

View Solution

If in the expansion of $(a-2b)^{n}$,the sum of the $5^{th}$ and $6^{th}$ term is zero,then the value of $\frac{a}{b}$ is

MediumWBJEE 2010

View Solution

In the expansion of ${\left( {3x - \frac{1}{{{x^2}}}} \right)^{10}}$,the $5^{th}$ term from the end is:

View Solution

The number of integral terms in the expansion of $(7^{1/3} + 11^{1/9})^{6561}$ is:

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

If the coefficient of the $4^{th}$ term in the expansion of $(a + b)^n$ is $56$,then $n$ is

Similar Questions

The sum of all rational terms in the expansion of $(2^{\frac{1}{5}} + 5^{\frac{1}{3}})^{15}$ is equal to :

The coefficient of the term independent of $x$ in the expansion of $(1 + x + 2x^3) \left( \frac{3}{2}x^2 - \frac{1}{3x} \right)^9$ is

If in the expansion of $(a-2b)^{n}$,the sum of the $5^{th}$ and $6^{th}$ term is zero,then the value of $\frac{a}{b}$ is

In the expansion of ${\left( {3x - \frac{1}{{{x^2}}}} \right)^{10}}$,the $5^{th}$ term from the end is:

The number of integral terms in the expansion of $(7^{1/3} + 11^{1/9})^{6561}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module