(C) The general term in the expansion of $(y^2 + \frac{c}{y})^5$ is given by $T_{r+1} = ^5C_r (y^2)^{5-r} (\frac{c}{y})^r$.$T_{r+1} = ^5C_r y^{10-2r}

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

(C) The general term in the expansion of $(y^2 + \frac{c}{y})^5$ is given by $T_{r+1} = ^5C_r (y^2)^{5-r} (\frac{c}{y})^r$.$T_{r+1} = ^5C_r y^{10-2r} c^r y^{-r} = ^5C_r c^r y^{10-3r}$.To find the coefficient of $y$,we set the exponent of $y$ equal to $1$:$10 - 3r = 1$$3r = 9$$r = 3$.Substituting $r = 3$ into the coefficient expression $^5C_r c^r$:Coefficient $= ^5C_3 c^3 = \frac{5 \times 4}{2 \times 1} c^3 = 10c^3$.

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 expansion of $(y^2 + \frac{c}{y})^5$,the coefficient of $y$ is:

A
$20c$
B
$10c$
C
$10c^3$
D
$20c^2$

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 three consecutive terms in the expansion of $(1+x)^n$ are in the ratio $1:5:20$,then the coefficient of the fourth term is $............$.

DifficultJEE MAIN 2023

View Solution

In the binomial expansion of $(a - b)^n, n \ge 5,$ the sum of the $5^{th}$ and $6^{th}$ terms is zero. Then $a/b$ equals:

MediumAIEEE 2007

View Solution

The coefficient of $x^{50}$ in the expansion of $(1+x)^{101}(1-x+x^2)^{100}$ is

MediumTS EAMCET 2023

View Solution

Find $a$ if the coefficients of $x^{2}$ and $x^{3}$ in the expansion of $(3+ax)^{9}$ are equal.

Difficult

View Solution

Let $n$ be a positive even integer. If the ratio of the largest coefficient and the $2^{nd}$ largest coefficient in the expansion of $(1+x)^{n}$ is $11:10$,then the number of terms in the expansion of $(1+x)^{n}$ is:

EasyWBJEE 2013

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 expansion of $(y^2 + \frac{c}{y})^5$,the coefficient of $y$ is:

Similar Questions

If the coefficients of the three consecutive terms in the expansion of $(1+x)^n$ are in the ratio $1:5:20$,then the coefficient of the fourth term is $............$.

In the binomial expansion of $(a - b)^n, n \ge 5,$ the sum of the $5^{th}$ and $6^{th}$ terms is zero. Then $a/b$ equals:

The coefficient of $x^{50}$ in the expansion of $(1+x)^{101}(1-x+x^2)^{100}$ is

Find $a$ if the coefficients of $x^{2}$ and $x^{3}$ in the expansion of $(3+ax)^{9}$ are equal.

Let $n$ be a positive even integer. If the ratio of the largest coefficient and the $2^{nd}$ largest coefficient in the expansion of $(1+x)^{n}$ is $11:10$,then the number of terms in the expansion of $(1+x)^{n}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module