Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • What is the coefficient of the middle term of  ?<div class='qna-option'

What is the coefficient of the middle term of  (x+y)^{49}?

Option: 1

^{49} C_{24}


Option: 2

^{49} C_{26}


Option: 3

^{49} C_{25}


Option: 4

Both A and C


Answers (1)

best_answer

Middle Term

The middle term in the expansion (x + y)n, depends on the value of 'n'. 

When 'n' is odd

In this case, the number of terms in the expansion will be n + 1. Since n is, odd so, n + 1 is even. Therefore, there will be two middle terms in the expansion, namely\left(\frac{n+1}{2}\right)^{t h} \text { and }\left(\frac{n+3}{2}\right)^{t h} term.

And these are given by

\mathrm{T}_{\frac{\mathrm{n}+1}{2}}=\left(\begin{array}{c}{\mathrm{n}} \\ {\frac{\mathrm{n}-1}{2}}\end{array}\right) \mathrm{x}^{\frac{\mathrm{n}+1}{2}} \cdot \mathrm{y}^{\frac{\mathrm{n}-1}{2}} \quad \,\,\,and\,\,\,\mathrm{T}_{\frac{\mathrm{n}+3}{2}}=\left(\begin{array}{c}{\mathrm{n}} \\ {\frac{\mathrm{n}+1}{2}}\end{array}\right) \mathrm{x}^{\frac{\mathrm{n}-1}{2}} \cdot \mathrm{y}^{\frac{\mathrm{n}+1}{2}}

 

Now,

n = 49 is odd hence 

 ^{n} C_{(n-1) / 2} \text{ and } ^{n} C_{(n+1) / 2} will be the coefficients of middle terms

So coefficient are ^{49} C_{(49-1) / 2}= \;^{49} C_{24} \text { and }^{49} C_{(49+1) / 2}=^{49} C_{25}.

Also both these are equal

option D is correct

Posted by

Shailly goel

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions