Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If the sum of the coefficients in the expansion of <img alt="(1+2 x)^{\mathrm{n}} \text { is } 6561," src="https://entrancecorner.oncodecogs.com/gif.latex?%281&plus;2%20x%29%5E%7B%5Cmathrm

If the sum of the coefficients in the expansion of (1+2 x)^{\mathrm{n}} \text { is } 6561, then the greatest coefficient in the expansion is equal to

Option: 1

2244


Option: 2

1120


Option: 3

2240


Option: 4

None of these


Answers (1)

best_answer

Put x=1

\begin{aligned} & 3^{\mathrm{n}}=6561 \\ & 3^{\mathrm{n}}=3^8 \\ & \mathrm{n}=8 \end{aligned}

The coefficient of the middle term is greatest

Middle\: term ={\frac{8}{2}+1=5

The coefficient of  T_{4+1}={ }^8 C_4(2)^4

\begin{aligned} & \frac{\8!}{\lfloor 4\lfloor 4} \times 2^4 \\ = & 1120 \end{aligned}

 

Posted by

Kuldeep Maurya

View full answer

JEE Main high-scoring chapters and topics

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

Similar Questions

Trending Articles/News

anam-khan

How to crack JEE Mains 2025 in 1 month? Follow study plan, revise high-score topics, experts advice
anam-khan

IIT JEE aspirant from Bihar found hanging in Kota hostel; 17th suicide this year
anam-khan

JEE Main 2025 just a month away; section-wise preparation tips, important topics, strategies

Latest Question