Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If the second term in the expansion <img alt="\left(\sqrt[13]{a}+\frac{a}{\sqrt{a^{-1}}}\right)^n \text { is } 14 a^{5 / 2}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%28%5Cs

If the second term in the expansion \left(\sqrt[13]{a}+\frac{a}{\sqrt{a^{-1}}}\right)^n \text { is } 14 a^{5 / 2}then the value of { }^n C_4 /{ }^n C_2 \text { is }

 

Option: 1

6


Option: 2

9


Option: 3

10


Option: 4

11


Answers (1)

best_answer

T_2=T_{1+1}={ }^n C_1(\sqrt[13]{a})^{n-1}\left(\frac{a}{\sqrt{a^{-1}}}\right)^1

\begin{aligned} & =n a^{\frac{n-1}{13}} a^{\frac{3}{2}}=n a^{\frac{2 n+37}{26}} \\ & \text { Also, } n a^{\frac{2 n+37}{26}}=14 a^{\frac{5}{2}} \quad \text { [Given] } \end{aligned}

\begin{aligned} & \Rightarrow n=14 \\ & \therefore \quad \frac{{ }^n C_4}{{ }^n C_2}=\frac{{ }^{14} C_4}{{ }^{14} C_2}=11 \end{aligned}

Posted by

Pankaj Sanodiya

View full answer

JEE Main high-scoring chapters and topics

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

Similar Questions

Latest Question