Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If <img alt="\frac{1}{\sqrt{2 x+1}} \times\left\{\left(\frac{1+\sqrt{2 x+1}}{2}\right)^n-\left(\frac{1-\sqrt{2 x+1}}{2}\right)^n\right\}" src="https://entrancecorner.oncodecogs.com/gif.latex?%

If \frac{1}{\sqrt{2 x+1}} \times\left\{\left(\frac{1+\sqrt{2 x+1}}{2}\right)^n-\left(\frac{1-\sqrt{2 x+1}}{2}\right)^n\right\}  is a polynomial of degree 5, then n = 

Option: 1

9


Option: 2

10


Option: 3

11


Option: 4

None of these


Answers (1)

best_answer

Now, \frac{1}{\sqrt{2 x+1}} \times\left\{\left(\frac{1+\sqrt{2 x+1}}{2}\right)^n-\left(\frac{1-\sqrt{2 x+1}}{2}\right)^n\right\}

=\frac{1}{2^n} \frac{2}{\sqrt{2 x+1}} \times\left\{{ }^n C_1 \sqrt{2 x+1}+{ }^n C_3(\sqrt{2 x+1})^3+{ }^n C_5(\sqrt{2 x+1})^5+\ldots . .\right\}

\begin{aligned} & = \\ & \frac{1}{2^{n-1}}\left\{{ }^n C_1+{ }^n C_3(2 x+1)+{ }^n C_5(2 x+1)^2+{ }^n C_7(2 x+1)^3+{ }^n C_9(2 x+1)^4+{ }^n C_{11}(2 x+1)^5+\ldots . .\right\} \end{aligned}

Since, this polynomial is given to be of degree 5, therefore, n can be 11 or 12.
 

Posted by

manish

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