Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Questions  >>  CBSE XI  >>  Math  >>  Binomial Theorem
Answer
Comment
Share
Q)

If the middle term of $(\large\frac{1}{x}$$+x\sin x)^{10}$ is equal to $7\large\frac{7}{8}$ then value of $x$ is

$\begin{array}{1 1}(A)\;2n\pi+\large\frac{\pi}{6}\\(B)\;n\pi+\large\frac{\pi}{6}\\(C)\;n\pi+(-1)^n\large\frac{\pi}{6}\\(D)\;n\pi+(-1)^n\large\frac{\pi}{3}\end{array} $

1 Answer

Comment
A)
Toolbox:
  • $T_{r+1}=nC_r a^{n-r}b^r$
  • Middle term :-If $n$ is even then the total number of term is n+1.
  • Hence there is only one middle term
  • (i.e) $(\large\frac{n}{2}$$+1)^{th}$
$n=10$
$(\large\frac{10}{2}$$+1)^{th}=6^{th}$ term
$T_6=10C_5.\large\frac{1}{x^5}.$$x^5 \sin ^5x$
$10C_5=\large\frac{10!}{5!5!}=\frac{10\times 9\times 8\times 7\times 6\times 5!}{5\times 4\times 3\times 2\times 5!}$
$\Rightarrow 252$
$252 \sin ^5 x=\large\frac{63}{8}$
$\Rightarrow \sin ^5 x=\large\frac{1}{8}$
$\Rightarrow \sin ^5 x=\large\frac{1}{2^5}$
$\Rightarrow \sin x=\large\frac{1}{2}$
$\Rightarrow x=n\pi +(-1)^n \large\frac{\pi}{6}$
Hence (C) is the correct answer.
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...