Email
Chat with tutor
logo

Ask Questions, Get Answers

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

The coefficient of $x^{32}$ in the expansion of $(x^4-\large\frac{1}{x^3})^{15}$ is

$\begin{array}{1 1}(A)\;-15C_3\\(B)\;15C_4\\(C)\;-15C_5\\(D)\;15C_2\end{array} $

1 Answer

Comment
A)
Toolbox:
  • $T_{r+1}=nC_r a^{n-r} b^r$
$T_{r+1}=15C_r (x^4)^{15-r}(-x^{\Large\frac{1}{3}})^r$
$\Rightarrow 15C_r x^{60-4r-3r}(-1^r)$
$\Rightarrow 15C_r (-1)^r x^{60-7r}$
$\Rightarrow 60-7r=32$
$\Rightarrow r=4$
$\therefore T_{r+1}=T_{4+1}=15C_4 (-1)^4x^{32}$
$\therefore$ Required coefficient =$15C_4$
Hence (B) 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.
...