Search any question & find its solution
Question:
Answered & Verified by Expert
Coefficient of $x^{13}$ in the expansion of $(1-x)^{5}\left(1+x+x^{2}+x^{3}\right)^{4}$ is
Options:
Solution:
2096 Upvotes
Verified Answer
The correct answer is:
4
Expression $=(1-x)^{5} \cdot(1+x)^{4}\left(1+x^{2}\right)^{4}$
$\begin{array}{l}
=(1-x)\left(1-x^{2}\right)^{4}\left(1+x^{2}\right)^{4} \\
=(1-x)\left(1-x^{4}\right)^{4}
\end{array}$
$\therefore$ Coefficient of $x^{13}=-{ }^{4} \mathrm{C}_{3}(-1)^{3}=4$
$\begin{array}{l}
=(1-x)\left(1-x^{2}\right)^{4}\left(1+x^{2}\right)^{4} \\
=(1-x)\left(1-x^{4}\right)^{4}
\end{array}$
$\therefore$ Coefficient of $x^{13}=-{ }^{4} \mathrm{C}_{3}(-1)^{3}=4$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.