The constant term in the expansion of ${\left( {2x + {1 \over {{x^7}}} + 3{x^2}} \right)^5}$ is ___________.
Answer (integer)
1080
Solution
Constant term in the expansion of
<br/><br/>
$$
\begin{aligned}
& \left(2 x+\frac{1}{x^{7}}+3 x^{2}\right)^{5} \\\\
& \frac{1}{x^{35}}\left(2 x^{8}+1+3 x^{9}\right)^{5} \\\\
& \frac{1}{x^{35}}\left(1+x^{8}(3 x+2)\right)^{5}
\end{aligned}
$$
<br/><br/>
Term independent of $x=$ coefficient of $x^{35}$ in
<br/><br/>
$$
\begin{aligned}
& ^{5} C_{4}\left(x^{8}(3 x+2)\right)^{4} \\\\
= & { }^{5} C_{4} \text { coefficient of } x^{3} \text { in }(2+3 x)^{4} \\\\
= & { }^{5} C_{4} \times{ }^{4} C_{3}(2)^{1}(3)^{3} \\\\
= & 5 \times 4 \times 2 \times 27 \\\\
= & 1080
\end{aligned}
$$
About this question
Subject: Mathematics · Chapter: Binomial Theorem · Topic: Binomial Expansion
This question is part of PrepWiser's free JEE Main question bank. 193 more solved questions on Binomial Theorem are available — start with the harder ones if your accuracy is >70%.