Jee Main 2024 01 02 2024 Shift 2 - Question7
Question 7
Let $m$ and $n$ be the coefficient of $7^{\text {th }}$ and $13^{\text {th }}$ term in expansion of $\left(\frac{1}{3} x^{1 / 3}+\frac{1}{2 x^{2 / 5}}\right)^{18}$, then $\left(\frac{m}{n}\right)^{1 / 3}$ is
(1) $\frac{1}{4}$
(2) $\frac{4}{7}$
(3) $\frac{1}{9}$
(4) $\frac{4}{9}$
Show Answer
Answer: (4)
Solution:
$T _7=m={ }^{18} C _6\left(\frac{1}{3}\right)^{12}\left(\frac{1}{2}\right)^{6}$
$$ T _{13}=n={ }^{18} C _{12}\left(\frac{1}{3}\right)^{6}\left(\frac{1}{2}\right)^{12} $$
$=\frac{\left(\frac{1}{3}\right)^{6}}{\left(\frac{1}{2}\right)^{6}}=\left[\left(\frac{2}{3}\right)^{6}\right]^{1 / 3}$
$=\frac{4}{9}$
BETA
