jee-main 2024 Q64

jee-main · India · session1_01feb_shift2 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Single Binomial Expansion

Let $m$ and $n$ be the coefficients of seventh and thirteenth terms respectively in the expansion of $\left(\frac{1}{3}x^{\frac{1}{3}} + \frac{1}{2x^{\frac{2}{3}}}\right)^{18}$. Then $\left(\frac{n}{m}\right)^{\frac{1}{3}}$ is:
(1) $\frac{4}{9}$
(2) $\frac{1}{9}$
(3) $\frac{1}{4}$
(4) $\frac{1}{4}$

Let $m$ and $n$ be the coefficients of seventh and thirteenth terms respectively in the expansion of $\left(\frac{1}{3}x^{\frac{1}{3}} + \frac{1}{2x^{\frac{2}{3}}}\right)^{18}$. Then $\left(\frac{n}{m}\right)^{\frac{1}{3}}$ is:\\
(1) $\frac{4}{9}$\\
(2) $\frac{1}{9}$\\
(3) $\frac{1}{4}$\\
(4) $\frac{1}{4}$

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