Let m and n be the coefficients of seventh and thirteenth terms respectively in the expansion of ( 1 3 x 1 3 + 1 2 x 2 3 ) 18 . Then ( n m ) 1 3 is: [2024]

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Solution

Q.
Let $m$ and $n$ be the coefficients of seventh and thirteenth terms respectively in the expansion of ${(\frac{1}{3} x^{\frac{1}{3}} + \frac{1}{2 x^{\frac{2}{3}}})}^{18} .$ Then ${(\frac{n}{m})}^{\frac{1}{3}}$ is: [2024]

1
$\frac{1}{9}$

2
$\frac{1}{4}$

3
$\frac{4}{9}$

4
$\frac{9}{4}$

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