If the coefficient of x¹⁵ in the expansion of (ax³ + 1/bx^(1/3))¹… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 30 January, Shift 1General Term

If the coefficient of $x^{15}$ in the expansion of $\left(ax^3 + \frac{1}{bx^{1/3}}\right)^{15}$ is equal to the coefficient of $x^{-15}$ in the expansion of $\left(ax^{1/3} - \frac{1}{bx^3}\right)^{15},$ where $a$ and $b$ are positive real numbers, then for each such ordered pair $(a, b)$ :

A
$a = b$
B
$ab = 1$
C
$a = 3b$
D
$ab = 3$

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