Mathematics · 2023
JEE Main · 30 January 2023, Shift 1 · Q71
If the coefficient of x^15 in the expansion of ( a x^3+1/(b x^1 / 3))^15 is equal to the coefficient of x^-15 in the expansion of ( a x^1 / 3-1/(b…
If the coefficient of $\displaystyle x^{15}$ in the expansion of $\displaystyle \left(\mathrm{a} x^3+\frac{1}{\mathrm{~b} x^{1 / 3}}\right)^{15}$ is equal to the coefficient of $\displaystyle x^{-15}$ in the expansion of $\displaystyle \left(\mathrm{a} x^{1 / 3}-\frac{1}{\mathrm{~b} x^3}\right)^{15}$, where a and b are positive real numbers, then for each such ordered pair $\displaystyle (\mathrm{a}, \mathrm{b})$ :
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle a b=1$
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JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.