Mathematics · 2022
JEE Main · 25 June 2022, Shift 1 · Q18
If the solution curve y=y(x) of the differential equation y^2 d x+(x^2-x y+y^2) d y=0, which passes through the point (1,1) and intersects the line…
If the solution curve $\displaystyle y=y(x)$ of the differential equation $\displaystyle y^2 \mathrm{~d} x+\left(x^2-x y+y^2\right) \mathrm{d} y=0$, which passes through the point $\displaystyle (1,1)$ and intersects the line $\displaystyle y=\sqrt{3} x$ at the point $\displaystyle (\alpha, \sqrt{3} \alpha)$, then value of $\displaystyle \log _{\mathrm{e}}(\sqrt{3} \alpha)$ is equal to :
Official answer
(3)
$\displaystyle \frac{\pi}{12}$
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JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.