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 y=\sqrt{3} x at the point (\alpha, \sqrt{3} \alpha), then value of \log _e(\sqrt{3} \alpha) is equal to : [25-Jun-2022-Shift-1]

JEE Main 25 June 2022 Shift 1 Solved Paper

Section: Mathematics

Question : 18 of 90

Marks: +1, -0

If the solution curve y=y(x) of the differential equation y2dx+(x2−xy+y2)dy=0, which passes through the point (1, 1) and intersects the line y=√3x at the point (α,√3α), then value of loge(√3α) is equal to :

[25-Jun-2022-Shift-1]

‌
π
3
‌
π
2
‌
π
12
‌
π
6

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