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JEE Main 2026 Mathematics question

MathematicsDifferential EquationJEE Main 2026

Let y=y(x) be the solution of the differential equation x\sin\left(\dfrac yx\right)dy=\left(y\sin\left(\dfrac yx\right)-x\right)dx, y(1)=π/2 and let . Then the number of integral values of p, for which the equation x²+y²−2px+2py+α+2=0 represents a circle of radius r≤6, is .

Answer: 6

Solution

Substituting v=y/x gives cos(v)=ln(x) (using y(1)=π/2). At x=e¹²: α=cos(y/x)=ln(e¹²)=12. The circle

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Question ID VK-015509