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JEE Main 2022 Mathematics question

MathematicsDifferential EquationJEE Main 2022

Let a smooth curve y = f(x) be such that the slope of the tangent at any point (x, y) on it is directly proportional to (−y)/x. If the curve passes through the points (1, 2) and (8, 1) then |y(1/8)| is equal to

Answer: (2)

Solution

dy/dx = −ky/x, so ln|y| = −k ln|x| + c. The point (1, 2) gives c = ln 2. The point (8, 1) gives 0 = −k

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Question ID VK-024724