jee-main 2022 Q76

jee-main · India · session2_25jul_shift2 Differential equations Solving Separable DEs with Initial Conditions

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 $\left(\frac{-y}{x}\right)$. If the curve passes through the points $(1, 2)$ and $(8, 1)$, then $\left|y\left(\frac{1}{8}\right)\right|$ is equal to
(1) $2\log_e 2$
(2) 4
(3) 1
(4) $4\log_e 2$

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 $\left(\frac{-y}{x}\right)$. If the curve passes through the points $(1, 2)$ and $(8, 1)$, then $\left|y\left(\frac{1}{8}\right)\right|$ is equal to\\
(1) $2\log_e 2$\\
(2) 4\\
(3) 1\\
(4) $4\log_e 2$

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