jee-main 2024 Q75

jee-main · India · session1_31jan_shift1 Differential equations Solving Separable DEs with Initial Conditions

The solution curve of the differential equation $y \frac { d x } { d y } = x \left( \log _ { e } x - \log _ { e } y + 1 \right) , \quad x > 0 , \quad y > 0$ passing through the point $(e, 1)$ is
(1) $\log _ { e } \frac { y } { x } = x$
(2) $\log _ { e } \frac { y } { x } = y ^ { 2 }$
(3) $\log _ { e } \frac { x } { y } = y$
(4) $2 \log _ { e } \frac { x } { y } = y + 1$

The solution curve of the differential equation $y \frac { d x } { d y } = x \left( \log _ { e } x - \log _ { e } y + 1 \right) , \quad x > 0 , \quad y > 0$ passing through the point $(e, 1)$ is\\
(1) $\log _ { e } \frac { y } { x } = x$\\
(2) $\log _ { e } \frac { y } { x } = y ^ { 2 }$\\
(3) $\log _ { e } \frac { x } { y } = y$\\
(4) $2 \log _ { e } \frac { x } { y } = y + 1$

Paper Questions

Q61 Q62 Q63 Q64 Q65 Q66 Q67 Q68 Q69 Q70 Q71 Q72 Q73 Q74 Q75 Q76