CUET Mathematics - The solution of the differential equation dr/dt = -rt, r(0) = r_0 is | PYQs + Solutions

CUET Mathematics 2025 22 May Shift 1

Calculus

Medium

common

$r = r_0 e^{t^2/2}$

$r = -r_0 e^{t^2/2}$

$r = r_0 e^{-t^2/2}$

$r = -r_0 e^{-t^2/2}$

✅ Correct Option: 3

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CUET Mathematics 2024 Slot 1

For the differential equation $\left(x \log _{e} x\right) d y=\left(\log _{e} x-y\right) d x$

(A) Degree of the given differential equation is $1$ .

(B) It is a homogeneous differential equation.

(C) Solution is $2y \log _{\mathrm{e}} \mathrm{x}+A=\left(\log _{\mathrm{e}} \mathrm{x}\right)^{2}$ , where $A$ is an arbitrary constant

(D) Solution is $2 y \log _{e} x+A=\log _{e}\left(\log _{e} x\right)$ , where $A$ is an arbitrary constant

Choose the correct answer from the options given below :

CUET Mathematics 2025 22 May Shift 1 PYQs