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1
MHT CET 2025 25th April Morning Shift
MCQ (Single Correct Answer)
+2
-0

$y=\mathrm{e}^x(\mathrm{~A} \cos x+\mathrm{B} \sin x)$ is the solution of the differential equation

A
$x^2 \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}+\left(1+y^2\right)=0$
B
$\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}-\frac{\mathrm{d} y}{\mathrm{~d} x}+y=0$
C
$\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}-2 \frac{\mathrm{~d} y}{\mathrm{~d} x}+2 y=0$
D
$x \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}-2 \frac{\mathrm{~d} y}{\mathrm{~d} x}+2 y=0$
2
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The rate of change of volume of spherical balloon at any instant is directly proportional to its surface area. If initially its radius is 3 cm , after 2 minutes its radius becomes 9 cm , then radius of balloon after 4 minutes is

A
12 cm
B
14 cm
C
15 cm
D
18 cm
3
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0
Solution of $(2 y-x) \frac{d y}{d x}=1$ is
A
$x=2(y-1)+\mathrm{ce}^{-y}$, where c is the constant of integration
B
$x=2(y-1)+\mathrm{ce}^{-x}$, where c is the constant of integration
C
$y=2(x-1)+\mathrm{ce}^{-x}$, where c is the constant of integration
D
$y=2(x-1)+\mathrm{ce}^{-y}$, where c is the constant of integration
4
MHT CET 2025 23rd April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The integrating factor of $y+\frac{\mathrm{d}}{\mathrm{d} x}(x y)=x(\sin x+\log x)$ is

A
$x$
B
$\log x^2$
C
$x^2$
D
$x^3$
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