1
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The particular solution of the differential equation, $x y \frac{\mathrm{~d} y}{\mathrm{~d} x}=x^2+2 y^2$ when $y(1)=0$ is

A
$\frac{x^2+y^2}{x^3}=1$
B
$x^2+y^2=x$
C
$x^2+y^2=x^4$
D
$x^2+2 y^2=x^4$
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of the differential equation $\mathrm{e}^{y-x} \frac{\mathrm{~d} y}{\mathrm{~d} x}=y\left(\frac{\sin x+\cos x}{1+y \log y}\right)$ is

A
$\mathrm{e}^y \log y=\mathrm{e}^{\mathrm{x}} \sin x+\mathrm{c}$, where c is a constant of integration.
B
$\mathrm{e}^y=\mathrm{e}^x \sin x+\mathrm{c}$, where c is a constant of integration.
C
$\log y=\mathrm{e}^x \sin x+\mathrm{c}$, where c is a constant of integration.
D
$y \log y=\mathrm{e}^x \sin x+\mathrm{c}$, where c is a constant of integration.
3
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A spherical rain drop evaporates at a rate proportional to its surface area. If initially its radius is 3 mm and after 1 second it is reduced to 2 mm , then at any time t its radius is (where $0 \leq \mathrm{t}<3$)

A
$\mathrm{3+t}$
B
$3-\mathrm{t}$
C
$4-\mathrm{t}$
D
$1+\mathrm{t}$
4
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The order of the differential equation, whose general solution is given by

$$y=\left(c_1+c_2\right) \cos \left(x+c_3\right)-c_4 e^{x+c 5}$$

where $c_1, c_2, c_3, c_4$ and $c_5$ are arbitrary constant, is

A
5
B
4
C
3
D
2
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