1
MHT CET 2021 24th September Morning Shift
+2
-0

The general solution of the differential equation $$(2 y-1) d x-(2 x+3) d y=0$$ is

A
$$(2 x+3)^2=c(2 y-1)$$
B
$$\frac{2 x+3}{2 y-1}=c$$
C
$$(2 x+3)(2 y-1)=c$$
D
$$(2 x+3)(2 y-1)^2=c$$
2
MHT CET 2021 24th September Morning Shift
+2
-0

The differential equation of the family of parabolas with focus at the origin and the $$X$$-axis a axis, is

A
$$-y\left(\frac{d y}{d x}\right)^2=2 x \frac{d y}{d x}-y$$
B
$$y\left(\frac{d y}{d x}\right)^2+2 x y \frac{d y}{d x}+y=0$$
C
$$y\left(\frac{d y}{d x}\right)^2+4 x \frac{d y}{d x}=4 x y$$
D
$$y\left(\frac{d y}{d x}\right)^2+y=2 x y \frac{d y}{d x}$$
3
MHT CET 2021 23rd September Evening Shift
+2
-0

Radium decomposes at the rate proportional to the amount present at any time. If $$\mathrm{P} \%$$ of amount disappears in one year, then amount of radium left after 2 years is

A
$$\left(10-\frac{\mathrm{P}}{10}\right)^2$$
B
$$\mathrm{x}_0\left[1+\frac{\mathrm{P}}{100}\right]^2$$
C
$$x_0\left[1-\frac{P}{100}\right]^2$$
D
$$\mathrm{x}_0\left[10-\frac{\mathrm{P}}{10}\right]^2$$
4
MHT CET 2021 23rd September Evening Shift
+2
-0

The differential equation obtained by eliminating A and B from $$y=A \cos \omega t+B \sin \omega t$$

A
$$\frac{d^2 y}{d t^2}+\omega^2 y=0$$
B
$$\frac{\mathrm{d}^2 y}{\mathrm{dt}^2}+\omega \mathrm{y}^2=0$$
C
$$\frac{d^2 y}{d t^2}-\omega^2 y=0$$
D
$$\frac{d^2 y}{d t^2}-\omega y^2=0$$
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