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

A population P grew at the rate given by the equation $$\frac{dP}{dt}=0.5P$$, then the population will become double in

A
20 (log 2) years
B
10 (log 2) years
C
5 (log 2) years
D
12 (log 2) years
2
MHT CET 2021 24th September Evening Shift
+2
-0

The differential equation of all parabolas whose axis is $$y$$-axis, is

A
$$\frac{d^2 y}{d x^2}-\frac{d y}{d x}=0$$
B
$$x \frac{d^2 y}{d x^2}+\frac{d y}{d x}=0$$
C
$$x \frac{d^2 y}{d x^2}-\frac{d y}{d x}=0$$
D
$$\frac{d^2 y}{d x^2}-y=0$$
3
MHT CET 2021 24th September Evening Shift
+2
-0

The general solution of the differential equation $$\frac{d y}{d x}=\tan \left(\frac{y}{x}\right)+\frac{y}{x}$$ is

A
$$\sin \left(\frac{y}{x}\right)=c y$$
B
$$\cos \left(\frac{y}{x}\right)=c y$$
C
$$\cos \left(\frac{y}{x}\right)=c x$$
D
$$\sin \left(\frac{y}{x}\right)=c x$$
4
MHT CET 2021 24th September Morning Shift
+2
-0

The particular solution of the differential equation $$\frac{d y}{d x}=\frac{x+y+1}{x+y-1}$$ when $$\mathrm{x}=\frac{2}{3}$$ and $$y=\frac{1}{3}$$ is

A
$$2 x+2 y-2=\log |x+y|$$
B
$$y-x+\frac{1}{3}=\log |x+y|$$
C
$$x+y-1=\log |x+y|$$
D
$$4 x-5 y-1=\log |x+y|$$
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