1
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

The differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{\sqrt{1-y^2}}{y}$$ determines a family of circles with

A
fixed radius of 1 unit and variable centres along the $$X$$-axis
B
fixed radius of 1 unit and variable centres along the $$Y$$-axis
C
variable radii and a fixed centre at $$(0,1)$$
D
variable radii and a fixed centre at $$(0,-1)$$
2
MHT CET 2021 24th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The particular solution of the differential equation $$\left(1+e^{2 x}\right) d y+e^x\left(1+y^2\right) d x=0$$ at $$x=0$$ and y = 1 is

A
$$\tan ^{-1} e^x-\tan ^{-1} y=0$$
B
$$\tan ^{-1} e^x+\tan ^{-1} y=\frac{\pi}{2}$$
C
$$2 \tan ^{-1} e^x+\tan ^{-1} y=\frac{3 \pi}{4}$$
D
$$\tan ^{-1} e^x-\tan ^{-1} y=\frac{3 \pi}{4}$$
3
MHT CET 2021 24th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The order and degree of the differential equation $$\sqrt{\frac{d y}{d x}}-4 \frac{d y}{d x}-7 x=0$$ are respectively.

A
2 and 2
B
1 and 2
C
1 and 1
D
2 and 1
4
MHT CET 2021 24th September Evening Shift
MCQ (Single Correct Answer)
+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
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