1
MHT CET 2021 20th September Morning Shift
+2
-0

The general solution of the differential equation $$x+y \frac{d y}{d x}=\sec \left(x^2+y^2\right)$$ is

A
$$\sin \left(x^2+y^2\right)=2 x+c$$
B
$$\sin \left(x^2+y^2\right)+2 x=c$$
C
$$\sin \left(x^2+y^2\right)+x=c$$
D
$$\cos \left(x^2+y^2\right)=2 x+c$$
2
MHT CET 2021 20th September Morning Shift
+2
-0

The differential equation of all circles which pass through the origin and whose centre lie on Y-axis is

A
$$\left(x^2-y^2\right) \frac{d y}{d x}-2 x y=0$$
B
$$\left(x^2+y^2\right) \frac{d y}{d x}-2 x y=0$$
C
$$\left(x^2+y^2\right) \frac{d y}{d x}+2 x y=0$$
D
$$\left(x^2-y^2\right) \frac{d y}{d x}+2 x y=0$$
3
MHT CET 2021 20th September Morning Shift
+2
-0

An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half the quantity of ice melts in 20 minutes, $$x_0$$ is the initial quantity of ice. If after 40 minutes the amount of ice left is $$\mathrm{Kx}_0$$, then $$\mathrm{K}=$$

A
$$\frac{1}{2}$$
B
$$\frac{1}{8}$$
C
$$\frac{1}{4}$$
D
$$\frac{1}{3}$$
4
MHT CET 2020 16th October Morning Shift
+2
-0

The differential equation obtained from the function $$y=a(x-a)^2$$ is

A
$$8 y^2=\left(\frac{d y}{d x}\right)^2\left[x+\frac{1}{4 y}\left(\frac{d y}{d x}\right)^2\right]^2$$
B
$$4 y^2=\left(\frac{d y}{d x}\right)^2\left[x-\frac{1}{4 y}\left(\frac{d y}{d x}\right)^2\right]^2$$
C
$$2 y^2=\left(\frac{d y}{d x}\right)^2\left[x-\frac{1}{4 y}\left(\frac{d y}{d x}\right)^2\right]^2$$
D
$$8 y^2=\left(\frac{d y}{d x}\right)^2\left[x-\frac{1}{4 y}\left(\frac{d y}{d x}\right)^2\right]^2$$
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