MHT CET 2021 22th September Evening Shift | Differential Equations Question 54 | Mathematics

A spherical raindrop evaporates at a rate proportional to its surface area. If its radius originally is 3 mm. and 1 hour later has been reduced to 2 mm, then the expression of radius r of the raindrop at any time t is (where 0 $$\le$$ t < 3)

r = t + 5

r = t $$-$$ 5

r = 3 $$-$$ t

r = t + 3

MHT CET 2021 22th September Evening Shift

MCQ (Single Correct Answer)

-0

The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is

$$x^2 \frac{d y}{d x}-y=0$$

$$x \frac{d y}{d x}+2 y=0$$

$$x \frac{d y}{d x}+y=0$$

$$2x \frac{d y}{d x}- y=0$$

MHT CET 2021 22th September Evening Shift

MCQ (Single Correct Answer)

-0

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

$$x y=4 x-6$$

$$x y=2 x-2$$

$$x y=x-2$$

$$x y=-x+4$$

MHT CET 2021 22th September Evening Shift

MCQ (Single Correct Answer)

-0

The general solution of $$\frac{d y}{d x}=\frac{x+y}{x-y}$$ is

$$\tan ^{-1} \frac{x}{y}+\frac{1}{2} \log \left|x^2+y^2\right|=c$$

$$\tan ^{-1} \frac{y}{x}+\frac{1}{2} \log \left|x^2+y^2\right|=c$$

$$\tan ^{-1} \frac{y}{x}-\frac{1}{2} \log \left|x^2+y^2\right|=c$$

$$\tan ^{-1} \frac{x}{y}-\frac{1}{2} \log \left|x^2+y^2\right|=c$$

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