MHT CET 2022 11th August Evening Shift | Differential Equations Question 32 | Mathematics

The general solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{3 x+y}{x-y}$$ is (where $$C$$ is a constant of integration.)

$$\tan ^{-1}\left(\frac{y}{x}\right)+\log \left(\frac{y^2+3 x^2}{x^2}\right)=\log (x)+C$$

$$\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{y}{x \sqrt{3}}\right)+\log \left(\frac{y^2+3 x^2}{x^2}\right)^{\frac{1}{2}}=\log (x)+C$$

$$\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{y}{x \sqrt{3}}\right)-\log \left(\frac{y^2+3 x^2}{x^2}\right)^{\frac{1}{2}}=\log (x)+C$$

$$\tan ^{-1}\left(\frac{x}{y}\right)+\log \left(\frac{y^2+3 x^2}{x^2}\right)=\log (x)+C$$

MHT CET 2022 11th August Evening Shift

MCQ (Single Correct Answer)

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

fixed radius of 1 unit and variable centres along the $$X$$-axis

fixed radius of 1 unit and variable centres along the $$Y$$-axis

variable radii and a fixed centre at $$(0,1)$$

variable radii and a fixed centre at $$(0,-1)$$

MHT CET 2021 22th September Evening Shift

MCQ (Single Correct Answer)

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The degree of the differential equation whose solution is $$y^2=8 a(x+a)$$, is

MHT CET 2021 22th September Evening Shift

MCQ (Single Correct Answer)

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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

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