Differential Equations PYQs - Last 5 Years

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All Differential Equations PYQs Last 10 Years Create chapter test

Practice 190 MHT CET Mathematics questions from Differential Equations. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 5 Years Differential Equations Questions

Showing 40 of 190 filtered questions.

1Differential Equations

If $\cos x \frac{\mathrm{~d} y}{\mathrm{~d} x}-y \sin x=6 x, 0 < x < \frac{\pi}{2}$, then general solution of the differential equation is

2Differential Equations

A radio-active substance has a half-life of h days, then its initial decay rate is given by (where radio-active substance has initial mass $\mathrm{m}_0$)

3Differential Equations

The general solution of $\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{x+y+1}{x+y-1}$ is

4Differential Equations

The order of the differential equation, whose general solution is given by
\(y=\left(c_1+c_2\right) \cos \left(x+c_3\right)-c_4 e^{x+c 5}\)
where $c_1, c_2, c_3, c_4$ and $c_5$ are arbitrary constant, is

5Differential Equations

A spherical rain drop evaporates at a rate proportional to its surface area. If initially its radius is 3 mm and after 1 second it is reduced to 2 mm , then at any time t its radius is (where $0 \leq \mathrm{t}<3$)

6Differential Equations

The general solution of the differential equation $\mathrm{e}^{y-x} \frac{\mathrm{~d} y}{\mathrm{~d} x}=y\left(\frac{\sin x+\cos x}{1+y \log y}\right)$ is

7Differential Equations

The particular solution of the differential equation \(\left(1+y^2\right) \mathrm{d} x-x y \mathrm{~d} y=0\) at \(x=1, y=0\), represents

8Differential Equations

The differential equation of all parabolas, whose axes are parallel to \(\mathrm{Y}\)-axis, is

9Differential Equations

The differential equation of all circles which pass through the origin and whose centres lie on \(\mathrm{Y}\)-axis is

10Differential Equations

General solution of the differential equation \(\log \left(\frac{d y}{d x}\right)=a x+b y\) is

11Differential Equations

The differential equation of \(y=\mathrm{e}^x(\mathrm{a} \cos x+\mathrm{b} \sin x)\) is

12Differential Equations

The money invested in a company is compounded continuously. If ₹ 200 invested today becomes ₹ 400 in 6 years, then at the end of 33 years it will become ₹

13Differential Equations

General solution of the differential equation \(\cos x(1+\cos y) \mathrm{d} x-\sin y(1+\sin x) \mathrm{d} y=0\) is

14Differential Equations

The differential equation representing the family of curves \(y^2=2 \mathrm{c}(x+\sqrt{\mathrm{c}})\), where \(\mathrm{c}\) is a positive parameter, is of

15Differential Equations

If a body cools from \(80^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\) in the room temperature of \(25^{\circ} \mathrm{C}\) in 30 minutes, then the temperature of the body after 1 hour is

16Differential Equations

If the slope of the tangent of the curve at any point is equal to \(-y+\mathrm{e}^{-x}\), then the equation of the curve passing through origin is

17Differential Equations

A right circular cone has height \(9 \mathrm{~cm}\) and radius of base \(5 \mathrm{~cm}\). It is inverted and water is poured into it. If at any instant, the water level rises at the rate $$\frac{\pi}{\mathrm{A}} \mathrm{cm} / \mathrm{sec}$...

18Differential Equations

The particular solution of differential equation \(\mathrm{e}^{\frac{d y}{d x}}=(x+1), y(0)=3\) is

19Differential Equations

Rate of increase of bacteria in a culture is proportional to the number of bacteria present at that instant and it is found that the number doubles in 6 hours. The number of bacteria becomes ________ times at the end of 18 hours.

20Differential Equations

The solution of the differential equation \(\mathrm{e}^{-x}(y+1) \mathrm{d} y+\left(\cos ^2 x-\sin 2 x\right) y \mathrm{~d} x=0\) at \(x=0\), \(y=1\) is

21Differential Equations

A radioactive substance, with initial mass \(m_0\), has a half-life of \(h\) days. Then, its initial decay rate is given by

22Differential Equations

The solution of \((1+x y) y d x+(1-x y) x d y=0\) is

23Differential Equations

If \(x d y=y(d x+y d y), y(1)=1, y(x)>0\), then \(y(-3)\) is

24Differential Equations

If \(\frac{\mathrm{d} y}{\mathrm{~d} x}=y+3\) and \(y(0)=2\), then \(y(\log 2)=\)

25Differential Equations

The differential equation \(\cos (x+y) \mathrm{d} y=\mathrm{d} x\) has the general solution given by

26Differential Equations

The decay rate of radio active material at any time \(t\) is proportional to its mass at that time. The mass is 27 grams when \(t=0\). After three hours it was found that 8 grams are left. Then the substance left after one more hour is

27Differential Equations

If \((2+\sin x) \frac{\mathrm{d} y}{\mathrm{~d} x}+(y+1) \cos x=0\) and \(y(0)=1\), then \(y\left(\frac{\pi}{2}\right)\) is

28Differential Equations

Water flows from the base of rectangular tank, of depth 16 meters. The rate of flow of the water is proportional to the square root of depth at any time \(\mathrm{t}\). If depth is \(4 \mathrm{~m}\) when \(\mathrm{t}=2\) hours, then after 3...

29Differential Equations

The solution of \(\mathrm{e}^{y-x} \frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{y(\sin x+\cos x)}{(1+y \log y)}\) is

30Differential Equations

A curve passes through the point \(\left(1, \frac{\pi}{6}\right)\). Let the slope of the curve at each point \((x, y)\) be \(\frac{y}{x}+\sec \left(\frac{y}{x}\right), x>0\), then, the equation of the curve is

31Differential Equations

The solution of the differential equation \(\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{1+y^2}{1+x^2}\) is

32Differential Equations

The solution of the differential equation \(\frac{\mathrm{d} y}{\mathrm{~d} x}+\frac{y}{x}=\sin x\) is

33Differential Equations

The solution of \(\frac{\mathrm{d} x}{\mathrm{~d} y}+\frac{x}{y}=x^2\) is

34Differential Equations

General solution of the differential equation \(\cos x(1+\cos y) \mathrm{d} x-\sin y(1+\sin x) \mathrm{d} y=0\) is

35Differential Equations

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

36Differential Equations

The population \(\mathrm{P}=\mathrm{P}(\mathrm{t})\) at time \(\mathrm{t}\) of certain species follows the differential equation \(\frac{d P}{d t}=0.5 P-450\). If \(P(0)=850\), then the time at which population becomes zero is

37Differential Equations

The differential equation of all circles, passing through the origin and having their centres on the \(\mathrm{X}\)-axis, is

38Differential Equations

The general solution of the differential equation \(\frac{\mathrm{d} y}{\mathrm{~d} x}+\left(\frac{3 x^2}{1+x^3}\right) y=\frac{1}{x^3+1}\) is

39Differential Equations

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.)

40Differential Equations

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