Differential equations is an important topic in the Mathematics section in MHT CET exam. Practising this topic will increase your score overall and make your conceptual grip on MHT CET exam stronger.
This article gives you a full set of MHT CET PYQs for Differential equations with explanations for effective preparation. Practice of MHT CET Mathematics PYQs including Differential equations questions regularly will improve accuracy, speed, and confidence in the MHT CET 2026 exam.
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MHT CET PYQs for Differential equations with Solutions
1.
Find the differential equation of the family of all circles, whose center lies on the x-axis and touches the y-axis at the origin.- \( 2xy \frac{dy}{dx} = y^2 - x^2 \)
- \( 2xy \frac{dy}{dx} = x^2 - y^2 \)
- \( x^2 + y^2 = 2xy \frac{dy}{dx} \)
- \( x^2 + y^2 = 2y \frac{dy}{dx} \)
2.
Let \( X \) be the discrete random variable representing the number (\( x \)) appeared on the face of a biased die when it is rolled. The probability distribution of \( X \) is as follows: \[ X = x: \quad 1, \, 2, \, 3, \, 4, \, 5, \, 6 \] \[ P(X = x): \quad 0.1, \, 0.15, \, 0.3, \, 0.25, \, k, \, k \] The variance of \( X \) is:- \( 1.64 \)
- \( 1.93 \)
- \( 2.16 \)
- \( 2.28 \)
3.
The particular solution of the differential equation \(e \frac{dy}{dx} = (x + 1)\), \(y(0) = 3\), is:- \(y = x\log(x) - x + 2\)
- \(y = (x + 1)\log(x + 1) - x + 3\)
- \(y = (x + 1)\log(x + 1) + x - 3\)
- \(y = x\log(x) + x - 2\)
4.
The general solution of the differential equation x2 + y2 – 2xy \(\frac {dy}{dx}\) = 0 is (where C is a constant of integration.)
2(x2 – y2) + x = C
x2 + y2 = Cy
x2 – y2 = Cx
x2 + y2 = Cx
5.
Let \( \vec{a} = \hat{i} + \hat{j} + \hat{k}, \, \vec{b} = \hat{i} + 3\hat{j} + 5\hat{k} \) and \( \vec{c} = 7\hat{i} + 9\hat{j} + 11\hat{k} \). Then the area of a parallelogram having diagonals \( \vec{a} + \vec{b} \) and \( \vec{b} + \vec{c} \) is:- \( 4\sqrt{6} \, \text{sq units} \)
- \( 4\sqrt{6} \, \text{sq units} \)
- \( \sqrt{6} \, \text{sq units} \)
- \( 6\sqrt{6} \, \text{sq units} \)
6.
The differential equation dy/dx=√1-y2/y determines a family of circles with
(A) Variable radius and fixed centre at (0,1)
(B) Variable radius and fixed centere at (0,-1)
(C) Fixed radius of 1 Unit and variable centre along the X-axis
(D) Fixed radius of 1 Unit and variable centre along the X- axis
7.
The maximum value of \(\frac{\log(x)}{x}\) is:- \(\frac{2}{e}\)
- \(e\)
- 7
- \(\frac{1}{e}\)
8.
If surrounding air is kept at 20 °C and body cools from 80 °C to 70 °C in 5 minutes, then the temperature of the body after 15 minutes will be
- 54.7 °C
- 51.7 °C
- 52.7 °C
- 50.7 °C
9.
The line whose vector equations are \(\vec{r}_1 = 2\hat{i} - 3\hat{j} + 7\hat{k} + \lambda(2\hat{i} + p\hat{j} + 5\hat{k})\) and \(\vec{r}_2 = \hat{i} + 2\hat{j} + 3\hat{k} + \mu(3\hat{i} - p\hat{j} + p\hat{k})\) are perpendicular for all values of \(\lambda\) and \(\mu\). The value of \(p\) is:- \( -1 \)
- \( 2 \)
- \( 5 \)
- \( 6 \)
10.
Find the solution $ \frac{d^2y}{dm^2} - k^3 \frac{dy}{dm} = y \cos m, \quad y(0) = 1 $- \( y^3 = 3y^3 \sin m \)
- \( y^3 = 3x^2 \sin m \)
- \( y^4 = 3y^3 \sin m \)
- \( y^3 = 5y^3 \sin m \)
11.
The general solution of the differential equation \( \frac{dy}{dx} = 3x^2 \) is:- \( y = x^3 + C \)
- \( y = 3x^3 + C \)
- \( y = \frac{3}{2} x^3 + C \)
- \( y = x^3 + 3C \)
12.
If the curve \(y^2 = 6x\) and \(9x^2 + by^2 = 16\) intersect each other at right angles, then the value of \(b\) is:- \(\frac{9}{2}\)
- \(4\)
- \(6\)
- \(\frac{7}{2}\)
13.
The general solution of differential equation \(e^{\frac {1}{2} (\frac {dy}{dx})}\) = 3x is (where C is a constant of integration.)
x = (log 3)y2 + C
y = x2log 3 + C
- y = xlog 3 + C
- y = 2xlog 3 + C
14.
General Solution of the differential equation:
\(cos\,x(1+cos\,y)dx-sin\,y(1+sin\,x)dy=0\) is:- \((1+cos\,x)(1+sin\,y)\)= c
- \(1+sin\,x+cos\,y=c\)
\((1+sin\,x)(1+cos\,y)=c\)
- \(1+sin\,x.cos\,y=c\)
15.
For the differential equation [1 + \((\frac {dy}{dx})^2\)]5/2 = 8 \((\frac {d^2y}{dx^2})\) has the order and degree_________respectively.
- 2 and 6
- 2 and 3
- 2 and 2
- 2 and 1
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