MHT CET PYQs for Differential Equations with Solutions: Practice MHT CET Previous Year Questions

Updated 3+ months ago

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.

MHT CET PYQs for Differential Equations with Solutions

1.
Find the general solution of the differential equation $ \frac{dy}{dx} + y = e^{-x} $.
- $ y = e^{-x}(x + C) $
- $ y = xe^{-x} + C $
- $ y = e^{x}(x + C) $
- $ y = e^{-x} + C $
View Solution
2.
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 $
View Solution
3.
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} $
View Solution
4.
If $\frac{dy}{dx} = y + 5$ and $y(0) = 4$, then $y(\log 2)$ is equal to
- $13$
- $15$
- $18$
- $9$
View Solution
5.
Find the general solution of the differential equation $\dfrac{dy}{dx} + y\cot x = \csc x$.
- $y\sin x = x + c$
- $y\cos x = x + c$
- $y\sin x = c - x$
- $y\cos x = c + x$
View Solution
6.
Find the general solution of the differential equation $ \dfrac{dy}{dx} + \dfrac{y}{x} = x^2 $.
- $ y = \dfrac{x^3}{4} + \dfrac{C}{x} $
- $ y = \dfrac{x^3}{3} + \dfrac{C}{x} $
- $ y = \dfrac{x^3}{2} + \dfrac{C}{x} $
- $ y = x^3 + \dfrac{C}{x} $
View Solution
7.
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
- $1+sin\,x+cos\,y=c$
- $(1+sin\,x)(1+cos\,y)=c$
- $1+sin\,x.cos\,y=c$
View Solution
8.
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 $
View Solution
9.
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} $
View Solution
10.
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 $
View Solution
11.
The particular solution of the differential equation $e \frac{dy}{dx} = (x + 1)$, $y(0) = 3$, is:
- $y = x\log(x) - x + 2$
- $y = (x + 1)\log(x + 1) - x + 3$
- $y = (x + 1)\log(x + 1) + x - 3$
- $y = x\log(x) + x - 2$
View Solution
12.
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
View Solution
13.
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 $
View Solution
14.
The maximum value of $\frac{\log(x)}{x}$ is:
- $\frac{2}{e}$
- $e$
- 7
- $\frac{1}{e}$
View Solution
15.
If the curve $y^2 = 6x$ and $9x^2 + by^2 = 16$ intersect each other at right angles, then the value of $b$ is:
- $\frac{9}{2}$
- $4$
- $6$
- $\frac{7}{2}$
View Solution

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MHT CET PYQs for Differential Equations with Solutions: Practice MHT CET Previous Year Questions

MHT CET PYQs for Differential Equations with Solutions

1.
Find the general solution of the differential equation \( \frac{dy}{dx} + y = e^{-x} \).

2.
Find the solution $ \frac{d^2y}{dm^2} - k^3 \frac{dy}{dm} = y \cos m, \quad y(0) = 1 $

3.
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.

4.
If $\frac{dy}{dx} = y + 5$ and $y(0) = 4$, then $y(\log 2)$ is equal to

5.
Find the general solution of the differential equation \(\dfrac{dy}{dx} + y\cot x = \csc x\).

6.
Find the general solution of the differential equation \( \dfrac{dy}{dx} + \dfrac{y}{x} = x^2 \).

7.
General Solution of the differential equation:
\(cos\,x(1+cos\,y)dx-sin\,y(1+sin\,x)dy=0\) is:

9.
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:

10.
The general solution of the differential equation \( \frac{dy}{dx} = 3x^2 \) is:

11.
The particular solution of the differential equation \(e \frac{dy}{dx} = (x + 1)\), \(y(0) = 3\), is:

12.
The differential equation dy/dx=√1-y2/y determines a family of circles with

13.
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:

14.
The maximum value of \(\frac{\log(x)}{x}\) is:

15.
If the curve \(y^2 = 6x\) and \(9x^2 + by^2 = 16\) intersect each other at right angles, then the value of \(b\) is:

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MHT CET PYQs for Differential Equations with Solutions

1.Find the general solution of the differential equation \( \frac{dy}{dx} + y = e^{-x} \).

2.Find the solution $ \frac{d^2y}{dm^2} - k^3 \frac{dy}{dm} = y \cos m, \quad y(0) = 1 $

3.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.

4.If $\frac{dy}{dx} = y + 5$ and $y(0) = 4$, then $y(\log 2)$ is equal to

5.Find the general solution of the differential equation \(\dfrac{dy}{dx} + y\cot x = \csc x\).

6.Find the general solution of the differential equation \( \dfrac{dy}{dx} + \dfrac{y}{x} = x^2 \).

7.General Solution of the differential equation:\(cos\,x(1+cos\,y)dx-sin\,y(1+sin\,x)dy=0\) is:

9.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:

10.The general solution of the differential equation \( \frac{dy}{dx} = 3x^2 \) is:

11.The particular solution of the differential equation \(e \frac{dy}{dx} = (x + 1)\), \(y(0) = 3\), is:

12.The differential equation dy/dx=√1-y2/y determines a family of circles with

13.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:

14.The maximum value of \(\frac{\log(x)}{x}\) is:

15.If the curve \(y^2 = 6x\) and \(9x^2 + by^2 = 16\) intersect each other at right angles, then the value of \(b\) is:

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1.
Find the general solution of the differential equation \( \frac{dy}{dx} + y = e^{-x} \).

2.
Find the solution $ \frac{d^2y}{dm^2} - k^3 \frac{dy}{dm} = y \cos m, \quad y(0) = 1 $

3.
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.

4.
If $\frac{dy}{dx} = y + 5$ and $y(0) = 4$, then $y(\log 2)$ is equal to

5.
Find the general solution of the differential equation \(\dfrac{dy}{dx} + y\cot x = \csc x\).

6.
Find the general solution of the differential equation \( \dfrac{dy}{dx} + \dfrac{y}{x} = x^2 \).

7.
General Solution of the differential equation:
\(cos\,x(1+cos\,y)dx-sin\,y(1+sin\,x)dy=0\) is:

9.
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:

10.
The general solution of the differential equation \( \frac{dy}{dx} = 3x^2 \) is:

11.
The particular solution of the differential equation \(e \frac{dy}{dx} = (x + 1)\), \(y(0) = 3\), is:

12.
The differential equation dy/dx=√1-y2/y determines a family of circles with

14.
The maximum value of \(\frac{\log(x)}{x}\) is:

15.
If the curve \(y^2 = 6x\) and \(9x^2 + by^2 = 16\) intersect each other at right angles, then the value of \(b\) is: