MHT CET PYQs for Straight lines with Solutions: Practice MHT CET Previous Year Questions

Educational Content Expert | Updated on - Nov 26, 2025

Straight lines 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 Straight lines with explanations for effective preparation. Practice of MHT CET Mathematics PYQs including Straight lines questions regularly will improve accuracy, speed, and confidence in the MHT CET 2026 exam.

MHT CET PYQs for Straight lines with Solutions

1.
If $ x = a(\cos \theta + \theta \sin \theta), \, y = a(\sin \theta - \theta \cos \theta) $, then $ \frac{d^2 y}{dx^2} $ equals
- $ \frac{\sec^3 \theta}{a \theta} $
- $ \frac{\sec^2 \theta}{a} $
- $ a \theta \cos^3 \theta $
- $ \frac{\sec^2 \theta}{a\theta} $
View Solution
2.
Joint equation of pair of lines through $ (3, - 2) $ and parallel to $ x^2 - 4xy + 3y^2 = 0 $ is
- $ x^2 + 3y^2 - 4xy - 14x + 24y + 45 = 0 $
- $ x^2 + 3y^2 + 4xy- 14x + 24y + 45 = 0 $
- $ x^2 + 3y^2 + 4 xy- 14x + 24y - 45= 0 $
- $ x^2 + 3y^2 + 4xy - 14x - 24y - 45 = 0 $
View Solution
3.
If the slope of one of the lines given by ax² + 2hxy + by² = 0 is two times the other, then
- 8h² = 9ab
- 8h = 9ab
- 8h² = 9ab²
- 8h = 9ab²
View Solution
4.
If $lim_{x \to \infty} (\frac{x^{2} + x + 1}{x + 1} - p x - q) = - 3$ , then $p$ and $q$ is:
- (A) p = 1, q = 3
- (B) p = 2, q = 3
- (C) p = 3, q = 1
- (D) p = 3, q = 2
View Solution
5.
What is the number of different messages that can be represented by three a’s and two b’s?
- (A) 7
- (B) 8
- (C) 9
- (D) 10
View Solution
6.
Find the maximum value of 15sin θ + 20cos θ.
- (A) 25
- (B) 35
- (C) 30
- (D) 5
View Solution
7.
The Points (1,3), (5,1) are Opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line y=2x+c, then one of the vertex on the other diagonal is?
- (1,-2)
- (0,-4)
- (2,0)
- (3,2)
View Solution
8.
The solution of differential equation $d y = (4 + y^{2}) d x$ is:
- (A) $y = 2 \tan (x + C)$
- (B) $y = 2 \tan (2 x + C)$
- (C) $2 y = \tan (2 x + C)$
- (D) $2 y = 2 \tan (x + C)$
View Solution
9.
Find the area bounded between the curve $y = x^{2}$ and $y = x^{3}$ .
- (A) $\frac{1}{2}$
- (B) $\frac{1}{12}$
- (C) $1$
- (D) $\frac{1}{24}$
View Solution
10.
Find the angle between two vectors $(\vec{a} = 2 \hat{i} + \hat{j} - 3 \hat{k})$ and $(\vec{b} = 3 \hat{i} - 2 \hat{j} - \hat{k})$ .
- (A) $- 160^{\circ}$
- (B) $- 60^{\circ}$
- (C) $160^{\circ}$
- (D) $60^{\circ}$
View Solution
11.
Ki are possible values of K for which lines $Kx + 2y + 2 = 0$, $2x + Ky + 3 = 0$, $3x + 3y + K = 0$ are concurrent, then $∑k_i$ has value.
- 0
- -2
- 2
- 5
View Solution
12.
A circle with center $(4, - 5)$ is tangent to the $y$ -axis in the standard $(x, y)$ coordinate plane. What is the radius of this circle?
- (A) $4$
- (B) $5$
- (C) $\sqrt{41}$
- (D) $16$
View Solution
13.
If $\sec^{2} θ + \tan^{2} θ = 3$ then find the value of $\cot θ$ .
- (A) 0
- (B) 1
- (C) 2
- (D) $\sqrt{3}$
View Solution
14.
The joint equation of lines passing through the origin and trisecting the first quadrant is ________
- $x^{2}+\sqrt{3}xy -y^{2} = 0$
- $x^{2}-\sqrt{3}xy -y^{2} = 0$
- $\sqrt{3}x^{2} -4xy +\sqrt{3}y^{2} = 0$
- $3x^{2} -y^{2} = 0 $
View Solution
15.
The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- -11
- 31
- 11
- -31
View Solution

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MHT CET PYQs for Straight lines with Solutions: Practice MHT CET Previous Year Questions

MHT CET PYQs for Straight lines with Solutions

1.
If \( x = a(\cos \theta + \theta \sin \theta), \, y = a(\sin \theta - \theta \cos \theta) \), then \( \frac{d^2 y}{dx^2} \) equals

2.
Joint equation of pair of lines through $ (3, - 2) $ and parallel to $ x^2 - 4xy + 3y^2 = 0 $ is

3.
If the slope of one of the lines given by ax² + 2hxy + by² = 0 is two times the other, then

4.
If $lim_{x \to \infty} (\frac{x^{2} + x + 1}{x + 1} - p x - q) = - 3$ , then $p$ and $q$ is:

5.
What is the number of different messages that can be represented by three a’s and two b’s?

6.
Find the maximum value of 15sin θ + 20cos θ.

7.
The Points (1,3), (5,1) are Opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line y=2x+c, then one of the vertex on the other diagonal is?

8.
The solution of differential equation $d y = (4 + y^{2}) d x$ is:

9.
Find the area bounded between the curve $y = x^{2}$ and $y = x^{3}$ .

10.
Find the angle between two vectors $(\vec{a} = 2 \hat{i} + \hat{j} - 3 \hat{k})$ and $(\vec{b} = 3 \hat{i} - 2 \hat{j} - \hat{k})$ .

11.
Ki are possible values of K for which lines \(Kx + 2y + 2 = 0\), \(2x + Ky + 3 = 0\), \(3x + 3y + K = 0\) are concurrent, then \(∑k_i\) has value.

12.
A circle with center $(4, - 5)$ is tangent to the $y$ -axis in the standard $(x, y)$ coordinate plane. What is the radius of this circle?

13.
If $\sec^{2} θ + \tan^{2} θ = 3$ then find the value of $\cot θ$ .

14.
The joint equation of lines passing through the origin and trisecting the first quadrant is ________

15.
The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is

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MHT CET PYQs for Straight lines with Solutions

1.If \( x = a(\cos \theta + \theta \sin \theta), \, y = a(\sin \theta - \theta \cos \theta) \), then \( \frac{d^2 y}{dx^2} \) equals

2.Joint equation of pair of lines through $ (3, - 2) $ and parallel to $ x^2 - 4xy + 3y^2 = 0 $ is

3.If the slope of one of the lines given by ax2 + 2hxy + by2 = 0 is two times the other, then

4.If limx→∞(x2+x+1x+1−px−q)=−3, then p and q is:

5.What is the number of different messages that can be represented by three a’s and two b’s?

6.Find the maximum value of 15sin θ + 20cos θ.

7.The Points (1,3), (5,1) are Opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line y=2x+c, then one of the vertex on the other diagonal is?

8.The solution of differential equation dy=(4+y2)dx is:

9.Find the area bounded between the curve y=x2 and y=x3.

10.Find the angle between two vectors (a→=2i^+j^−3k^) and (b→=3i^−2j^−k^).

11.Ki are possible values of K for which lines \(Kx + 2y + 2 = 0\), \(2x + Ky + 3 = 0\), \(3x + 3y + K = 0\) are concurrent, then \(∑k_i\) has value.

12.A circle with center (4,−5) is tangent to the y -axis in the standard (x,y) coordinate plane. What is the radius of this circle?

13.If sec2⁡θ+tan2⁡θ=3 then find the value of cot⁡θ.

14.The joint equation of lines passing through the origin and trisecting the first quadrant is ________

15.The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is

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1.
If \( x = a(\cos \theta + \theta \sin \theta), \, y = a(\sin \theta - \theta \cos \theta) \), then \( \frac{d^2 y}{dx^2} \) equals

2.
Joint equation of pair of lines through $ (3, - 2) $ and parallel to $ x^2 - 4xy + 3y^2 = 0 $ is

3.
If the slope of one of the lines given by ax² + 2hxy + by² = 0 is two times the other, then

4.
If $lim_{x \to \infty} (\frac{x^{2} + x + 1}{x + 1} - p x - q) = - 3$ , then $p$ and $q$ is:

5.
What is the number of different messages that can be represented by three a’s and two b’s?

6.
Find the maximum value of 15sin θ + 20cos θ.

7.
The Points (1,3), (5,1) are Opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line y=2x+c, then one of the vertex on the other diagonal is?

8.
The solution of differential equation $d y = (4 + y^{2}) d x$ is:

9.
Find the area bounded between the curve $y = x^{2}$ and $y = x^{3}$ .

10.
Find the angle between two vectors $(\vec{a} = 2 \hat{i} + \hat{j} - 3 \hat{k})$ and $(\vec{b} = 3 \hat{i} - 2 \hat{j} - \hat{k})$ .

11.
Ki are possible values of K for which lines \(Kx + 2y + 2 = 0\), \(2x + Ky + 3 = 0\), \(3x + 3y + K = 0\) are concurrent, then \(∑k_i\) has value.

12.
A circle with center $(4, - 5)$ is tangent to the $y$ -axis in the standard $(x, y)$ coordinate plane. What is the radius of this circle?

13.
If $\sec^{2} θ + \tan^{2} θ = 3$ then find the value of $\cot θ$ .

14.
The joint equation of lines passing through the origin and trisecting the first quadrant is ________

15.
The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is