MHT CET PYQs for Slope of a line with Solutions: Practice MHT CET Previous Year Questions

Content Curator | Updated on - Nov 2, 2026

Slopes of lines is a topic from the Straight Line chapter of Class 12 Mathematics, and it is part of the Mathematics section of the MHT CET for candidates who are preparing for the PCM (Physics, Chemistry, and Mathematics).

The key topics covered in Slopes of lines PYQs are:

Slopes of the lines given by a pair of lines
Sum and product of the slopes
Relation between the slopes

Practising Slopes of lines MHT CET PYQ helps candidates to understand question pattern, improve calculation speed, and identify concepts which were asked in previous exams.

Based on chapter-wise analysis of the MHT CET Mathematics paper, you can get less than 1 mark per paper by covering Slopes of lines. The chapter recorded 2 questions across the 80 shifts in the data, and 2 of them came in the 2025 and 2026 papers, which is fewer than 1 of the 50 Mathematics questions in a typical shift.

MHT CET Slopes of lines Topic: Question Count, Marks and Weightage:

What it shows	Number
Questions in the PDF (2025-2026)	2
Questions in the 2025 and 2026 papers (33 shifts)	2
Questions in the 2018 to 2026 papers (80 shifts)	2
Typical number of Mathematics questions from this topic in one shift	Fewer than 1 out of 50
Marks for each question	2

The PDF holds 2 questions from MHT CET 2026 to 2025, newest first, each with its exam date and shift. Options are as printed and answer keys are not included.

Slopes of lines PYQ Statistics (2022-2026)

The table below shows the number of questions asked in MHT CET Slopes of lines PYQs. Every shift has 50 Mathematics questions, and the last column is the number of questions asked divided by the shifts held, rounded to a whole number.

Year	Questions Asked	Shifts Held	Typical Questions in One Shift
2026	1	16	Fewer than 1 out of 50
2025	1	17	Fewer than 1 out of 50
2024	0	18	Fewer than 1 out of 50
2023	0	12	Fewer than 1 out of 50
2022	0	1	Fewer than 1 out of 50

The 2018 to 2021 papers in the PDF add 0 more questions: 2021 had none, 2020 had none, 2019 had none, 2018 had none.

Pair PYQs with Other Study Material for MHT CET 2027

Click on the link to practise problems and time management skills:

Resource	Link
MHT CET Sample Paper	Check Here
MHT CET Mock Test	Check Here

Question Style in MHT CET Slopes of lines PYQs

Both questions in this PDF are single-correct MCQs on the slopes of the lines represented by a second degree equation.

Question Style	What it Tests
Ratio of slopes	The ratio of the slopes of the lines represented by a given equation
Condition on slopes	The value of an expression when the slopes of the lines satisfy a given condition

How to Use the Slopes of lines PYQ PDF for MHT CET

Start with the 2025 and 2026 papers first, because they hold 2 of the 2 questions.
For the equation ax² + 2hxy + by² = 0, remember that the sum of the slopes is −2h/b and the product is a/b.
Write the condition in the question in terms of the sum and the product of the slopes.
Solve year-wise PYQs by timing yourself, as time management is crucial.
Re-attempt only the questions you got wrong, and note which formula or step you missed.

Video: Slopes of lines PYQs and MCQs

Source: Maths with Sandip sir

Slopes of lines PYQ for MHT CET Mathematics FAQs

Ques. How many questions come from Slopes of lines every year?

Ans. In this PDF, the questions are 1 from 2026 and 1 from 2025. In 2025 and 2026 together the topic had 2 questions across 33 shifts, which is fewer than 1 in a typical shift.

Ques. What kind of questions are asked from Slopes of lines?

Ans. Single-correct MCQs on the slopes of the lines represented by a pair of lines.

Ques. What is the best way to practise Slopes of lines PYQs?

Ans. First solve the 2025 and 2026 questions completely, then the older ones, and finally re-attempt the questions you got wrong.

Ques. Can I score full marks from Slopes of lines?

Ans. In 2025 and 2026 together the topic had 2 questions across 33 shifts. Learning the sum and the product of the slopes of a pair of lines is enough to secure it. Each Mathematics question in MHT CET is worth 2 marks.

Ques. Does the Slopes of lines PYQ PDF include solutions?

Ans. No. The PDF contains the questions with their exam date and shift, without answer keys or solutions.

1.
Form the differential equation of $y = a e^{3 x} \cos (x + b)$ Where $y^{'} = \frac{d y}{d x}$ and $y^{n} = \frac{d^{2} y}{d x^{2}}$ ?
- (A) $y^{''} - 6 y^{'} + 10 y = 0$
- (B) $y^{''} - 6 y^{'} - 10 y = 0$
- (C) $y^{''} + 6 y^{'} - 10 y = 0$
- (D) $y^{''} + 6 y^{'} + 10 y = 0$
View Solution
2.
The slope of the line through the origin which makes an angle of $30^\circ$ with the positive direction of Y-axis measured anticlockwise is :
- $-\frac{2}{3}$
- $-\sqrt{3}$
- $\frac{3}{2}$
- $-\frac{1}{\sqrt{3}}$
View Solution
3.
The angle between the lines $x + y - 3 = 0$ and $x - y + 3 = 0$ is $α$ and the acute angle between the lines $x - \sqrt{3} y + 2 \sqrt{3} = 0$ and $\sqrt{3} x - y + 1 = 0$ is $β$ . Which one of the following is correct?
- (A) $α = β$
- (B) $α > β$
- (C) $α < β$
- (D) $α = 2 β$
View Solution
4.
If the angle between two lines is $\frac{\pi}{4}$ and the slope of one of the lines is $\frac{1}{2}$, then the slope of the other line is
- $3$ or $-\frac{1}{3}$
- $4$ or $-\frac{1}{4}$
- $2$ or $-\frac{1}{2}$
- $3$ or $-3$
View Solution

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MHT CET PYQs for Slope of a line with Solutions: Practice MHT CET Previous Year Questions

Slopes of lines PYQ Statistics (2022-2026)

Pair PYQs with Other Study Material for MHT CET 2027

Question Style in MHT CET Slopes of lines PYQs

How to Use the Slopes of lines PYQ PDF for MHT CET

Video: Slopes of lines PYQs and MCQs

Slopes of lines PYQ for MHT CET Mathematics FAQs

1.
Form the differential equation of $y = a e^{3 x} \cos (x + b)$ Where $y^{'} = \frac{d y}{d x}$ and $y^{n} = \frac{d^{2} y}{d x^{2}}$ ?

2.
The slope of the line through the origin which makes an angle of $30^\circ$ with the positive direction of Y-axis measured anticlockwise is :

3.
The angle between the lines $x + y - 3 = 0$ and $x - y + 3 = 0$ is $α$ and the acute angle between the lines $x - \sqrt{3} y + 2 \sqrt{3} = 0$ and $\sqrt{3} x - y + 1 = 0$ is $β$ . Which one of the following is correct?

4.
If the angle between two lines is $\frac{\pi}{4}$ and the slope of one of the lines is $\frac{1}{2}$, then the slope of the other line is

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Slopes of lines PYQ Statistics (2022-2026)

Pair PYQs with Other Study Material for MHT CET 2027

Question Style in MHT CET Slopes of lines PYQs

How to Use the Slopes of lines PYQ PDF for MHT CET

Video: Slopes of lines PYQs and MCQs

Slopes of lines PYQ for MHT CET Mathematics FAQs

1.Form the differential equation of y=ae3xcos⁡(x+b) Where y′=dydx and yn=d2ydx2?

2.The slope of the line through the origin which makes an angle of $30^\circ$ with the positive direction of Y-axis measured anticlockwise is :

3.The angle between the lines x+y−3=0 and x−y+3=0 is α and the acute angle between the lines x−3y+23=0 and 3x−y+1=0 is β. Which one of the following is correct?

4.If the angle between two lines is $\frac{\pi}{4}$ and the slope of one of the lines is $\frac{1}{2}$, then the slope of the other line is

Comments

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1.
Form the differential equation of $y = a e^{3 x} \cos (x + b)$ Where $y^{'} = \frac{d y}{d x}$ and $y^{n} = \frac{d^{2} y}{d x^{2}}$ ?

2.
The slope of the line through the origin which makes an angle of $30^\circ$ with the positive direction of Y-axis measured anticlockwise is :

3.
The angle between the lines $x + y - 3 = 0$ and $x - y + 3 = 0$ is $α$ and the acute angle between the lines $x - \sqrt{3} y + 2 \sqrt{3} = 0$ and $\sqrt{3} x - y + 1 = 0$ is $β$ . Which one of the following is correct?

4.
If the angle between two lines is $\frac{\pi}{4}$ and the slope of one of the lines is $\frac{1}{2}$, then the slope of the other line is