Last Updated on April 25, 2025 by XAM CONTENT
Hello students, we are providing assertion reason questions for class 10. Assertion Reason questions are the new question format that is introduced in CBSE board. The resources for assertion reason questions are very less. So, to help students we have created chapterwise assertion reason questions for class 10 maths. In this article, you will find assertion reason questions for CBSE Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables. It is a part of Assertion Reason Questions for CBSE Class 10 Maths Series.
| Chapter | Pair of Linear Equations in Two Variables |
| Type of Questions | Assertion Reason Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 10 |
| Subject | Maths |
| Useful for | Class 10 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 10 Maths Chapterwise Assertion Reason |
Assertion Reason Questions on Pair of Linear Equations in Two Variables
Assertion and Reason Questions
Directions: Each of the following questions consists of two statements: an Assertion (A) and a Reason (R). Answer them by selecting the correct option:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.
Q1. Assertion (A): The pair of equations $2 x+3 y=6$ and $4 x+6 y=12$ has infinitely many solutions.
Reason (R): The two equations represent the same line.
Answer: Option (a) is correct.
Explanation: Both equations are multiples of each other, meaning they represent the same line. Hence, every point on the line is a common solution.
Difficulty Level: Moderate
Q2. Assertion (A): If a pair of linear equations is inconsistent, then it has exactly one solution.
Reason (R): Inconsistent equations represent parallel lines.
Answer: Option (d) is correct.
Explanation: Inconsistent equations represent parallel lines, which never meet, so they have no solution, not one.
Difficulty Level: Moderate
Q3. Assertion (A): The substitution method can be used to solve a pair of linear equations.
Reason (R): In substitution, one variable is expressed in terms of the other.
Answer: Option (a) is correct.
Explanation: This is the basic definition of the substitution method. The variable expression is substituted in the second equation.
Difficulty Level: Easy
Q4. Assertion (A): A pair of linear equations $a x+b y=c$ and $d x+e y=f$ has a unique solution if $\frac{a}{d} \neq \frac{b}{e}$.
Reason (R): The condition implies that the lines intersect at exactly one point.
Answer: Option (a) is correct.
Explanation: If the ratio of coefficients of x and y are not equal, the lines are not parallel and will intersect exactly once.
Difficulty Level: Moderate
Q5. Assertion (A): Graphically, two coincident lines represent a pair of inconsistent equations.
Reason (R): Coincident lines have infinite points of intersection.
Answer: Option (c) is correct.
Explanation: Coincident lines represent consistent equations with infinite solutions, so the assertion is false but the reason is true.
Difficulty Level: Tough
Also check
- Some Applications of Trigonometry Class 10 Assertion Reason Questions Maths Chapter 9
- Introduction to Trigonometry Class 10 Assertion Reason Questions Maths Chapter 8
- Coordinate Geometry Class 10 Assertion Reason Questions Maths Chapter 7
- Triangles Class 10 Assertion Reason Questions Maths Chapter 6
- Arithmetic Progressions Class 10 Assertion Reason Questions Maths Chapter 5
- Quadratic Equations Class 10 Assertion Reason Questions Maths Chapter 4
- Pair of Linear Equations in Two Variables Class 10 Assertion Reason Questions Maths Chapter 3
- Polynomials Class 10 Assertion Reason Questions Maths Chapter 2
- Real Numbers Class 10 Assertion Reason Questions Maths Chapter 1
Topics from which assertion reason questions may be asked
- Graphical Method
- Substitution, Elimination, Cross Multiplication
- Applications
Solving two-variable equations enables us to find intersections and real-life outcomes.
Assertion reason questions from the above given topic may be asked.
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Frequently Asked Questions (FAQs) on Pair of Linear Equations in Two Variables Assertion Reason Questions Class 10
Q1: What does the chapter ‘Pair of Linear Equations in Two Variables’ cover?
A1: It builds key concepts related to pair of linear equations in two variables and prepares you for logical reasoning-based questions.
Q2: What are assertion reason questions?
A2: These consist of two statements: an assertion and a reason. Students need to determine their correctness and relationship.
Q3: Why practice assertion reason questions in Pair of Linear Equations in Two Variables?
A3: They strengthen core concepts and boost confidence in tackling tricky scenarios from pair of linear equations in two variables.
Q4: Are assertion reason questions part of CBSE board exams?
A4: Yes, they are included under competency-based formats to test depth of understanding.
