CBSE Class 9 Maths Chapter 2: Introduction to Linear Polynomials — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 2: Introduction to Linear Polynomials from the NCERT Class 9 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Assertion & Reason Questions
1
Assertion (A): A non-zero polynomial of degree one is called a linear polynomial.
Reason (R): Its highest power of the variable is one.
Reason (R): Its highest power of the variable is one.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Degree is defined by the highest exponent with a non-zero coefficient.
2
Assertion (A): Terms and coefficients are components of an algebraic expression.
Reason (R): A univariate polynomial involves only one variable and its non-negative integral powers.
Reason (R): A univariate polynomial involves only one variable and its non-negative integral powers.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are correct, but the definition of a univariate polynomial does not explain the roles of terms and coefficients.
3
Assertion (A): The expression 5 - 4y is a linear polynomial in y.
Reason (R): Its degree is four because the coefficient of y has magnitude 4.
Reason (R): Its degree is four because the coefficient of y has magnitude 4.
Answer: (c)
A is true, but R is false. Degree depends on the exponent of the variable, which is one, not on the coefficient.
4
Assertion (A): The expression x(10 - x) is a linear polynomial.
Reason (R): After expansion it becomes 10x - x^2, which has degree two.
Reason (R): After expansion it becomes 10x - x^2, which has degree two.
Answer: (d)
A is false, but R is true. The non-zero x^2 term makes the expression quadratic.
5
Assertion (A): A linear number pattern has a constant difference between consecutive terms.
Reason (R): Adding the same fixed amount at each step produces that constant difference.
Reason (R): Adding the same fixed amount at each step produces that constant difference.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Repeated addition creates linear growth or decay depending on the sign of the amount.
6
Assertion (A): Linear growth increases by a fixed amount over equal intervals.
Reason (R): Linear decay decreases by a fixed amount over equal intervals.
Reason (R): Linear decay decreases by a fixed amount over equal intervals.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both definitions are correct, but the definition of decay does not explain growth.
7
Assertion (A): An arithmetic sequence is an example of a linear pattern.
Reason (R): Each new term in every linear pattern is obtained by multiplying the previous term by a fixed number.
Reason (R): Each new term in every linear pattern is obtained by multiplying the previous term by a fixed number.
Answer: (c)
A is true, but R is false. A linear pattern is characterised by a fixed difference, not a fixed ratio.
8
Assertion (A): An expression containing x^-1 is a polynomial in x.
Reason (R): Polynomial exponents are non-negative integers.
Reason (R): Polynomial exponents are non-negative integers.
Answer: (d)
A is false, but R is true. A negative exponent places the variable in a denominator and violates the polynomial definition.
9
Assertion (A): The graph of y = ax + b is a straight line when a and b are constants.
Reason (R): The constant a gives the slope and b gives the y-intercept.
Reason (R): The constant a gives the slope and b gives the y-intercept.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. A constant rate of change produces a straight-line graph with those parameters.
10
Assertion (A): For p(x) = ax + b, the graph crosses the y-axis at (0, b).
Reason (R): The x-intercept is found by solving p(x) = 0.
Reason (R): The x-intercept is found by solving p(x) = 0.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true intercept facts, but the method for finding the x-intercept does not explain the y-intercept.
11
Assertion (A): A positive slope represents linear growth as x increases.
Reason (R): A negative slope also represents linear growth for increasing x.
Reason (R): A negative slope also represents linear growth for increasing x.
Answer: (c)
A is true, but R is false. A negative slope makes y decrease as x increases and therefore represents linear decay.
12
Assertion (A): The line y = 3x + 2 passes through the origin.
Reason (R): A line of the form y = ax passes through the origin.
Reason (R): A line of the form y = ax passes through the origin.
Answer: (d)
A is false, but R is true. Substituting x = 0 into y = 3x + 2 gives y = 2, not zero.
13
Assertion (A): The slope of a line through two points can be found by dividing the change in y by the change in x.
Reason (R): Slope measures the constant rate of change in a linear relationship.
Reason (R): Slope measures the constant rate of change in a linear relationship.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The ratio of coordinate changes gives that rate.
14
Assertion (A): If b = 0 in y = ax + b, the line passes through the origin.
Reason (R): A positive value of a produces a rising line from left to right.
Reason (R): A positive value of a produces a rising line from left to right.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are correct, but the sign of the slope does not explain why a zero intercept places the line through the origin.
15
Assertion (A): A non-zero constant polynomial has degree zero.
Reason (R): Every constant polynomial is therefore a linear polynomial.
Reason (R): Every constant polynomial is therefore a linear polynomial.
Answer: (c)
A is true, but R is false. A linear polynomial has degree one, not zero.
16
Assertion (A): Every linear polynomial must involve exactly two variables.
Reason (R): A linear polynomial studied here is a degree-one polynomial in one variable.
Reason (R): A linear polynomial studied here is a degree-one polynomial in one variable.
Answer: (d)
A is false, but R is true. Expressions such as 2x + 3 are linear polynomials in a single variable.
17
Assertion (A): Two distinct non-vertical lines with the same slope are parallel.
Reason (R): Changing only the y-intercept shifts a line without changing its inclination.
Reason (R): Changing only the y-intercept shifts a line without changing its inclination.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Equal slopes give equal inclination, while different intercepts keep the lines distinct.
18
Assertion (A): The graph of a linear polynomial is a straight line.
Reason (R): The zero of ax + b, with a non-zero, is x = -b/a.
Reason (R): The zero of ax + b, with a non-zero, is x = -b/a.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both facts are correct, but the root formula does not explain why the graph is straight.
19
Assertion (A): Parallel lines of the form y = ax + b have the same slope.
Reason (R): Two lines with different slopes are always parallel.
Reason (R): Two lines with different slopes are always parallel.
Answer: (c)
A is true, but R is false. Different slopes give different inclinations, so the lines intersect unless a special non-Euclidean context is introduced.
20
Assertion (A): The expression p(x) = ax + b remains a linear polynomial when a = 0.
Reason (R): For p(x) to have degree one, the coefficient a must be non-zero.
Reason (R): For p(x) to have degree one, the coefficient a must be non-zero.
Answer: (d)
A is false, but R is true. When a = 0, the polynomial becomes constant rather than linear.
❓ Frequently Asked Questions
What is covered in CBSE Class 9 Maths Chapter 2 Introduction to Linear Polynomials?
This chapter covers all key topics from Introduction to Linear Polynomials as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 9 board exam preparation covering the complete syllabus.
Are these CBSE Class 9 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 9 Maths?
All chapters of CBSE Class 9 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
Can I study Introduction to Linear Polynomials online for free?
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