Assertion and Reason Questions for Class 9 Maths Chapter 2 Polynomials

Here we are providing assertion reason questions for class 9 maths. In this article, we are covering assertion reason questions for class 9 Maths Chapter 2 Polynomials. Solutions are also provided. Students are suggested to solve the questions by themselves. After completing all questions, refer to answers and solutions for better understanding.

Assertion and Reason Questions for Class 9 Maths Chapter 2 Polynomials

Directions: Choose the correct answer out of the following choices :
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

Q.1. Assertion : 3x² + x – 1 = (x + 1) (3x – 2) + 1.
Reason : To factorise ax² + bx + c, write b as sumof two numbers whose product is ac.

Answer

Answer: (a)

Q.2. Assertion : The value of 593 × 607 is 359951.
Reason : (a + b) (a – b) = a² – b²

Answer

Answer: (a)

Q.3. Assertion : The degree of the polynomial(x² – 2)(x – 3)(x + 4) is 3.
Reason : A polynomial of degree 3 is called a cubic polynomial.

Answer

Answer: (d)

Q.4. Assertion : The expression 3x⁴ – 4x^3/2 + x² = 2is not a polynomial because the term – 4x^3/2 contains a rational power of x.
Reason : The highest exponent in various terms of an algebraic expression in one variable is called its degree.

Answer

Answer: (b)

Q.5.. Assertion : If 2x² – 32 is the volume of a cuboid, then length of cuboid can be x – 8.
Reason : Volume of a cuboid = l × b × h.

Answer

Answer: (d)

Q.6. Assertion : –7 is a constant polynomial.
Reason : Degree of a constant polynomial is zero.

Answer

Answer: (a)

Questions for practice:

Directions:
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false.
(d) Assertion is false but reason is true

1. Assertion : If f(x) = 3x⁷ – 4x⁶ + x + 9 is a polynomial, then its degree is 7.
Reason : Degree of a polynomial is the highest power of the variable in it.

Answer

Answer:

2. Assertion : (x + 2) and (x – 1) are factors of the polynomial x⁴ + x³ + 2x² + 4x – 8.
Reason : For a polynomial p(x) of degree ≥ 1, x – a is a factor of the polynomial p(x) if and only if p(a) ≥1 .

Answer

Answer:

3. Assertion : 3x² + x – 1 = (x + 1)(3x – 2x) + 1.
Reason : If p(x) and g(x) are two polynomials such that degree of p(x) ≥ degree of g(x) and g(x) ≥ 0 then we can find polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x) , where r(x) = 0 of degree of r(x) <degree of g(x).

Answer

Answer:

4. Assertion : (x + 2) is a factor of x³ + 3x²+ 5x + 6 . and of 2x + 4
Reason : If p(x)be a polynomial of degree greater than or equal to one, then (x – a) is a factor of p(x), if p(a) = 0

Answer

Answer:

5. Assertion : The remainder when p(x) = x³ – 6x² + 2x – 4 is divided by (3x – 1) is – 107/27.
Reason : If a polynomial p(x) is divided by ax –b , the remainder is the value of p(x) at x = b/a.

Answer

Answer:

6. Assertion : If (x + 1) is a factor of f(x) = x² + ax + 2 then a = – 3 .
Reason : If (x – a ) is a factor of p(x), if p(a) = 0.

Answer

Answer:

7. Assertion : If f(x) = x⁴ + x³ – 2x² + x + 1 is divided by (x – 1) , then its remainder is 2.
Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x – a , then the remainder is p(- a ) .

Answer

Answer:

8. Assertion : The degree of the polynomial (x – 2 )(x – 3 )(x + 4) is 4.
Reason : The number of zeroes of a polynomial is the degree of that polynomial.

Answer

Answer:

9. Assertion : If p(x) = ax + b , a≠ 0 is a linear polynomial, then x = – b/a is the only zero of p(x).
Reason : A linear polynomial has one and only one zero.

Answer

Answer:

What are Assertion Reason Questions?

Certainly, Assertion Reason questions are a specific kind of questions often found in tests, especially in subjects like science and logic. In these questions, there are two statements: one is the Assertion (a statement) and the other is the Reason (an explanation). Your job is to see how these two statements relate to each other and decide if they are both correct or not.

Here’s a breakdown of the structure of an Assertion Reason question:

Assertion: The Assertion is a statement presented as a fact or claim. It may be true or false, and it is typically written in a straightforward manner.
Reason: The Reason is a statement that provides an explanation or justification for the Assertion. It can support or challenge the Assertion, depending on the accuracy of the Reasoning provided.
Options: Multiple options are typically provided alongside the Assertion Reason pair. The test-taker must choose the correct option that reflects the logical relationship between the Assertion and the Reason.

The possible options typically include:

a) If both the Assertion and the Reason are true, and the Reason is a correct explanation of the Assertion.

b) If both the Assertion and the Reason are true, but the Reason is not a correct explanation of the Assertion.

c) If the Assertion is true, but the Reason is false.

d) If the Assertion is false, but the Reason is true.

e) If both the Assertion and the Reason are false.

To answer Assertion Reason questions correctly, the test-taker needs to analyze the accuracy and logical connection between the two statements. It requires critical thinking, reasoning abilities, and a thorough understanding of the subject matter.

It is important to note that Assertion Reason questions can be challenging, as the test-taker needs to evaluate both statements independently and then determine the relationship between them. Careful reading, logical reasoning, and knowledge of the subject are essential for accurately answering such questions.

Preparation Tips to Score More in Assertion Reason Questions for Class 9 Maths

Assertion-reasoning questions can be daunting for CBSE students as they demand a deeper grasp and analytical thinking compared to regular multiple-choice queries. Such questions have two parts: an assertion and a reason. Students must decide if both are true and if the reason supports the assertion.

These questions go beyond rote knowledge, needing understanding of connections between facts. Fear might arise if students lack confidence in analyzing and judging the data. Also, their significant marks can intensify exam pressure.

However, with practice and a solid understanding of the concepts, students can overcome their fear of assertion-reasoning questions and perform well on their exams. It is important for students to read the questions carefully, understand the meaning of each statement, and analyze the relationship between the two statements before selecting their answer.

Preparing for assertion-reasoning questions can be challenging, but by adopting effective strategies, you can enhance your abilities and excel in exams. Here’s how you can prepare:

Understand the Concepts
Practice Regularly
Develop Analytical Skills
Take Notes
Seek Help

By following these strategies and putting in the effort to practice, you can improve your skills and perform well on assertion-reasoning questions.

Assertion and Reason Questions for Class 9 Maths Chapter 2 Polynomials

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