Last Updated on August 26, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 9 maths. 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 9 maths. In this article, you will find assertion reason questions for CBSE Class 9 Maths Chapter 1 Number Systems. It is a part of Assertion Reason Questions for CBSE Class 9 Maths Series.

Chapter | Number Systems |

Type of Questions | Assertion Reason Questions |

Nature of Questions | Competency Based Questions |

Board | CBSE |

Class | 9 |

Subject | Maths |

Useful for | Class 9 Studying Students |

Answers provided | Yes |

Difficulty level | Mentioned |

Important Link | Class 9 Maths Chapterwise Assertion Reason |

### Assertion Reason Questions on Number Systems

**Questions**:

Q. 1. Assertion (A): The rationalising factor of $8-\sqrt{7}$ is $8+\sqrt{7}$.

Reason (R): If the product of two irrational numbers is rational, then each one is said to be the rationalising factor of the other.

Q. 2. Assertion (A): The sum of two irrational numbers $3-\sqrt{5}$ and $5+\sqrt{5}$ is rational number.

Reason (R): The sum of two irrational numbers is always an irrational number.

Q. 3. Assertion (A): The simplified form of $7^4 \times 7^5$ is $7^{20}$.

Reason (R): If $a>0$ be a real number and $p$ and $q$ be rational numbers. Then $a^p \times a^q=a^{p+q}$.

**Solutions:**

1. (a) Assertion (A): It is true that the rationalising factor of $8-\sqrt{7}$ is $8+\sqrt{7}$.

Reason (R): It is true to say that each one is rationalising factor in the product of two irrational numbers.

Hence, both Assertion (A) and Reason (R) are true and Reason $(R)$ is the correct explanation of Assertion (A).

2. (c) Assertion (A): Here, $3-\sqrt{5}+5+\sqrt{5}=8$, which is a rational number.

So, Assertion (A) is true.

Reason (R): It is not always true to say that sum of two irrational number is always an irrational number.

Hence, Assertion (A) is true but Reason (R) is false.

3. (d) Assertion (A) is false but Reason (R) is true.

### Also check

- Polynomials Class 9 Assertion Reason Questions Maths Chapter 2
- Number Systems Class 9 Assertion Reason Questions Maths Chapter 1

### Topics from which assertion reason questions may be asked

- Representation on number line
- Concept of rationalizing the denominator
- Rationalizing the denominator of expressions with square roots
- Applying the laws of exponents to simplify expressions
- Rationalizing surds

The sum or difference of a rational number and an irrational number is irrational.

The product or quotient of a non-zero rational number with an irrational number is irrational.

Assertion reason questions from the above given topic may be asked.

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### Frequently Asked Questions (FAQs) on Number Systems Assertion Reason Questions Class 9

#### Q1: What are assertion reason questions?

A1: Assertion-reason questions consist of two statements: an assertion (A) and a reason (R). The task is to determine the correctness of both statements and the relationship between them. The options usually include:

(i) Both A and R are true, and R is the correct explanation of A.

(ii) Both A and R are true, but R is not the correct explanation of A.

(iii) A is true, but R is false.

(iv) A is false, but R is true. or A is false, and R is also false.

#### Q2: Why are assertion reason questions important in Maths?

A2: Students need to evaluate the logical relationship between the assertion and the reason. This practice strengthens their logical reasoning skills, which are essential in mathematics and other areas of study.

#### Q3: How can practicing assertion reason questions help students?

A3: Practicing assertion-reason questions can help students in several ways:**Improved Conceptual Understanding:**Â It helps students to better understand the concepts by linking assertions with their reasons.**Enhanced Analytical Skills:**Â It enhances analytical skills as students need to critically analyze the statements and their relationships.**Better Exam Preparation:**Â These questions are asked in exams and practicing them can improve your performance.

#### Q4: What strategies should students use to answer assertion reason questions effectively?

A4: Students can use the following strategies:**Understand Each Statement Separately:**Â Determine if each statement is true or false independently.**Analyze the Relationship:**Â If both statements are true, check if the reason correctly explains the assertion.

#### Q5: What are common mistakes to avoid when answering Assertion Reason questions?

A5: Common mistakes include:

Not reading the statements carefully and missing key details.

Assuming the Reason explains the Assertion without checking the logical connection.

Confusing the order or relationship between the statements.

Overthinking and adding information not provided in the question.

#### Q6: **Are all integers also rational numbers?**

A6: Yes, all integers are rational numbers because they can be expressed as a fraction where the denominator is 1. For example, 5 can be written as 5/1â€‹, making it a rational number.

#### Q7: **What are the key concepts covered in Chapter 1 of CBSE Class 9 Maths regarding number systems?**

**What are the key concepts covered in Chapter 1 of CBSE Class 9 Maths regarding number systems?**A7: Chapter 1 of CBSE Class 9 Maths covers concepts such as understanding rational numbers, irrational numbers and Laws of exponents.

(i) Review of representation of natural numbers and Integers on number line

(ii) Rational numbers on the number line.

(iii) Rational numbers as recurring/ terminating decimals

(iv) Operations on real numbers.

(v) Definition of nth root of a real number

(vi) Law of exponents with integral powers

#### Q8: **Can a number be both rational and irrational?**

**Can a number be both rational and irrational?**A8: No, a number cannot be both rational and irrational. A rational number can be expressed as a fraction of two integers, while an irrational number cannot. They are mutually exclusive categories.

#### Q9: **What are the important keywords for CBSE Class 9 Maths Number Systems?**

A9: List of important keywords given below â€“**Natural Numbers:Â **Positive Counting number starting from 1.**Whole Number:**Â All natural numbers together with 0.**Integers (Z):**Â Set of all whole numbers and negative of natural numbers**Rational Number:**Â Numbers which can be expressed in p/q form, where qÂ **â‰ **Â 0 and p and q are integers.**Fraction:Â **Numbers which can be expressed in form of p/q but are only positive**Equivalent Rational Numbers:**Â Two rational numbers are said to be equivalent, if numerator and denominators of both rational numbers are in proportion or they are reducible to be equal.

#### Q10: **Are there any online resources or tools available for practicing linear equations in one variable assertion reason questions?**

A10: A9: We provide assertion reason questions for CBSE Class 8 Maths on ourÂ website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visitÂ Physics GurukulÂ website. they are having a large collection of case study questions for all classes.