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# NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions - PDF Download

NCERT Solutions for class 12 maths chapter 1 introduces students to the fundamental concepts of Relations and Functions. Step-by-step instructions are used to solve each question.The chapter is divided into four sections, each of which serves a specific purpose. To improve their knowledge of math chapter 1, students can download and read through these NCERT solutions for Class 12 Math available on eSaral.

To develop a solid command of the Class 12 Maths Relations and Functions, it is advised that students not only comprehend the chapter's fundamentals but also understand  its complex sections. The students' board and competitive examination preparation will benefit from practicing these NCERT Solutions. On the official eSaral website, NCERT Solutions for Class 12 Maths Chapter-1 PDF is available to be downloaded. The relation and function class 12 PDF contains all of the answers to the questions that are included in this NCERT chapter. Here, each topic is properly discussed in Chapter 1 of Math for Class 12. These Relations and Functions Class 12 NCERT Solutions were created by subject-matter specialists at eSaral. Each answer has been developed in a straightforward manner so that students can easily understand it.

## NCERT Solutions for Class 12 Maths Chapter 1 - Relations and Functions I Free PDF

Students learn about several types of relations including equivalence relations, composition of functions, invertible functions, and binary operations in NCERT Class 12 Maths Chapter 1. The NCERT Solutions for Class 12 Maths Chapter 1 can be used by students as a quick reference for learning challenging concepts.

NCERT Solutions for Class 12 Maths Chapter 1 are available here on eSaral for all exercises. When studying Relations and Functions, you may also download this NCERT Solutions PDF to refer to at any time.

### Important Topics Covered in Chapter 1 - Relations and Functions

 Topics 1.1 Introduction 1.2 Types of Relations 1.3 Types of Functions 1.4 Composition of Functions and Invertible Functions

The following are the key concepts covered in this chapter:

1. Empty Relation -  Empty Relation is a relation if relation has no elements

We write R = Ø    ⊂ X×X

1. Universal Relation - If all elements of A is related to every element of A is called universal relation

R = A×A

1. Reflexive Relation - If (a,a)  ∈ R, for every a∈A

2. Symmetric Relation - If (a,b) ∈ R, then (b,a)∈R

3. Transitive Relation - If  (a,b) ∈ R & (b,c) ∈ R, then (a,c) ∈ R

4. Equivalence Relation - If a relation is reflexive, symmetry and transitive it is called equivalence relation.

1. To prove one-one & onto injective, surjective, bijective

2. Composition of Functions and Invertible Functions

## NCERT Solutions for Class 12 Maths Chapter 1 Exercises

Chapter 1 of NCERT Maths Class 12 Book provides a strong foundation in the concepts of relations and functions. By mastering these fundamental principles, students are better equipped to solve more advanced mathematical topics in higher grades and various competitive examinations. The exercises in this chapter play a crucial role in strengthening students' problem-solving abilities, logical reasoning, and mathematical skills. As students progress through the exercises, they will gain confidence in handling mathematical challenges and develop a deeper appreciation for the utility of mathematics.

Chapter 1 Relations and Functions contains three exercises.

 Exercise 1.1 16 Questions & Solutions Exercise 1.2 12 Questions & Solutions Miscellaneous Exercise 7 Questions & Solutions

Utilizing NCERT Solutions Class 12 Maths Chapter 1 Relation and Functions offers a clear and thorough grasp of the subject, which is one of the main advantages. The way the solutions are organized makes it simple for learners to understand the material and get ready for their exams. Additionally, to reflect the most recent modifications to the syllabus and examination formats, the solutions are regularly updated. Utilizing NCERT Solutions Class 12 Maths Chapter 1 Relation and Functions has another significant advantage in that it offers several examples, illustrations, and case studies to aid students in understanding the concepts. Step-by-step explanations of the solutions are also provided in the solutions, which aids students in better comprehending the concepts.

Chapter 1 Relation and Functions, NCERT Solutions for Class 12 Math In order to learn functions and their properties, it is vital to have a solid foundation. For students to succeed in their Class 12 Math exams, it is crucial that they have a solid understanding of the concepts discussed in chapter 1.

There are some of the following additional benefits:

1. The most persuasive reasons are provided for every solution to a question.

2. Students can use these NCERT Solutions to their advantage in assignments and competitive exams.

3. Experts in the subject have carefully solved these NCERT exercises.

Question 1. How many exercises are in Chapter 1 of the NCERT textbook for Class 12 Math?

Answer 1. There are two exercises and one other exercise in Chapter 1 of Class 12 Math, and these exercises are made up of different types of questions.

1. Exercise 1.1
2. Exercise 1.2
3. Miscellaneous Exercise

Question 2. Can you briefly summarize the chapter's main topics and subtopics?

Answer 2. The following list includes the key topics and subtopics covered in this chapter.

1. Introduction
2. Types of Relations
3. Types of Functions
4. Composition of Functions and Invertible Functions