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

## NCERT Solutions for Class 12 Maths Chapter 1 – Free PDF Download

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions provides solutions for all the questions enlisted under the chapter, which is included in the CBSE syllabus 2023-24. All exercise questions are solved using a step-by-step approach. Solving the questions from the Class 12 Maths NCERT textbook helps grasp the concepts correctly. Students can download and go through these NCERT Solutions for Class 12 Maths to sharpen their Maths skills.

Students should understand not only the basics of this chapter but also the advanced portions to get a command over the chapter Relations and Functions. Practising these NCERT Solutions for Class 12 Maths will help the students in their exam preparation in such a way that they will find even the difficult questions from this chapter to be extremely easy. Download the NCERT Solutions PDF of this chapter from the link provided below.

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

### Access Answers of Class 12 NCERT Maths Chapter 1 Relations and Functions                                                              Also Access NCERT Exemplar for Class 12 Maths Chapter 1 CBSE Notes for Class 12 Maths Chapter 1

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

In NCERT Class 12 Maths Chapter 1, students study different types of relations and equivalence relations, composition of functions, invertible functions and binary operations. Students can utilise the NCERT Solutions for Class 12 Maths Chapter 1 for any quick reference to comprehend complex topics.

The main features of this chapter are as follows:

• Empty relation
• Universal relation
• Reflexive relation
• Symmetric relation
• Transitive relation
• Equivalence relation
• A function f: X → Y is one-one (or injective) if f (x1) = f(x2) ⇒ x1 = x2 ∀ x1, x2 ∈ X.
• A function f: X → Y is onto (or surjective) if given any y ∈ Y, ∃ x ∈ X such that f(x) = y.
• A function f: X → Y is one-one and onto (or bijective), if f is both one-one and onto.
• A function f: X → Y is invertible if and only if f is one-one and onto.

NCERT Solutions For Class 12 Maths Chapter 1 Exercises:

Get detailed solutions for all the questions listed under the below exercises:

Exercise 1.1 Solutions : 16 Questions (14 Short Answers, 2 MCQ)

Exercise 1.2 Solutions : 12 Questions (10 Short Answers, 2 MCQ)

Exercise 1.3 Solutions : 14 Questions (12 Short Answers, 2 MCQ)

Exercise 1.4 Solutions : 13 Questions (12 Short Answers, 1 MCQ)

Miscellaneous Exercise Solutions: 19 Questions (7 Long answers, 9 Short Answer Type, 3 MCQs)

The main topics covered in this chapter include:

 Exercise Topic 1.1 Introduction 1.2 Types of Relations 1.3 Types of Functions 1.4 Composition of Functions and Invertible Function 1.5 Binary Operations Others Miscellaneous Q&A

### Key Features of NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

1. These NCERT exercises are meticulously solved by subject experts.
2. Simple and easy language is used.
3. All questions are solved with the best possible explanations given.
4. These NCERT Solutions are a valuable help to students in their assignments and competitive exams.

Students can also access the NCERT Solutions for Class 12 of any subject while preparing for the board examinations apart from Mathematics. All the solutions are in accordance with the latest CBSE Syllabus and guidelines.

Disclaimer –

Dropped Topics – 1.4 Composition of Functions and Invertible Function (upto ‘This leads to the following definition’), Page 13-14 Full Pages, Page 15 Examples 24 and 25, Page 16-25 Full Pages, Page 26 Question 12 and 13, Page 27-28 Examples 45 and 49, Page 29-31 Ques. 1–3, 6–7, 9, 11–14, 18–19, Page 31-32 Summary points 11-13 and 15-19.

## Frequently Asked Questions on NCERT Solutions for Class 12 Maths Chapter 1

Q1

### What are the concepts explained in NCERT Solutions for Class 12 Maths Chapter 1?

The concepts covered in the NCERT Solutions for Class 12 Maths Relations and Functions are types of relations, types of functions, the composition of functions and invertible functions and binary operations. The solutions to the exercise-wise problems are solved by a set of highly experienced faculty members. The main objective of providing solutions is to help students score well in Class 12 Maths board exams.
Q2

### What are the key features of NCERT Solutions for Class 12 Maths Chapter 1?

The NCERT exercises are solved by the subject matter experts having vast knowledge about the important concepts. Each and every step is explained in easy and simple language to help students grasp the method of solving complex problems effortlessly. The solutions are solved in a stepwise manner based on the marks weightage of the CBSE exam.
Q3

### Are NCERT Solutions for Class 12 Maths Chapter 1 enough to prepare for the CBSE exams?

Chapter 1-Relations and Functions, covers all the important topics based on the latest update of CBSE guidelines. There are four exercises in this chapter, providing the students with numerous problems to solve independently. The solutions are designed in such a way as to boost the confidence in the minds of students before appearing for the CBSE exams.