NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.3 Relations and Functions in Hindi and English Medium for CBSE and State Board. Welcome to our detailed guide on Class 12 Maths Chapter 1 Exercise 1.3. This chapter, an integral part of the Class 12 Mathematics curriculum, delves into the fascinating world of Relations and Functions. Understanding these concepts is crucial for excelling in not just your board exams but also in various competitive exams. Our solutions are crafted to provide you with a clear and thorough understanding of each problem in Exercise 1.3.

## Class 12 Maths Exercise 1.3 Solution in Hindi and English Medium

### NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.3

Grade XII Mathematics ex. 1.3 solutions for CBSE Board, MP Board, UP Board, Bihar and Uttarakhand (UK Board), etc., for academic session 2023-24. NCERT Solutions or UP Board solutions are applicable for all boards who are using NCERT Textbooks for their exams.

**Understanding Relations and Functions**

Before diving into the solutions, it’s essential to grasp the basics of Relations and Functions. This chapter introduces you to the fundamental concepts of mapping pairs of a set and the relationship between two different sets of numbers. It lays the foundation for more complex topics in calculus and algebra.

Class: 12 | Mathematics |

Chapter 1: | Exercise 1.3 |

Topic Name: | Relations and Functions |

Content: | NCERT Exercise Solutions |

Content Mode: | Online Text and Videos Format |

Medium: | English and Hindi Medium |

#### 12th Maths Exercise 1.3 Solutions

NCERT Solutions for Class 12 Maths Chapter 1 Exercise 1.3 Relations and Functions in English Medium PDF to download free to use it offline updated for new academic session. All NCERT solutions are updated according to NCERT Books on the basis of latest CBSE Syllabus. Ask your doubts related to NIOS board as well as CBSE Board through Discussion Forum. This is a platform for sharing of knowledge with each other.

**Exercise 1.3 Overview**

Exercise 1.3 in Chapter 1 tests your understanding of these concepts through a series of thought-provoking problems. It challenges you to apply theoretical knowledge to practical scenarios, enhancing your analytical skills. Our solutions are designed to guide you step-by-step through each problem, ensuring you grasp the underlying principles.

#### Class 12 Maths Exercise 1.3 Solution in Videos

**Step-by-Step Solutions**

Our solutions to Exercise 1.3 are detailed and easy to follow. We break down each problem, providing explanations for every step. This approach not only helps you find the right answer but also enables you to understand the methodology behind it. Whether it’s a tricky problem or a straightforward one, our comprehensive solutions ensure you won’t be left puzzled.

**Tips and Tricks**

To excel in Maths, understanding the solution is just one part of the equation. We also provide valuable tips and tricks to help you solve problems more efficiently. These strategies will be particularly helpful in managing your time effectively during exams.

##### About 12 Maths Exercise 1.3

In 12th Mathematics Exercise 1.3 of Relations and Functions, the questions are based on one – one and onto relations. If a relation is one – one and onto, then it is called invertible relations and hence the inverse of the relation exists. The knowledge of the concepts of Exercise 1.1, as to fog and gof will be implemented in this exercise. All the questions are done in simplified way, so that students of English Medium as well as Hindi Medium can understand easily. If you still find any difficulty to understand the solutions, please notify us, we will try to simplified further as much as possible. Our only aim to prepare the contents which are on user friendly interface as well as easy to learn.

**Practice Makes Perfect**

We believe in the power of practice. Alongside the solutions, we offer additional practice problems to help you master the concepts of Relations and Functions. Regular practice using these problems will boost your confidence and prepare you for any challenge that your exams might throw at you.

###### Feedback & Suggestions

We are updating NCERT Solutions as per the suggestions received by the users. If the solutions are not matching with NCERT Books or any other problem, please inform us to rectify these problems. Join the discussion forum to ask your doubts related to any subject, whether related to CBSE Syllabus or not, and get the proper answer from experts and other users.

**Beyond the Textbook**

Learning doesn’t stop with the textbook. We encourage students to explore real-life applications of these mathematical concepts. Understanding how these theories apply in the real world will deepen your appreciation and interest in mathematics.

**Conclusion**

Our goal is to make learning Class 12 Maths enjoyable and enriching. With our comprehensive solutions to Exercise 1.3, we hope to ease your journey through this challenging yet rewarding subject. Remember, mathematics is not just about solving problems; it’s about understanding them and enjoying the process of finding solutions.

Keep practicing, stay curious, and never hesitate to seek help when needed. Your journey through Class 12 Maths is not just about passing exams; it’s about laying a solid foundation for your future academic and career pursuits.

### What are the main concepts on which exercise 1.3 of 12th Maths is based?

There are two main concepts on which exercise 1.3 of grade 12th Maths is based. These concepts are:

1. **Compositions of Functions**.

Let f: A → B and g: B → C be two functions. Then the composition of f and g, denoted by gof, is defined as the function gof: A → C given by gof(x) = g(f(x)), ∀ x ∈ A.

2. **Invertible Function**.

If f is invertible, then f must be one-one and onto and conversely, if f is one-one and onto, then f must be invertible. This fact significantly helps for proving a function f to be invertible by showing that f is one-one and onto, specially when the actual inverse of f is not to be determined.

### How long it take to prepare exercise 1.3 (chapter 1) of class 12th Maths?

Students need a maximum of four days to prepare exercise 1.3 (chapter 1) of class 12th Maths if they give 1-2 hours per day to this exercise. This time also depends on student’s working speed, efficiency, capability, and many other factors.

### Is exercise 1.3 of Class12th Maths important for CBSE Exams?

Yes, exercise 1.3 of grade 12th Maths is important from the exam point of view. Every year questions are asked from this exercise in the board exams. All the questions of this exercise are important and can come in the exams. But the most important questions of this exercise are examples 18, 19, 20, 21, 23, 25, 27 and questions 3, 5, 6, 8, 9, 10, 13, 14.

### In which type of sums of exercise 1.3 in 12th Maths, students face problems while solving?

In exercise 1.3 of grade 12th Maths, most students face problems in those questions in which they have to find out the inverse of a given function.

### What are the theorems to know before doing exercise 1.3 of grade 12th Maths?

There are two theorems before exercise 1.3 of grade 12th Maths.

Two theorems are:

1. If f: X → Y, g: Y → Z and h: Z → S are functions, then ho(gof)=(hog)of.

2. Let f: X → Y and g: Y → Z be two invertible functions. Then gof is also invertible with (gof)⁻¹ = f⁻¹o g⁻¹.