Dear students, if you want detailed information about **NCERT Maths**

**Solutions for Class 12 Chapter 1**and are looking for its solution, then this article is for you only.

If you read this entire article today, then I can say with the whole claim that you will not have any doubt related to class 12 NCERT solutions Chapter 1.

We will also know as well as what is asked in class 12 CBSE and ICSE Board, and which questions are important, we will know the complete information about chapter 1, whose name is relation and function, in this round we talk about relation. Let us study this chapter to express the relationship between any two movies mathematically.

**All the topics that we have in this chapter**

Main Topics | Exercise |

Introduction | 1 |

Types of Relations | 1.1 |

Types of Functions | 1.2 |

Composition of Functions and Invertible Function | 1.3 |

Binary Operations | 1.4 |

And Miscellaneous Solutions | All Mixed |

This chapter shows the relationship between 2 objects. We will study in this chapter how the two functions are related to each other. Apart from this, this chapter makes us study different types of relations and functions, combinations of functions and invertible functions and binary operations.

All the topics we have written above are contained in our NCERT Maths Solutions for Class 12 Chapter 1. Today we will also give you a PDF of relation and function, with the help of which you can improve your studies.

**NCERT Maths Solutions for Class 12 Chapter 1 PDF Free **

I am giving you the solution for all the exercises in one PDF. You will get the complete solutions for Class 12 Maths Chapter 1 in this PDF so that you can improve your preparation.

If you want CBSE Maths Previous Year Question Paper Class 12th With Solutions Free PDF, then you can practice your exam by taking that too. I have also given detailed information about the important questions asked in the previous year on this blog, which you can read.

Relations and functions is an important topic in mathematics that is covered in class 12th. Here are some key points to keep in mind:

- A relation is a set of ordered pairs, where the first element is from a set called the domain and the second element is from a set called the range.
- A function is a special type of relation, where each element in the domain is related to exactly one element in the range.
- Functions can be represented using mapping diagrams, graphs, or algebraic equations.
- One-to-one functions have the property that each element in the domain is related to a unique element in the range.
- Onto functions have the property that every element in the range is related to at least one element in the domain.
- Compositions of functions involve combining two or more functions to create a new function.
- Inverse functions are functions that undo the effects of each other.
- The domain of a function is the set of all possible input values, while the range is the set of all possible output values.
- The inverse of a function exists if and only if the function is one-to-one.
- Functions can be classified as even, odd, periodic, or discontinuous based on their algebraic properties and graphical behaviour.

These are some of the key points to keep in mind when studying relations and functions in class 12th. It is important to have a solid understanding of these concepts in order to excel in mathematics.

## NCERT Maths Solutions for Class 12 Chapter 1 Exercise 1.1

NCERT Maths Solutions for Class 12 Chapter 1 Exercise 1.1 is the first exercise in the chapter “Relations and Functions”. This exercise consists of eight questions which are based on the basic concepts of relations and functions.

In NCERT Maths Solutions for Class 12 Chapter 1, “Relations and Functions,” students learn about different types of relations between sets. In Exercise 1.2 of the chapter, “Types of Relations,” students are introduced to various types of relations such as reflexive, symmetric, transitive, and equivalence relations.

- Reflexive Relation
- Symmetric Relation
- Transitive Relation
- Equivalence Relation

A reflexive relation is a relation in which every element of the set is related to itself. For example, the relation “is equal to” is reflexive as every element is equal to itself.

A symmetric relation is a relation in which if (a, b) is a part of the relation, then (b, a) must also be a part of the relation. For example, the relation “is a friend of” is symmetric as if A is a friend of B, then B is also a friend of A.

A transitive relation is a relation in which if (a, b) and (b, c) are a part of the relation, then (a, c) must also be a part of the relation. For example, the relation “is taller than” is transitive as if A is taller than B and B is taller than C, then A is taller than C.

An equivalence relation is a relation that is reflexive, symmetric, and transitive. For example, the relation “is equal to” is an equivalence relation as it satisfies all three properties.

In this exercise, students learn to identify different types of relations and understand their properties. They also learn to apply these properties to solve problems and prove theorems. This exercise provides a strong foundation for students to learn more advanced topics in the field of mathematics.

## NCERT Maths Solutions for Class 12 Chapter 1 Exercise 1.2

NCERT Maths Solutions for Class 12 Chapter 1 Exercise 1.2 is the second exercise in the chapter “Relations and Functions”. This exercise consists of ten questions which are based on various concepts related to relations and functions.

In NCERT Maths Solutions for Class 12 Chapter 1, “Relations and Functions,” students learn about different types of relations between sets. In Exercise 1.2 “Relations and Functions,” students learn about different types of functions between sets. In Exercise 1.3 of the chapter, “Types of Functions,” students are introduced to various types of functions such as injective, surjective, bijective, and inverse functions.

- Injective Function
- Surjective Function
- Bijective Function
- Inverse Function

An injective function is a function in which every element in the domain is mapped to a unique element in the range. In other words, no two distinct elements in the domain are mapped to the same element in the range.

A surjective function is a function in which every element in the range has at least one pre-image in the domain. In other words, the range is equal to the image of the function.

A bijective function is a function that is both injective and surjective. In other words, every element in the domain is mapped to a unique element in the range, and every element in the range has exactly one pre-image in the domain.

An inverse function is a function that “undoes” the action of another function. In other words, if a function f maps an element x to y, then its inverse function f^(-1) maps y to x.

In this exercise, students learn to identify different types of functions and understand their properties. They also learn to apply these properties to solve problems and prove theorems. This exercise provides a strong foundation for students to learn more advanced topics in the field of mathematics.

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

NCERT Maths Solutions for Class 12 Chapter 1 Exercise 1.3 is a comprehensive exercise that covers the concept of inverse trigonometric functions. This exercise contains nine questions, all of which are designed to test a student’s understanding of inverse trigonometric functions and their properties.

In NCERT Maths Solutions for Class 12 Chapter 1, “Relations and Functions,” Exercise 1.3 covers the composition of functions and invertible functions. In this exercise, students learn about the composition of two functions and how to determine whether a function is invertible.

The composition of two functions, f and g, is a new function obtained by applying g to the output of f. The resulting function is denoted by gof and is read as “g composed with f.” For example, if f(x) = x^2 and g(x) = 2x + 1, then g o f(x) = g(f(x)) = 2(x^2) + 1.

A function is invertible if it has a unique inverse that “undoes” the action of the function. In other words, if a function f maps an element x to y, then its inverse function f^(-1) maps y back to x. For a function to be invertible, it must be both injective and surjective.

In this exercise, students learn to determine the composition of two functions and to find the inverse of a function. They also learn to apply these concepts to solve problems and prove theorems. This exercise provides a strong foundation for students to learn more advanced topics in the field of mathematics, such as calculus and abstract algebra.

## NCERT Maths Solutions for Class 12 Chapter 1 Exercise 1.4

NCERT Maths Solutions for Class 12 Chapter 1 Exercise 1.4 is an important exercise that deals with the topic of mathematical induction. This exercise contains a total of nine questions that are designed to help the students understand the concepts of mathematical induction and its applications.

By using these solutions, students can develop a strong foundation in the topic of mathematical induction and gain the confidence to tackle more complex problems in the future. The solutions provided in NCERT Maths Solutions for Class 12 Chapter 1 Exercise 1.4 act as a helpful guide for students to prepare for their examinations and score good marks in the subject.

In Class 12 Maths, Chapter 1, “Relations and Functions,” Exercise 1.4 covers binary operations. In this exercise, students learn about binary operations, their properties, and how to solve problems related to them.

A binary operation is a mathematical operation that takes two elements from a set and produces a third element from the same set. For example, addition and multiplication are binary operations on a set of real numbers.

There are several properties associated with binary operations, such as commutativity, associativity, identity, and inverse. A binary operation is commutative if changing the order of the operands does not change the result. A binary operation is associative if changing the grouping of the operands does not change the result. An identity element is an element that, when used as an operand in a binary operation, leaves the other operand unchanged. An inverse element is an element that, when used as an operand in a binary operation, “undoes” the action of the other operand.

In this exercise, students learn to identify the properties of binary operations and to use them to solve problems related to the operations. They also learn to apply these concepts to solve real-world problems, such as those related to computer programming and cryptography. This exercise provides a strong foundation for students to learn more advanced topics in the field of mathematics, such as abstract algebra and number theory.

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

The Miscellaneous exercise of Relations and Functions in Class 12th Maths covers a range of questions that test the student’s understanding of the concepts covered in the chapter. Here are a few examples of the types of questions that may be included in the Miscellaneous exercise:

- Finding ordered pairs that belong to a given relation: This type of question requires the student to understand how a relation is defined and find the ordered pairs that satisfy the condition. For example, “Let R be the relation on the set A = {1, 2, 3, 4, 5} defined by R = {(a, b) : |a − b| ≤ 2}. Write down the ordered pairs that belong to R.”
- Showing that a relation is not an equivalence relation: This question requires the student to understand the properties of an equivalence relation and check if the given relation satisfies those properties. For the best example, “If R is a relation on the set of real numbers given by R = {(x, y) : y = x^2}, then show that R is not an equivalence relation.”
- Finding the domain and range of a function: This type of question requires the student to understand the definition of a function and find the set of input values (domain) and output values (range) that the function can take. For example, “Find the domain and range of the function f(x) = 2x^2 − 3x + 1.”
- Identifying the type of function based on its properties: This type of question requires the student to understand the different types of functions (even, odd, periodic, etc.) and identify the type of function based on its algebraic properties and graphical behaviour. For the best example, “Determine whether the function f(x) = x^3 − 2x is even, odd, or neither.”
- Finding the inverse of a function: This type of question requires the student to understand the concept of inverse functions and find the inverse of a given function. For example, “Find the inverse of the function f(x) = 3x − 1.”

These are just a few examples of the types of questions that may be included in the Miscellaneous exercise of Relations and Functions in Class 12th Maths. Students should practice a variety of such questions to develop a solid understanding of the concepts and excel in the subject.

**Conclusion:** Dear students, I have covered all the exercises related to **NCERT Maths**

**Solutions for Class 12 Chapter 1**in this entire article and that too with their solutions. I have also given PDF to you for free, with the help of which you can make your studies better. You must share this with all your friends so that they also come to know about this article and they too can take advantage of it.

Here are some frequently asked questions (FAQs) about NCERT Maths Solutions for Class 12 Chapter 1: Relations and Functions:

### What are NCERT Maths Solutions for Class 12 Chapter 1?

NCERT Maths Solutions for Class 12 Chapter 1 is a set of solutions provided to help students solve the questions and exercises given in the textbook. These solutions are prepared by subject experts who have years of experience in teaching and preparing study material for students.

### Why should I refer to NCERT Maths Solutions for Class 12 Chapter 1?

Referring to NCERT Maths Solutions for Class 12 Chapter 1 is important because it provides you with accurate solutions to all the questions and exercises in the textbook. The solutions are prepared according to the latest CBSE syllabus and guidelines, which makes them reliable and helpful for students to score better marks in their exams.

### Are NCERT Maths Solutions for Class 12 Chapter 1 free?

Yes, NCERT Maths Solutions for Class 12 Chapter 1 are free of cost and available online on various platforms. You can easily access them and use them to prepare for your exams.

### Can NCERT Maths Solutions for Class 12 Chapter 1 help me score better marks in the exams?

Yes, NCERT Maths Solutions for Class 12 Chapter 1 can definitely help you score better marks in the exams. These solutions provide you with a clear understanding of the concepts and a step-by-step explanation of how to solve the problems. If you practice these solutions regularly, you will be able to solve any type of question that can be asked in the exams.

### Are NCERT Maths Solutions for Class 12 Chapter 1 enough for exam preparation?

NCERT Maths Solutions for Class 12 Chapter 1 is definitely an important part of exam preparation. However, you should also practice other reference books and sample papers to gain more exposure and practice different types of questions. Additionally, you should also focus on revising the concepts and solving as many problems as possible to score better marks in the exams.