NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

Class 12 Maths Chapter 1 contains four exercises in total and all of these exercises consist of various kinds of questions such as short answer type, multiple choice questions.

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

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

• Miscellaneous Exercise: 13 Questions (12 Short Answers, 1 MCQ)

The main topics and sub-topics covered in this chapter are given below. There is also a Miscellaneous Q&A section at the end of Chapter 1. 

• 1.1 - Introduction

• 1.2 - Types of Relations

• 1.3 - Types of Functions

• 1.4 - Binary Operations

There are various reasons behind why every Class 12 student should opt for the NCERT Solutions for Class 12 Maths Chapter 1 as the best study guide. A few are given in the following. Take a look: 

• All the answers to the questions asked in the textbook exercises are aimed at providing an effortless solution in solving the problems from Chapter 1 of Class 12 Maths named Relation and Function.

• NCERT solutions for Class 12 Maths provide the list of all the important formulas under one roof.

• NCERT Solutions are carefully created by some of the excellent subject matter experts from the relevant industry.

• These solutions can be beneficial while studying for various competitive exams such as JEE Main, Olympiad etc. apart from the board exams.

• These solutions help you to learn the question patterns, marks weightage etc. 

The first chapter of Class 12 Maths is “Relation and Functions,” and it gives an introduction to new concepts, as well as concepts learned previously that might be used in Class 12. It covers types of relations, types of functions, and binary operations. Each exercise in the Chapter has about 12 questions. It provides all the necessary formulas required to understand the concepts with sufficient examples.

Relation is the concept that describes the relationship between two sets of quantities with each other. The relations can be described as empty or universal. These concepts along with examples explaining them step-by-step can be found in the NCERT Solutions for Chapter 1 of Class 12 Maths. All the exercises are also solved for the reference of students and extra questions for practice are provided as well.

The NCERT Maths textbook for Class 12 Maths has a total of 12 chapters including Chapter 1. All these chapters are covered in the NCERT Solutions PDF provided by Vedantu. The solutions book explains all the chapters with enough examples that help students understand the concepts better. Each exercise is solved with step-by-step answers for the students to follow. Extra questions based on previous years' papers and patterns are also provided for practice. These solutions are prepared by subject matter experts and are based on the latest exam guidelines. So these solutions are 100% reliable.

The NCERT Solutions for Chapter 1 of Class 12 Maths is available for download free of cost on the Vedantu website and the Vedantu app. The NCERT Solutions PDF is written keeping in mind the easy learning of students and how each student has a different caliber. All the concepts and examples are explained in an easy language for the students to understand. It helps you familiarise with the kind of questions to expect in the exam. The questions and solutions are formulated by professionals.

Board exams are very important in determining a student’s future and  Chapter 1 of Class 12 Maths is important. Chapter 1 is important not only for the board but also for various competitive exams, including JEE. The students should practice all the questions and examples from the NCERT textbook thoroughly. The students can refer to the solutions PDF for extra questions and explanations. Students should also practice sample papers and papers from previous years for the students to know the kind of questions to expect in the exam and be well-versed with it.

The NCERT Solutions for Class 12 Maths Relations and Functions cover the following concepts: types of relations, types of functions, function composition, invertible functions, and binary operations. A team of highly experienced faculty members solves the exercise-related concerns. The primary goal of providing solutions is to help students perform well on Class 12 Maths board exams.

• Relation: A collection of ordered pairs that describes a connection between elements in two sets. Think of it as a mapping, but an element in the first set can have multiple corresponding elements in the second set.

• Function: A special type of relation where each element in the first set (called the domain) has exactly one corresponding element in the second set (called the codomain, often denoted as the range when the function uses all elements in the codomain). It's like a stricter mapping where there are no ambiguities in outputs for a given input.

Every function is inherently a relation because it fulfills the basic definition of a relation: a collection of ordered pairs. However, not all relations are functions because they might violate the "one input, one output" rule.

Mathematics is a vast field built upon the contributions of many mathematicians throughout history. These concepts have evolved over time, with important figures like Gottfried Wilhelm Leibniz and Leonhard Euler making significant contributions.

Here are some ways to identify if a relation is a function:

• Arrow Test: Draw arrows between elements in the first set and their corresponding elements in the second set. If any element in the first set has multiple outgoing arrows, the relation is not a function.

• Vertical Line Test (for functions graphed on a coordinate plane): If a vertical line intersects the graph of the relation in more than one point, it's not a function.

Every function is inherently a relation. It satisfies the definition of a relation (ordered pairs) and adds the extra constraint of one input, one output.

Both relations and functions describe connections between elements in sets using ordered pairs. They can be represented in various ways, including tables, arrow diagrams, and graphs.