NCERT Solutions for Class 12 Mathematics Chapter 1 are available on the Extramarks website for all students preparing for the term one exam. The chapter is about Relation and Function, and our solutions offer theoretical knowledge and answer to all questions from the NCERT textbook. We provide a step-by-step guide and solutions for students to understand each concept thoroughly. In addition, our solutions are derived from the NCERT books CBSE syllabus for the latest year.
Chapter 1 Class 12 Mathematics dives into the basic concepts of Relations and Function. In this chapter, students can review their previous Class 11 Mathematics learning. The chapter covers the introduction, types of relations, functions, and binary operations. Students will learn about the nature of the concepts and undergo preparation to cover Chapter 1 for Class 12 Mathematics. Besides, Extramarks solutions cover vital concepts, theories, and solved exercises to comprehend the topic. If you are looking for perfect study material for Relations and Function, you may refer to Extramarks NCERT Solutions Class 12 Mathematics Chapter 1.
The primary purpose of delivering the solutions is to help students score perfectly. With the help of Extramarks NCERT Solutions for Class 12 Mathematics Chapter 1, students can eventually substitute a set of numbers with a binary process. This chapter will also help students understand the concepts better by explaining the formula of the pair that relates to the elements.
As a student, you can visit the Extramarks website for the latest information and syllabus updates. You can also view articles on notes for NCERT Solutions Class 1, NCERT Solutions Class 2, and NCERT Solutions Class 3.
Key Topics Covered In NCERT Solutions for Class 12 Mathematics Chapter 1
In Extramarks NCERT Solutions Class 12 Mathematics Chapter 1, students can expect all exercises and concepts to be explained in detail. The NCERT Solution begins with introducing Relation and Functions, and students will get to hold on to the basic concepts and properties of functions. Experts have updated the latest syllabus, and the main topics covered in NCERT Solution for Class 12 Mathematics Chapter 1 are:
| Exercise |
Topic |
| 1.1 |
Introduction |
| 1.2 |
Recall |
| 1.3 |
Types of Function |
| 1.4 |
Composition of Function and Invertible Function |
| 1.5 |
Binary Operations |
1.1 Introduction
In this introductory part, students will get a complete idea regarding concepts of Relations and Functions. It will also recap their learning from Class 11 Mathematics Chapter 1 and through all chapters. However, in the introduction, students will get a clear idea of what is present in the curriculum. Students can also get a proper set of instructions to understand the relationship between two objects belonging to the sets.
Students will get a proper set of instructions which will enable them to understand the relationship between two objects belonging to the sets. So, students get clarity and essential elements of the syllabus. It includes the concepts of relation and function, properties, formulas, and definitions. Chapter 1 Mathematics Class 12 is necessary to prepare for the integers and binary numbers part of their syllabus.
Some of the main features of this chapter are as follows:
- Empty relation
- Symmetric relation
- Equivalence relation
- Transitive relation
1.2 Recall
In NCERT Solutions for Class 12 Mathematics Chapter 1, students can learn and revise previous concepts and topics of Class 11 Mathematics. Overall, they can expect one quick revision and a deeper understanding of real numbers in this section. In addition, students will get more clarity on vertible and invertible functions, usage of addition, multiplication, division, and subtraction. This section is essential as it covers all the basics and paves the way towards complex concepts. Students get a good experience and the overall idea of the main topics, including polynomial function and modulus function.
1.3 Types of Functions
The students will grab all the essential elements of Relation and Functions, including identity, constant, modulus, signum, and rational functions. In addition, they will get proper knowledge and in-depth concepts of the injective and the subjective part. In NCERT Solutions Class 12 Mathematics Chapter 1, students can acquire accurate information of the elements of three different numbers and understand finite and infinite sets.
Some of the main functions explained in the chapter are as follows:
- A function f: X → Y is one-one. For example if f (x1) = f(x2) ⇒ x1 = x2 ∀ x1, x2 ∈ X.
- A function f: X → Y is onto. For example, if given any y ∈ Y, ∃ x ∈ X such that f(x) = y.
- A function f: X → Y is one-one and onto. For example, if f is both one-one and onto.
1.4 Composition of Functions and Invertible Function
The topic is one of the most critical sections, as it covers the composition of the function. Therefore, students can benefit from a complete understanding of the sets and the codes. In addition, examples are present in this section with short and long questions to practice.
1.5 Binary Operations
Studying binary operation is essential for students because it covers the integration and derived concepts. Students appearing for JEE Mains shall learn this section more precisely. Binary operations consist of integers, commutativity, associativity, rational numbers, and positive integers.
NCERT Solution for Class 12 Mathematics Chapter 1- covers all the important elements of the binary operation. Students can get a proper explanation of the arbitrary number set with concerns about the binary process. Further to this, the subject matter expert also elaborated the binary functions in correlation to two integers into one. Extramarks has covered all the essential formulae in NCERT Solutions Class 12 Mathematics Chapter 1 in the notes provided for reference.
List of NCERT Solutions Class 12 Mathematics Chapter 1 Exercise & Answer Solutions
NCERT Solutions for Class 12 Mathematics Chapter 2 Relation and Functions is available on the Extramarks website for free. It has step-by-step solutions for the examples present in the NCERT textbooks. The solution covers all the essential concepts and theories and is based on the latest CBSE 2022-2023 Syllabus guidelines. Students can also view the NCERT Solutions of other chapters from the Extramarks website.
Click on the below links to view NCERT Solutions Class 12 Mathematics Chapter 1:
Students can also view and explore other NCERT Solutions on our Extramarks website:
- NCERT Solutions Class 4
- NCERT Solutions Class 5
- NCERT Solutions Class 6
- NCERT Solutions Class 7
- NCERT Solutions Class 8
- NCERT Solutions Class 9
- NCERT Solutions Class 10
NCERT Exemplar Class 12 Mathematics
NCERT Exemplar Class 12 Mathematics is available on the Extramarks website for all the CBSE students. As the Term One exam approaches, students must consider referring to the NCERT Exemplar to gather complete mathematics concepts. Each exercise consists of solutions and problems with proper explanation.
Exemplar books play a vital role in preparing for competitive exams and help score more in CBSE exams. If students want to score more in the examination, referring to NCERT Exemplar Class 12 Mathematics is ideal. Students can start by preparing from Chapter 1 – Relation and Function. It becomes a great companion in the learning journey for preparing for competitive exams such as NEET and JEE Mains. At Extramarks, students get worksheets and best practising materials for the preparation.
Key Features of NCERT Solutions Class 12 Mathematics Chapter 1
NCERT Solutions Class 12 Mathematics Chapter 1 provides in-depth solutions to various problems mentioned in the syllabus. To compete and score dynamically in exams like NEET and JEE, students must have a strong command of Mathematics. NCERT books cover all the challenging topics that help boost the brain with fast calculations.
Students get more exposure to all kinds of questions, pushing them to attempt the most challenging question in the competitive questions. For this purpose, students can refer to NCERT Solutions Class 12 Mathematics Chapter 1. Some of the other reasons include:
- Extramarks NCERT Solutions Class 12 Mathematics Chapter 1 is prepared by Subject Matter Experts.
- The NCERT Solutions are explained such that it helps the students enjoy the learning process.
- With the help of Relation and Functions chapter solutions, students can easily attempt complex problems in the exam.
- Students will score more in the exams as the answers are short, self-explanatory, and well structured.