NCERT solutions for class 12 maths chapter 1 exercise 1.1, 1.2, 1.3, 1.4 and miscellaneous of Relations and Functions free PDF in Hindi Medium as well as English Medium download. Download assignments based on Relations and functions and **Previous Years Questions** asked in CBSE board, important questions for practice as per latest **CBSE Curriculum – 2018-2019**. Revision book is provided for the complete revision of this chapter including solved example and exercises. Download books in pdf form or buy **NCERT** books online.

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## NCERT solutions for class 12 maths chapter 1 Relations and Functions

### Solutions of NCERT exercises given in the chapter

- 12 Maths Chapter 1 Exercise 1.1 Solutions
- 12 Maths Chapter 1 Exercise 1.2 Solutions
- 12 Maths Chapter 1 Exercise 1.3 Solutions
- 12 Maths Chapter 1 Exercise 1.4 Solutions
- 12 Maths Chapter 1 Miscellaneous Exercise 1 Solutions
- Study Online Miscellaneous Exercise 1
- Miscellaneous Exercise 1 Solutions in English
**विविध प्रश्नावली 1 का हल हिंदी में****Download Miscellaneous Exercise 1 in PDF**

### NCERT Chapter to study online and answers given in the end of NCERT books.

### These books are very good for revision and more practice. These book are also confined to NCERT Syllabus.

### Assignments for practice

**Mixed Chapter Tests**

Chapter 1, 2, 3 & 4

**Level 1 Test 1 **

**Level 2 Test 1 **

**Level 3 Test 1 Test 2 **

*EXPECTED BACKGROUND KNOWLEDGE*

Before studying this lesson, you should know:

- Concept of set, types of sets, operations on sets
- Concept of ordered pair and cartesian product of set.
- Domain, co-domain and range of a relation and a function

**Relation**

Let A and B be two sets. Then a relation R from Set A into Set B is a subset of A × B.

Types of Relations

(i) Reflexive Relation

(ii) Symmetric Relation

(iii) Transitive Relation

**EQUIVALENCE RELATION**

A relation R on a set A is said to be an equivalence relation on A iff

(i) it is reflexive

(ii) it is symmetric

(iii) it is transitive

**CLASSIFICATION OF FUNCTIONS**

Let f be a function from A to B. If every element of the set B is the image of at least one element of the set A i.e. if there is no unpaired element in the set B then we say that the function f maps the set A onto the set B. Otherwise we say that the function maps the set A into the set B.

Functions for which each element of the set A is mapped to a different element of the set B are said to be one-to-one.

A function can map more than one element of the set A to the same element of the set B. Such a type of function is said to be many-to-one. A function which is both one-to-one and onto is said to be a bijective function.

**BINARY OPERATIONS:**

Let A, B be two non-empty sets, then a function from A × A to A is called a binary operation on A.

If a binary operation on A is denoted by *, the unique element of A associated with the ordered pair (a, b) of A × A is denoted by a * b.

The order of the elements is taken into consideration, i.e. the elements associated with the pairs (a, b) and (b, a) may be different i.e. a * b may not be equal to b * a.

Let A be a non-empty set and ‘*’ be an operation on A, then