In Class XI we already study in brief about relations and functions, range, domain and codomain with different types of specific realvalued functions and their graphs. In chapter Relations and Functions, we are going to learn about different types of relations and functions, invertible functions, the composition of functions and also binary operations. In this chapter, there are 4 exercises with 55 questions in them and 19 questions in the miscellaneous exercise. The NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions are solved and explained by the subject experts.
Meaning of the term ‘relation’ in mathematics is the same as the meaning of relation in the English language. Relation means two quantities or objects are related if there is a link between two quantities or objects. In other words, we can say that it is a connection between or among things.
Let's understand with an example of NCERT Class 12 Maths Chapter Relations and Functions  let A is the set of students of Class XII of a school and B is the set of students of Class XI of the same school. Then some of the examples of relations from A to B are
(i) {(a, b) ∈A × B: a is a brother of b},
(ii) {(a, b) ∈A × B: a is a sister of b},
(iii) {(a, b) ∈A × B: age of a is less than the age of b}.
If (a, b) ∈ R, we can say that ‘a’ is related to ‘b’ under the relation ‘R’ and we write as ‘a R b’. To understand the topic in depth, after every concept, solved examples and exercises are given in CBSE Class 12 Chapter Relations and Functions. In this chapter total 51 solved examples are there, to clear students doubt.
1.1 Introduction
1.2 Types of Relations
1.3 Types of Functions
1.4 Composition of Functions and Invertible Function
1.5 Binary Operations
Question Determine whether each of the following relations are reflexive, symmetric and transitive:
(i) Relation in the set defined as
Solution
Since, so is not reflexive.
Since, but so is not symmetric.
Since, but so is not transitive.
Hence, is neither reflexive nor symmetric and nor transitive.
(ii) Relation R in the set N of natural numbers defined as
Solution
Since,
so is not reflexive.
Since, but
so is not symmetric.
Since,there is no pair in such that so this is not transitive.
Hence, is neither reflexive nor symmetric and
nor transitive.
NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Solved Exercise Questions
NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Exercise 1.1
NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Exercise 1.2
NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Exercise 1.3
NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Exercise 1.4
NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Miscellaneous
Chapter 2 

Chapter 3 

Chapter 4 

Chapter 5 

Chapter 6 

Chapter 7 

Chapter 8 

Chapter 9 

Chapter 10 

Chapter 11 

Chapter 12 

Chapter 13 
Q. 12 Consider the binary operations and defined as
and . Show that ∗ is commutative but not
associative, is associative but not commutative. Further, show that ,
. [If it is so, we say that the operation ∗ distributes
over the operation ]. Does distribute over ∗? Justify your answer.
Q. 11 Let and . Find of the following functions F from S
to T, if it exists.
(ii)
Q.2 For each operation ∗ defined below, determine whether ∗ is binary, commutative
or associative.
(ii) On , define