Maths · Class 11 · Sets, Relations and Functions

Sets, Relations and Functions for JEE

Everything you need for this topic on one page: the ideas, the formulas, the traps, and free lectures that explain it well.

Last updated: 26 October 2026

Direct answer

Sets and operations, types of relations (reflexive, symmetric, transitive, equivalence), and functions: domain, range, one-one, onto, composition and inverse.

Key ideas

Sets, Relations and Functions: what you must understand

Equivalence relation = reflexive + symmetric + transitive
A function has an inverse only if it is one-one and onto
Domain first: denominators ≠ 0, even roots ≥ 0, log arguments > 0
fog(x) means f(g(x))

Formula sheet

Must-know formulas for Sets, Relations and Functions

n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
Number of relations on a set with n elements = 2^(n²)
Number of functions from A (m) to B (n) = nᵐ
One-one functions = ⁿPₘ (n ≥ m)

One-page formula sheet

Printable Sets, Relations and Functions formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.

Avoid

Common mistakes students make

Skipping a domain condition
Assuming every relation is a function
Order of composition

For the exam

How this topic is asked in JEE

Appears frequently. Relations and functions questions appear almost every shift and are usually short.

NCERT map

Where Sets, Relations and Functions is in NCERT

Chapter names follow the current rationalised NCERT textbooks. Read these sections before solving PYQs.

Class	Book	Chapter	Sections JEE asks from
Class 11	Mathematics	Sets	Sets and their Representations; Types of Sets; Subsets; Operations on Sets; Complement of a Set
Class 11	Mathematics	Relations and Functions	Cartesian Product of Sets; Relations; Functions; Some Functions and their Graphs; Algebra of Real Functions
Class 12	Mathematics Part I	Relations and Functions	Types of Relations; Types of Functions; Composition of Functions and Invertible Function

JEE Advanced level

A JEE Advanced-level example on Sets, Relations and Functions

Question. Let A = {1, 2, 3, 4, 5} and f: A → A be a function such that f(f(x)) = x for all x ∈ A. If f(1) = 2 and f(2) = 1, find the number of such functions f that are onto.

Show solution

f(f(x)) = x means f is an involution (applying f twice gives back x). This forces elements to either be fixed points where f(x) = x, or swap in pairs where f(a) = b and f(b) = a.
Given f(1) = 2 and f(2) = 1, so 1 and 2 already form a swapping pair. We need to determine what happens to {3, 4, 5}.
Since f: A → A must be onto and f(f(x)) = x, f must be a bijection. For {3, 4, 5}, we partition into fixed points and swapping pairs.
Case 1: All three are fixed points (f(3)=3, f(4)=4, f(5)=5). This gives 1 function.
Case 2: One fixed point and one swapping pair. Choose the fixed point in C(3,1) = 3 ways, remaining two elements swap. This gives 3 functions.
Total = 1 + 3 = 4 functions.

Answer: 4

This example was solved twice independently and both solutions agree.

Free lectures

Best free lectures for Sets, Relations and Functions

Full-chapter free lectures picked from YouTube search results by views, from established JEE channels (mostly in Hinglish). Use the subtopic list to jump straight to the part you need (timestamps come from each video's own chapter list). Watch one, then solve PYQs the same day.

RELATIONS & FUNCTIONS in One Shot: All Concepts & PYQs Covered | JEE Main & Advanced — JEE Wallah, 6:15:01
Jump to a subtopic (29)
- 00:00 Introduction
- 06:27 Topics to be covered
- 07:50 Cartesian product of 2 sets
- 12:00 Relations
- 23:59 Number of Relations
- 29:39 Range and Co-domain of a Relation
- 36:58 Types of Relation
- 1:31:10 Number of Reflexive Relations
- 1:36:50 Functions
- 1:43:52 Arrow diagram - Vertical line test
- 1:46:58 Identifying Functions
- 1:48:54 Domain & Co-domain of a Function
- 2:03:15 Range of a Function
- 2:29:30 Types of Functions
- 2:40:25 Methods to check one-one
- 2:53:58 Greatest integer function
- 3:10:25 Fractional Function
- 3:19:30 Properties of [x] & {x}
- 3:37:29 Signum Function y=sgn(x)
- 3:41:52 Break
- 4:06:19 Graphical Transformation
- 4:45:29 Composite of a Function
- 5:06:14 Inverse of a Function
- 5:13:58 Properties of Inverse of a Function
- 5:19:46 Even & odd Functions
- 5:26:57 Periodic Functions
- 5:44:08 Functional Identities
- 6:12:56 Homework
- 6:14:30 Thank you bachhon
Sets Class 11 | One Shot | JEE Main & Advanced | Arvind Kalia Sir — JEE Nexus by Unacademy, 2:12:01
Jump to a subtopic (8)
- 0:00 Introduction & Nature of Chapter
- 04:15 Index
- 05:51 Definition & Description of sets
- 15:58 Types of sets
- 22:00 Subsets
- 36:06 Power set
- 41:32 Operation on sets
- 01:08:50 Cardinality based Problems

Practise

Where to practise for free

17 JEE Main 2026 PYQs on Sets, Relations and Functions, with solutions.
Read the chapter in NCERT textbooks (official, free), then solve its NCERT Exemplar (official, free) questions.
Chapter-wise past questions: JEE Main and Advanced PYQs and question bank.
Timed practice tests: NTA Abhyas practice tests (official, free) and our free mock tests.
See it move: interactive simulation.

FAQs

Frequently asked questions

Is Sets, Relations and Functions important for JEE Main 2027?

Appears frequently. It is part of the official 'Sets, Relations and Functions' unit in the JEE Main 2027 syllabus.

What are the most important formulas in Sets, Relations and Functions?

n(A ∪ B) = n(A) + n(B) − n(A ∩ B); Number of relations on a set with n elements = 2^(n²); Number of functions from A (m) to B (n) = nᵐ.

How should I study Sets, Relations and Functions for JEE?

Understand the key ideas from NCERT or one full lecture, learn the formula sheet, then solve 25–30 past JEE questions on the topic. Relations and functions questions appear almost every shift and are usually short.