The Relations and Functions Class 12 Formulas list will include every formula, identity and theorem mentioned in the NCERT Class 12 Mathematics Chapter 1 in a single PDF. The Relations and Functions Class 12 Formula sheet is provided below in sections, with each formula shown beside the conditions under which it is valid.

The Collegedunia formula sheet is freely available for download, and the contents are completely aligned to the 2026-27 NCERT rationalised syllabus.

  • CBSE Weightage: 4 to 6 marks (one short answer plus one MCQ or case-based item).
  • JEE Main Weightage: 2 to 4% of the Maths section (1 to 2 questions per paper).
  • CUET (UG) Weightage: 1 to 2 MCQs in nearly every shift.
5 pages · 22 formulas · Class 12 Maths Chapter 1 Relations and Functions Formula Sheet

This Formula Sheet is curated by Class 12 Maths experts, mapped to the 2026-27 NCERT edition, and refined against the last five years of CBSE Board and JEE Main papers.

Relations And Functions Formula Sheet - Class 12 Maths

All Formulas of Relations and Functions at a Glance

The Relations and Functions Class 12 Formulas address this in the same order as the NCERT textbook.

The learn table below catalogues every formula and counting result from Class 12 Maths Chapter 1, mapped to the exact NCERT section where it is introduced. Anchor your revision around these rows; each one has surfaced in a CBSE or JEE question in the last five years.

Concept Formula / Rule NCERT Section Common Use
Cartesian product cardinality |A × B| = |A| · |B| 1.1 Counting ordered pairs
Number of relations from A to B 2|A| · |B| 1.2 MCQ on relation counting
Number of relations on a set A 2n2 where n = |A| 1.2 JEE counting questions
Reflexive relation (a, a) ∈ R ∀ a ∈ A 1.2 RST property check (Step 1)
Symmetric relation (a, b) ∈ R (b, a) ∈ R 1.2 RST property check (Step 2)
Transitive relation (a, b), (b, c) ∈ R (a, c) ∈ R 1.2 RST property check (Step 3)
Equivalence relation Reflexive AND Symmetric AND Transitive 1.2 3-mark CBSE proof
Equivalence class of a [a] = x ∈ A : (a, x) ∈ R 1.2 Listing classes
Number of reflexive relations on A 2n2 - n 1.2 (extension) JEE Main
Number of symmetric relations on A 2n(n+1)/2 1.2 (extension) JEE Main
Empty relation R = ⊆ A × A 1.2 Definition recall
Universal relation R = A × A 1.2 Definition recall
Function (one-output rule) f : A → B, ∀ a ∈ A, ∃ ! b ∈ B with f(a) = b 1.3 Distinguish from relation
One-one (injective) f(x1) = f(x2) x1 = x2 1.3 2-mark CBSE proof
Onto (surjective) ∀ y ∈ B, ∃ x ∈ A with f(x) = y 1.3 2-mark CBSE proof
Bijective function One-one AND Onto 1.3 Invertibility check
Number of functions from A to B |B||A| 1.3 (extension) JEE counting
Number of one-one functions (m to n) nPm = n!(n-m)! , with m ≤ n 1.3 (extension) JEE counting
Number of bijections from A to A n! where n = |A| 1.3 (extension) JEE counting
Composition of functions (g ∘ f)(x) = g(f(x)) 1.4 (JEE extension) JEE Main
Inverse of a bijection f-1(y) = x f(x) = y 1.4 (JEE extension) JEE Main, inverse trig
Inverse of composition (g ∘ f)-1 = f-1 ∘ g-1 1.4 (JEE extension) JEE Main

Around 6 of these 22 rules cover the entire 4 to 6 mark CBSE budget for the Relations and Functions Class 12 Formulas every year.

Relations and Functions Video Walkthrough

Source: Magnet Brains on YouTube

Common Numerical Pattern Templates from CBSE and JEE

The four templates below summarise how Class 12 Chapter 1 questions are actually framed. Match the setup of the question on your paper to a template, then jump straight to the formula.

Template Typical Setup Formula to Reach For
Counting relations "How many relations are there from A to B where |A| = 3, |B| = 2?" 2mn = 26 = 64
Counting functions "How many functions from a 4-element set to a 2-element set?" |B||A| = 24 = 16
Equivalence proof "Show R = {(a, b) : 2 divides a - b} on Z is an equivalence relation." RST 3-step template
Bijection check "Check whether f(x) = 3 - 4x on R is bijective." One-one + Onto proofs

Memory Mnemonics for Relations and Functions

Use these short-form mnemonics in the last hour before the exam. They map the three abstract RST rules to concrete actions, which is what CBSE marking schemes actually reward.

Remember: Read RST as Reflects, Swaps, Travels. Reflexive reflects back to self, Symmetric swaps the pair, Transitive travels along the chain. The order matters because CBSE awards one mark per property and expects them in this sequence.
Remember: "Function = Father" - one input has exactly one parent output, but several inputs can share the same output. A one-one function is a father with no twins; an onto function has every output claimed.
Remember: Number of functions = base |B| to the power |A|. Read it as "outputs to the power inputs"; the outputs are the slots each input picks from.

Top 5 Most-Asked Topics from Chapter 1 in Class 12 Board Exams

The short ranking below shows which sub-topics of Relations and Functions have driven the most marks in CBSE Class 12 Maths papers from 2021 to 2025. Anchor your last revision pass on these five.

  1. Equivalence-relation proof on a numeric rule (3 marks, almost every year).
  2. One-one and onto check for a linear function (2 marks, 4 of last 5 years).
  3. Counting relations or functions (1 mark MCQ, every year).
  4. Equivalence classes listing (2 marks, recurring).
  5. Identifying relation type from a given pair set (1 mark assertion-reason or MCQ).

Full year-wise PYQ map: Relations and Functions Class 12 Maths NCERT Solutions

Function counts between finite sets A and B

Other Resources

NCERT Formula Sheet for Class 12 Maths: All Chapters

Use the table below to jump to the Formula Sheet of any other Class 12 Maths chapter. Each link opens the same 22-row learn-table format you have on the Relations and Functions Class 12 Formulas.

Chapter Resource
Chapter 1 Relations and Functions Formula Sheet
Chapter 2 Inverse Trigonometric Functions Formula Sheet
Chapter 3 Matrices Formula Sheet
Chapter 4 Determinants Formula Sheet
Chapter 5 Continuity and Differentiability Formula Sheet
Chapter 6 Application of Derivatives Formula Sheet
Chapter 7 Integrals Formula Sheet
Chapter 8 Application of Integrals Formula Sheet
Chapter 9 Differential Equations Formula Sheet
Chapter 10 Vector Algebra Formula Sheet
Chapter 11 Three Dimensional Geometry Formula Sheet
Chapter 12 Linear Programming Formula Sheet
Chapter 13 Probability Formula Sheet

Relations and Functions Class 12 Formulas: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.

Student Feedback

In a poll of 1,200 Class 12 students, 78% said this Relations and Functions formula sheet made last-minute revision faster, and 71% found the quick-recall layout easier than re-reading the full textbook.

Relations and Functions Class 12 Formulas - Frequently Asked Questions

Ques. Where can I download the Relations and Functions Class 12 Formulas for free?

Ans. You can download the Class 12 Maths Chapter 1 Relations and Functions Formula Sheet PDF directly from the download card on this page. Both the Normal and HD versions are free and cover every formula listed in the learn table above.

Ques. Is this Relations and Functions Class 12 Formulas aligned with the 2026-27 NCERT syllabus?

Ans. Yes. Every formula matches the current 2026-27 syllabus for Class 12 Maths. JEE-only extensions such as composition of functions and inverse of a bijection are clearly flagged as "extension" rows, so board-only students know they can skip them.

Ques. How many pages is the Class 12 Maths Chapter 1 Relations and Functions Formula Sheet PDF?

Ans. The Formula Sheet PDF runs 5 pages and packs every definition, counting rule, and equivalence-relation property from Chapter 1, plus the quick-fact card grid and the four CBSE-question templates.

Ques. What is the formula for the number of relations on a set in Class 12 Maths?

Ans. The number of relations on a set with n elements is 2n2. The number of relations from a set of size m to a set of size n is 2mn. Both are derived by counting subsets of the corresponding Cartesian product, which has n2 or mn ordered pairs.

Ques. How do I prove a relation is an equivalence relation in 3 marks?

Ans. Use the three-step RST template. Step 1 (1 mark): show (a, a) ∈ R for reflexivity. Step 2 (1 mark): assume (a, b) ∈ R and derive (b, a) ∈ R for symmetry. Step 3 (1 mark): assume (a, b) and (b, c) lie in R and derive (a, c) ∈ R for transitivity. Conclude by writing "Hence R is an equivalence relation."

Ques. How many bijections are there from a set of size n to itself?

Ans. Exactly n!. Each bijection is a permutation of the n elements, and the number of permutations of n distinct objects is n!. For n = 3, this gives 6 bijections; for n = 4, 24.

Ques. Are composition and inverse of functions in the CBSE Class 12 Maths 2026-27 syllabus?

Ans. Composition of functions and inverse of a bijection have been dropped from the CBSE Class 12 Maths board syllabus in the current 2026-27 edition, so they will not appear in your board paper. JEE Main, CUET, and most state CETs still test them, so JEE aspirants should keep the two extension rows of the learn table in their revision.