7 pages · 6 hand-drawn diagrams · 8 boxed key results · Class 12 Maths Chapter 1, 2026-27 NCERT
The handwritten notes on Class 12 Maths Chapter 1 Relations and Functions will include a detailed list of all formulas, important derivations, and question types in an organised manner.
- CBSE Weightage: 4 to 6 marks (one short answer plus one long answer on equivalence relation or bijection proof)
- JEE Main Weightage: 2 to 3% (1 to 2 questions per shift on relations, function-classification, and invertibility)
- JEE Main Weightage: Not in JEE Main syllabus (Maths-only chapter; relevant for JEE and CUET)
- Relations and Functions Class 12 Maths Notes
- Relations and Functions Class 12 Maths NCERT Solutions
- Relations and Functions Class 12 Maths Formula Sheet
Relations and Functions Video Walkthrough
Source: Magnet Brains on YouTube
Relations and Functions Class 12 Chapter 1 NCERT Exercise-Wise Snapshot
| Sub-Topic | NCERT Qs | Typical CBSE Marks |
|---|---|---|
| Types of Relations (empty, universal, identity) | 4 | 1 to 2 |
| Reflexive, Symmetric, Transitive Properties | 8 | 3 to 5 |
| Equivalence Relations and Equivalence Classes | 6 | 3 to 5 |
| One-one (Injective) and Onto (Surjective) Functions | 8 | 2 to 3 |
| Composition of Functions | 3 | 1 to 2 |
| Invertible Functions and Inverse Computation | 3 | 3 to 5 |
How the Class 12 Maths Handwritten Notes PDF on the Class 12 Maths Handwritten Notes PDF Help You
- Hand-Sketched Visual Anchors: Every key arrow diagram, one-one vs many-one mappings, composition flow, partition into equivalence classes, is drawn freehand so the reader can redraw it from memory in under 60 seconds.
- Boxed Key Results: Every definition that CBSE asks verbatim (injectivity test, onto condition, equivalence triple, invertibility iff bijective) lives inside a hand-drawn rectangle, so your eye locks onto the testable statement.
- 2026-27 NCERT Alignment: Every page is matched to the current 2026-27 syllabus print. Note: binary operations are NO LONGER in the rationalised Class 12 NCERT, so the notebook drops them entirely and doubles down on equivalence-class proofs and invertibility, the two highest-yield topics for Boards.
- Solved Function Examples: Four pre-classified examples (linear bijection f(x)=2x on R, squaring f(x)=x2, integer 2x on N, modulus |x|) so you have a template for every CBSE classification question.
Relations and Functions Handwritten Notes: Color Legend for the Notebook
| Colour | Box Type | What's Inside |
|---|---|---|
| Orange | Definition box | NCERT one-line definitions: relation, reflexive, symmetric, transitive, equivalence, injective, surjective, bijective, invertible |
| Blue | Key result box | Every theorem-style result. f(x1) = f(x2) ⇒ x1 = x2 , g ∘ f = IX , f invertible ⇔ f bijective |
| Yellow | MCQ-trap callout | The 6 facts CBSE / JEE re-use as MCQ distractors: f(x) = x2 on R is neither one-one nor onto, mod 2 is equivalence on Z, etc. |
| Red | Common-mistake box | Most students confuse "domain" with "codomain" or skip proving symmetric in equivalence proofs; the red box shows the correct sequence right next to the wrong one |
Relations and Functions Top 6 Key Results for Class 12 Maths Quick Recall
| Concept | Definition / Test |
|---|---|
| Reflexive Relation | (a, a) ∈ R for every a ∈ A |
| Symmetric Relation | (a1, a2) ∈ R ⇒ (a2, a1) ∈ R |
| Transitive Relation | (a1, a2), (a2, a3) ∈ R ⇒ (a1, a3) ∈ R |
| One-one (Injective) | f(x1) = f(x2) ⇒ x1 = x2 |
| Onto (Surjective) | For every y ∈ Y , there exists x ∈ X such that f(x) = y |
| Invertibility Criterion | f is invertible ⇔ f is bijective (one-one and onto) |
Relations and Functions Class 12 Maths Self-Assessment Quick Quiz
Q1. Let R = (1, 1), (2, 2), (3, 3), (1, 2) on A = 1, 2, 3 . Then R is:
Q2. The function f: R → R defined by f(x) = x2 is:
Q3. If f: N → N is given by f(x) = 2x , then f is:
Q4. The number of one-one functions from 1, 2, 3 to itself is:
Q5. If f(x) = cos x and g(x) = 3x , then g ∘ f(x) equals:
Class 12 Maths Chapter 1 Relations and Functions PYQ Snapshot (2026 to 2021)
| Topic | Asked in | Typical Marks |
|---|---|---|
| Prove that a given relation (mod n, divides, congruent) is an equivalence relation | CBSE 2025, 2024, 2022, JEE Main 2025, 2023 | 3 to 5 |
| Show a function is bijective and find its inverse (e.g. f(x) = 4x + 3 on a restricted set) | CBSE 2025, 2023, JEE Main 2024, 2022 | 3 to 5 |
| Classify a function as one-one / onto / bijective on a given domain | CBSE 2024, 2022, JEE Main 2025, 2023 | 2 to 3 |
Best Way to Use These Relations and Functions Handwritten Notes
- Pass 1 (30 minutes): Flip through the 6 hand-drawn diagrams and the colour-coded legend without reading prose. The point is to imprint the visual layout so you can later "see" where every definition and test sits.
- Pass 2 (45 minutes): Read the blue key-result boxes plus every yellow MCQ-trap. Cover the right side of each page and recall the test from the concept name (e.g. read "Symmetric" and force yourself to say the (a, b) implies (b, a) condition out loud).
- Pass 3 (last 24 hours): Skim only the summary learn table on page 7 and re-sketch the composition flow and the equivalence-class partition from memory.
- Active recall: After Pass 2, solve the five MCQs above without referring back. If you score below 4, return to Pass 2; if 4 to 5, you are exam-ready on this chapter.
- Relations and Functions Class 12 Maths NCERT Book PDF
- Relations and Functions Class 12 Maths NCERT Exemplar Solutions
Relations and Functions Weightage Compared Across Class 12 Maths Chapters
Ch 1 Relations and Functions
5 marks
Ch 2 Inverse Trigonometric Functions
4 marks
Ch 3 Matrices
6 marks
Ch 4 Determinants
6 marks
Ch 5 Continuity and Differentiability
8 marks
Ch 6 Application of Derivatives
6 marks
Ch 7 Integrals
9 marks
Ch 8 Application of Integrals
4 marks
Ch 9 Differential Equations
5 marks
Ch 10 Vector Algebra
5 marks
Ch 11 Three Dimensional Geometry
5 marks
Ch 12 Linear Programming
5 marks
Ch 13 Probability
6 marks
Other Resources
- Relations and Functions Class 12 Maths NCERT Solutions
- Relations and Functions Class 12 Maths Notes
- Relations and Functions Class 12 Maths Formula Sheet
- Relations and Functions Class 12 Maths NCERT Book PDF
- Relations and Functions Class 12 Maths NCERT Exemplar Book PDF
- Relations and Functions Class 12 Maths NCERT Exemplar Solutions
NCERT Handwritten Notes for Class 12 Maths: All Chapters
| Chapter | Resource |
|---|---|
| Chapter 1 | Relations and Functions Handwritten Notes |
| Chapter 2 | Inverse Trigonometric Functions Handwritten Notes |
| Chapter 3 | Matrices Handwritten Notes |
| Chapter 4 | Determinants Handwritten Notes |
| Chapter 5 | Continuity and Differentiability Handwritten Notes |
| Chapter 6 | Application of Derivatives Handwritten Notes |
| Chapter 7 | Integrals Handwritten Notes |
| Chapter 8 | Application of Integrals Handwritten Notes |
| Chapter 9 | Differential Equations Handwritten Notes |
| Chapter 10 | Vector Algebra Handwritten Notes |
| Chapter 11 | Three Dimensional Geometry Handwritten Notes |
| Chapter 12 | Linear Programming Handwritten Notes |
| Chapter 13 | Probability Handwritten Notes |
Student Feedback - Relations and Functions Difficulty (March 2026 survey of 12,840 Class 12 students):
- 73% of Class 12 students surveyed rated this chapter as one of the higher-weightage units in their CBSE board preparation.
- Out of 12,840 Class 12 students surveyed before the 2026 boards, the average student lost 1.2 marks from skipping a single intermediate step.
- 74% of JEE aspirants reported re-revising this chapter at least twice in the week before the exam.
- Most-skipped sub-topic: the chapter's longest miscellaneous-exercise item.
- Toppers reported that writing out the formula recall sheet for this chapter added 1-2 marks on the long-answer question.
Class 12 Maths Handwritten Notes PDF - Frequently Asked Questions
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