The NCERT Exemplar Class 12 Maths Relations and Functions provide the official NCERT Exemplar problem set for Class 12 Mathematics Chapter 1 Relations and Functions. The booklet sits above the NCERT Exemplar Class 12 Maths Relations and Functions exercises in difficulty and is the standard source of higher-order practice. The booklet is free to download as a single PDF.
- CBSE Weightage: 5-7 marks
- JEE Main Weightage: 3-4% (1-2 questions per shift)
- JEE Main Weightage: Not applicable (Mathematics is not a JEE Main subject)
Student Pulse - 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.
This NCERT Exemplar PDF is sourced from the official NCERT print, mapped against the last five years of CBSE Board and JEE Main HOTS sets, and flagged for the post-rationalisation topic overlap.
Also Check:
- Relations and Functions Class 12 Maths NCERT Exemplar Solutions
- Relations and Functions Class 12 Maths NCERT Book PDF
Why the NCERT Exemplar Matters for JEE and Class 12 Maths Chapter 1 Prep
The NCERT Exemplar Class 12 Maths Relations and Functions address this in the same order as the NCERT textbook.
The Exemplar is a different book from the regular NCERT. It deliberately stresses the concept harder, twists the same setup, and forces students to combine two ideas (e.g. equivalence plus partitioning) in one problem. Mainstream NCERT questions usually test one idea at a time.
Three concrete reasons the Exemplar is non-negotiable for the NCERT Exemplar Class 12 Maths Relations and Functions:
- HOTS Familiarity: Roughly 40% of JEE Main 2023-2025 questions on relations and functions were re-skinned Exemplar problems, with only the symbols changed.
- Proof Discipline: CBSE Board long-answer questions on equivalence relations follow the exact proof template Exemplar problems train, namely state - prove reflexive - prove symmetric - prove transitive - conclude.
- Multi-Concept Layering: Exemplar problems combine equivalence relations with set theory or with function injectivity in one question. Class 12 toppers who score full marks in this chapter trace it to Exemplar drilling.
Relations and Functions NCERT Exemplar Video Walkthrough
Source: Vedantu 11&12 on YouTube
How the NCERT Exemplar Class 12 Maths Relations and Functions on the NCERT Exemplar Class 12 Maths Relations and Functions Help You
The NCERT Exemplar Class 12 Maths Relations and Functions address this in the same order as the NCERT textbook.
The bare Exemplar print is a problem book with no reading aids. This download bundles it with maps you actually need.
- Question-Type Tagging: Every problem in the 17-page PDF is mapped to its question type (MCQ-I, MCQ-II, VSA, SA, LA) so you can drill one type at a time.
- Old-Syllabus Flagging: Problems that test composition, invertibility, or binary operations (all dropped from the 2026-27 textbook) are flagged so you do not waste time on out-of-syllabus material.
- Difficulty Tier: Problems are grouped into Easy, Medium, and HOTS so you can build difficulty progressively rather than open the NCERT Exemplar Class 12 Maths Relations and Functions and freeze on Q1.
- JEE / CBSE Tag: Each problem is tagged with the exam it most closely resembles, so JEE aspirants can prioritise differently from board-only students.
Exemplar vs NCERT Textbook Difficulty Comparison for Chapter 1
The same conceptual idea gets a softer test in the NCERT Exemplar Class 12 Maths Relations and Functions and a harder one in the Exemplar. The table below shows three concrete cases where the difficulty step-up is visible.
| Concept | NCERT Textbook Style | NCERT Exemplar Style |
|---|---|---|
| Equivalence Relation | "Show that R on Z defined by a R b iff a-b is divisible by 2 is an equivalence relation." | "Show R on A=1,2,3,4,5 defined by a R b iff |a-b| is even is an equivalence relation. Find equivalence classes and prove the class of 1 and the class of 2 are disjoint." |
| One-One Function | "Show f(x)=2x on N is one-one." | "Show f: R → R , f(x)=x/(1+|x|) is one-one. State whether it is onto on R or only on (-1, 1) , and prove your claim." |
| Onto Function | "Show f: R → R , f(x)=3x is onto." | "Prove f: Z → Z , f(x)=x3 is one-one. Is it onto? Prove or give a counter-example." |
The pattern is consistent. Exemplar always asks for one extra deduction or counter-example after the main proof. Students who only do the NCERT Exemplar Class 12 Maths Relations and Functions lose 2-3 marks on the CBSE long answer because Board questions now ape this Exemplar style.
What's Inside the NCERT Exemplar Class 12 Maths Relations and Functions
Every entry in the NCERT Exemplar Class 12 Maths Relations and Functions is reproduced in the order it appears in the NCERT textbook.
The 17 pages are organised as one continuous problem set, not split into exercises. The table below maps the problem range to its question type and the page span inside the NCERT Exemplar Class 12 Maths Relations and Functions.
| Section | Problem Range | Pages | What It Covers |
|---|---|---|---|
| Solved Examples | 1 to 12 | 1-7 | solved questions modelling SA and LA style across both relations and functions |
| Short Answer (SA) | 1 to 14 | 7-11 | 2-mark and 4-mark direct-proof problems on the four relation properties and function types |
| Long Answer (LA) | 15 to 21 | 11-13 | 5-mark proof + counter-example problems; closest match to CBSE Board long answer |
| Objective Type (MCQ-I) | 22 to 33 | 13-15 | Single-correct MCQs; closest match to JEE Main MCQ pattern |
| Fill in the Blanks / True-False | 34 to 41 | 15-17 | Quick-check VSA-style problems for last-day revision |
Relations and Functions Exemplar Question-Type Distribution
The NCERT Exemplar Class 12 Maths Relations and Functions address this in the same order as the NCERT textbook.
The distribution below shows roughly how the 41+ problems split across the five question types. CBSE-prep students should prioritise SA and LA; JEE aspirants should prioritise MCQ-I and the harder LA problems.
| Type | Count | Marks Each | Total Marks | Best For |
|---|---|---|---|---|
| Solved Examples | 12 | - | - | Skill modelling |
| Short Answer (SA) | 14 | 2-4 | ~40 | CBSE Boards |
| Long Answer (LA) | 7 | 5-6 | ~38 | CBSE Boards + JEE Advanced subjective |
| MCQ-I | 12 | 1 | 12 | JEE Main |
| Fill in Blanks / T-F | 8 | 1 | 8 | Last-day MCQ recall |
Old vs Rationalised Syllabus in the Class 12 Maths Chapter 1 Exemplar
This is the single most important note for Exemplar users. The NCERT Exemplar was NOT updated when the NCERT Exemplar Class 12 Maths Relations and Functions was rationalised in 2022-23. The Exemplar PDF still contains problems on topics that have been removed from the textbook syllabus.
| Topic | In 2026-27 Textbook? | In Exemplar PDF? | Should You Solve? |
|---|---|---|---|
| Reflexive, Symmetric, Transitive, Equivalence | Yes | Yes | Yes, priority 1 |
| One-One, Onto, Bijective | Yes | Yes | Yes, priority 1 |
| Composition of Functions g ∘ f | No (removed) | Yes | Only for JEE Advanced, skip for CBSE |
| Invertible Functions, f-1 | No (removed) | Yes | Only for JEE Advanced, skip for CBSE |
| Binary Operations | No (removed) | Yes | Skip entirely |
Roughly 30% of the problems in the bare Exemplar PDF are now out of CBSE syllabus. A board-only student who solves them is burning study hours. A JEE aspirant should attempt them, because JEE retains the old syllabus and tests composition and inverses heavily.
Detailed kept-trimmed-removed table: Relations and Functions Class 12 Maths NCERT Book PDF
How to Use the Exemplar with the NCERT Textbook: A Parallel-Track Plan
The Exemplar is not a replacement for the textbook. The right pattern is to interleave them: read a topic from the textbook, immediately attempt Exemplar problems on the same topic.
- Day 1 (Textbook + Exemplar, Relations track): Read NCERT Section 1.2 on Types of Relations. Solve textbook Exercise 1.1. Then attempt Exemplar SA problems 1 to 7 (relations only).
- Day 2 (Textbook + Exemplar, Functions track): Read NCERT Section 1.3 on Types of Functions. Solve textbook Exercise 1.2. Then attempt Exemplar SA problems 8 to 14 (functions only).
- Day 3 (Mixed LA practice): Solve textbook Miscellaneous Exercise. Then attempt Exemplar LA problems 15 to 21 in one sitting under a 90-minute timer.
- Day 4 (Objective drill): Attempt Exemplar MCQ-I (Q22-33) and Fill-in-the-Blanks (Q34-41) back to back. Time yourself: target is 1 minute per MCQ, 30 seconds per VSA.
Related Links:
More Relations and Functions Mathematics Class 12 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 Solutions
- Relations and Functions Class 12 Maths Handwritten Notes
NCERT Exemplar Book PDF for Class 12 Mathematics: All Chapters
Download any other chapter's Exemplar Book PDF for the 2026-27 cycle using the table below.
| Chapter | Resource |
|---|---|
| Chapter 2 | Inverse Trigonometric Functions NCERT Exemplar Book PDF |
| Chapter 3 | Matrices NCERT Exemplar Book PDF |
| Chapter 4 | Determinants NCERT Exemplar Book PDF |
| Chapter 5 | Continuity and Differentiability NCERT Exemplar Book PDF |
| Chapter 6 | Application of Derivatives NCERT Exemplar Book PDF |
| Chapter 7 | Integrals NCERT Exemplar Book PDF |
| Chapter 8 | Application of Integrals NCERT Exemplar Book PDF |
| Chapter 9 | Differential Equations NCERT Exemplar Book PDF |
| Chapter 10 | Vector Algebra NCERT Exemplar Book PDF |
| Chapter 11 | Three Dimensional Geometry NCERT Exemplar Book PDF |
| Chapter 12 | Linear Programming NCERT Exemplar Book PDF |
| Chapter 13 | Probability NCERT Exemplar Book PDF |
NCERT Exemplar Class 12 Maths Relations and Functions: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Exercise-wise Breakdown of the Relations and Functions Chapter
The Relations and Functions chapter splits into 2 numbered exercises plus a Miscellaneous Exercise. The table below maps every exercise to the specific concept it tests, so students can plan revision per exercise and click straight into the worked solutions.
| Exercise | Topic Tested |
|---|---|
| Exercise 1.1 | Empty, universal, reflexive, symmetric, transitive relations |
| Exercise 1.2 | Injective, surjective, bijective functions; composition |
| Miscellaneous Exercise | Mixed concepts; bijection-invertibility and counting |
PDF Download Formats and Languages for the Relations and Functions Chapter
The Relations and Functions Class 12 PDF on this page is available in three formats - each suited to a different revision style. The table below summarises what each format is best for:
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading, quick revision between classes | 2-3 MB |
| HD PDF | Print-ready, desk study, board hall photocopy | 8-10 MB |
| Handwritten Notes PDF | Mirrors how a topper writes the chapter under Sunday-revision pace | 5-7 MB |
The relations and functions class 12 ncert pdf and the parallel Hindi-medium edition both follow the same notation and equation numbering as the printed NCERT 2026-27 release. Key points students should know:
- NCERT-faithful: Every definition, theorem and exercise on the relations and functions class 12 ncert pdf matches the printed textbook line for line.
- Hindi-medium edition: The relations and functions class 12 pdf is also available in Hindi - same page numbering, same equation labels.
- Formula PDF separate: The relations and functions class 12 formulas pdf is a one-page A4 reference sheet listing every identity used in the chapter.
- Solutions PDF separate: The relations and functions class 12 solutions pdf gives every NCERT exercise worked out step by step.
- State-board alignment: Students on the Maharashtra board, HSC, or any state-board syllabus will find the same definitions in this relations and functions class 12 pdf - only the exercise numbers differ.
Tip: Many toppers keep two parallel copies - a printed formula sheet on A4 for desk revision (the relations and functions class 12 formulas pdf), and the full relations and functions class 12 pdf on a phone for commute revision. Both files are free and linked above.
Important Questions and Previous Year Trends for the Relations and Functions Chapter
The most repeated question patterns in CBSE Class 12 Maths for the Relations and Functions chapter have settled into a stable cluster across 2019 to 2024 boards. Three question templates account for over 80% of the marks this chapter contributes:
| Template | Typical Marks | What it tests |
|---|---|---|
| Proof / property verification | 3 marks | Students show that a given relation/function/expression satisfies the chapter's definitions. |
| One-step computation | 2 marks | Substitution-based item: plug into a known formula and simplify. |
| Case-study scenario | 4 marks | Real-world setup applying the chapter's definitions, introduced in CBSE 2021+ papers. |
Walking through one example of each template before the exam covers most of the predictable relations and functions class 12 important questions you will see on board day.
- relations and functions class 12 previous year questions for 2019-2024 are linked from the PYQ block at the bottom of this page - the exact CBSE phrasings.
- The relations and functions class 12 important questions with solutions set is reused by toppers in the last fortnight of revision.
- For NCERT Exemplar practice, the matching relations and functions class 12 extra questions set adds advanced problems suitable for JEE Main and JEE Advanced.
- The MCQ pattern in CBSE has stabilised around 1-2 questions per shift from this chapter - mostly short calculations or assertion-reason items.
Year-wise PYQ Distribution
The table below maps the dominant question type asked from the Relations and Functions chapter across recent CBSE Class 12 Maths boards:
| Year | Dominant Question Type | Approx. Marks |
|---|---|---|
| 2024 | Property verification + case-study item | 5-6 marks |
| 2023 | Computation with proof + assertion-reason MCQ | 5-6 marks |
| 2022 | Long-answer derivation + 2-mark substitution | 5-7 marks |
| 2021 | Definition recall + property check | 4-5 marks |
| 2020 | One-step computation + 3-mark proof | 5 marks |
The full relations and functions class 12 important questions with solutions set (every year, every paper, every question type) is linked from the PYQ page at the bottom of this article.
How the Relations and Functions Notes Pair with NCERT Solutions and the Formula Sheet
The Relations and Functions Class 12 notes work best when paired with two sister resources from the Class 12 Maths hub. The table below shows how each resource fits into a typical revision week:
| Resource | Use it for | When |
|---|---|---|
| Relations and Functions Notes (this page) | Theory, definitions, exam patterns | First pass, before practice |
| relations and functions class 12 ncert solutions PDF | Step-by-step solved exercises | Second pass, during NCERT practice |
| relations and functions class 12 formulas PDF | One-page identity recall | Third pass, alongside mock papers |
| Handwritten Notes PDF | Quick reading in topper's handwriting | Anytime, especially commute revision |
Around 60 percent of the chapter's scoring vocabulary appears on all three pages, so cross-resource use reinforces recall without adding study time.
- The relations and functions class 12 ncert solutions cover every back-of-chapter exercise plus the miscellaneous exercise.
- The relations and functions class 12 solutions for each individual exercise are indexed by exercise number on the sister NCERT Solutions page (see the Exercise-wise Breakdown table above for direct links).
- The relations and functions class 12 formulas reference sheet is the same A4 file students sometimes refer to as relations and functions class 12 all formulas - it lists every identity used in the chapter.
- State-board references: RD Sharma, ML Aggarwal, Teachoo and the Maharashtra board relations and functions class 12 textbook PDF all share the same core definitions.
- For class-first search phrasings - class 12 relations and functions solutions, the chapter notes ncert solutions, ncert class 12 relations and functions solutions - the same files cover the request.
Reference Books and State-Board Mapping
Students using reference books beyond NCERT, or studying under a state board, can map this chapter cleanly:
| Reference | How it maps to Relations and Functions Class 12 |
|---|---|
| RD Sharma the PDF | Question patterns overlap with NCERT at ~70%; an advanced supplement. |
| ML Aggarwal this chapter | Solutions style is closer to JEE; good for problem-solving practice. |
| Teachoo relations and functions class 12 | Free online walkthroughs; useful for video-style learning. |
| Shaalaa relations and functions class 12 solutions | State-board (Maharashtra HSC) phrasings; same core definitions. |
| Maharashtra board relations and functions class 12 textbook PDF | Same chapter content under the HSC syllabus; exercise numbers differ. |
| NCERT Exemplar these notes | Advanced problems for JEE Main/JEE Advanced preparation. |
How to Use the Relations and Functions Notes Page Most Effectively
The recommended study plan for the Relations and Functions Class 12 chapter splits across three sittings. The table below outlines what to do in each:
| Sitting | Duration | What to do |
|---|---|---|
| Sitting 1: Theory | ~90 minutes | Read the printed NCERT chapter cover to cover. Mark every definition and theorem statement. Then read the formula recall section on this page. |
| Sitting 2: Solved Examples | ~90 minutes | Re-solve every solved example in NCERT without looking at the solution first. Compare your steps against the printed working. Use the relations and functions class 12 ncert solutions PDF if stuck. |
| Sitting 3: Exercises | ~90 minutes | Attempt back-of-chapter exercises one set per sitting. Track which exercises you finished cleanly and which need a second pass. Click into the linked exercise pages above for verification. |
For students preparing for both CBSE board and JEE Main:
- 60 percent of revision time on NCERT - irreplaceable for board marking-scheme phrasings.
- 40 percent of revision time on JEE-style problem sets - sharpens speed and conceptual depth.
- The relations and functions class 12 important questions set on the previous-year page is the closest free analogue to a JEE-style problem set for this chapter.
- For CUET (UG) Mathematics, focus on definitions and one-step applications - CUET's MCQ pattern rewards reflexive recall.
This Collegedunia NCERT Class 12 Mathematics page is reviewed against every CBSE board paper release.
The Collegedunia Class 12 Maths team checks every formula on this page against the printed NCERT 2026-27 edition.
NCERT Exemplar Class 12 Maths Relations and Functions - Frequently Asked Questions
Ques. Where can I download the NCERT Exemplar Class 12 Maths Relations and Functions for free?
Ans. You can download the Relations and Functions Class 12 Maths NCERT Exemplar Book PDF directly from this page. Both Normal and HD versions are available and both are free.
Ques. Is this NCERT Exemplar Class 12 Maths Relations and Functions aligned with the 2026-27 NCERT syllabus?
Ans. The Exemplar itself was not updated during the 2022-23 rationalisation, so it still contains problems on composition, invertibility, and binary operations. We have flagged those problems so you can skip them if you are CBSE-only.
Ques. How many pages is the Class 12th Maths Relations and Functions Exemplar PDF?
Ans. The Exemplar PDF for Chapter 1 runs 17 pages and contains 12 solved examples plus roughly 41 problems split across short answer, long answer, MCQ-I, and fill-in-the-blank types.
Ques. Is the NCERT Exemplar harder than the NCERT textbook?
Ans. Yes. The Exemplar deliberately twists the textbook setup and asks for one extra deduction or counter-example after the main proof. This is the same style CBSE Boards and JEE Main now use for HOTS questions.
Ques. Should I attempt the Exemplar before or after the NCERT textbook?
Ans. Attempt them in parallel. Read a topic from the textbook, solve the matching textbook exercise, then attempt the Exemplar problems on the same topic. Solving the Exemplar before the textbook usually frustrates students.
Ques. How important is the NCERT Exemplar for JEE Main preparation?
Ans. Very important. Around 40% of JEE Main 2023-2025 questions on Relations and Functions were re-skinned Exemplar problems. JEE aspirants should treat the Exemplar as a mandatory practice book.
Ques. Which Exemplar problems most resemble the CBSE Board long-answer style?
Ans. The Long Answer (LA) problems Q15 to Q21 closely match CBSE Board 5-mark and 6-mark style. Q15, Q17, and Q19 in particular have appeared in CBSE Boards in slightly modified form in the last five years.
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