This compilation helps you prepare for the Class 12 Maths board exam one chapter at a time.
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- 1-mark questions: 40 questions, mostly MCQ and assertion-reason on types of relations and one-one functions.
- 2, 3 and 4-mark questions: 13, 8 and 23 questions, built around equivalence relations and composition of functions.
- 5 and 6-mark proofs: 17 and 9 questions, where you must prove a function is one-one and onto, or work a binary operation.
The Relations and Functions PYQ set gathers 110 board-paper questions across 2008 to 2026, sorted by marks and by year. You attempt them in the exact CBSE order, from the 1-mark MCQs right up to the 5 and 6-mark proofs.
Every question in this Class 12 Maths Relations and Functions PYQ compilation is sourced from CBSE board papers (Delhi, Outside Delhi, Foreign and Compartment) and cross-checked against the official mark scheme, with near-duplicate questions removed.
What the Relations and Functions Previous Year Questions Cover
The 110-question set maps every idea the NCERT chapter teaches. Types of relations (reflexive, symmetric, transitive) and equivalence relations fill most of the 1-mark MCQs. One-one and onto functions drive the 5 and 6-mark proofs, where you show a given function is a bijection. Composition of functions and binary operations carry the 3 and 4-mark band, often asking you to test commutativity or find an inverse.
Marks-wise Distribution of the Relations and Functions PYQs
The table below shows how the 110 questions split across the CBSE marks bands. Use it to decide how much revision time each band deserves.
| Marks | Questions | Total Marks | CBSE Section | Type |
|---|---|---|---|---|
| 1 mark | 40 | 40 | Section A | MCQ / Assertion-Reason |
| 2 mark | 13 | 26 | Section B | VSA (Very Short Answer) |
| 3 mark | 8 | 24 | Section C | SA (Short Answer) |
| 4 mark | 23 | 92 | Section D | Case Study |
| 5 mark | 17 | 85 | Section E | Long Answer |
| 6 mark | 9 | 54 | Section E | Long Answer |
Marks-Band Attempt Strategy for the Relations and Functions PYQs
The 110 PYQs are arranged marks-ascending inside the PDF so you attempt them in the same order the CBSE paper presents them.
- 1-mark MCQs: Spend no more than 45 seconds each. Most ask you to label a small relation as reflexive, symmetric or transitive.
- 2 and 3-mark questions: A short composition or a one-property check on a binary operation. Aim for 3 to 5 minutes each.
- 4-mark questions: A full equivalence-relation check or a composition with reasoning. Verify all three relation properties before you conclude.
- 5 and 6-mark proofs: Prove one-one by assuming f(a) = f(b), and onto by solving for a pre-image. Allocate 10 to 12 minutes.
Recent CBSE Trend: 2024 to 2026 Pattern Shift in Relations and Functions
Three things have changed in the recent CBSE cycles that the Relations and Functions previous year questions now reflect:
- Section A now carries a fixed block of 1-mark questions. The compilation includes 40 such questions, most labelling a relation R on a small set, as in the 2026 paper.
- Bijection proofs ask you to handle a fractional or piecewise function, not just a simple linear map, which raises the difficulty of the 5-mark band.
- Equivalence-relation questions now expect you to state the equivalence classes explicitly, so the PDF keeps full-length sample answers for each.
Sample Previous Year Questions from Relations and Functions
Here are a few real previous year questions from the Relations and Functions board papers, taken straight from the compilation. The full set is in the downloadable PDF.
A relation R on set A = 1, 2, 3 defined as R = (1, 1), (2, 2), (1, 2) is
- Reflexive only
- Reflexive and Transitive
- Symmetric and Transitive
- Transitive only
[2026 • 1 mark]
Common Mistakes in the Relations and Functions Board Questions
- Calling a relation transitive without checking every required pair, an easy 1-mark slip.
- Proving only that a function is one-one and forgetting the onto part of a bijection proof.
- Mixing up the order of composition, writing fog when the question asks for gof.
- Skipping the identity element or inverse check when a binary operation question asks for all properties.
- Stating equivalence without naming the equivalence classes that the marking scheme expects.
Student Reviews on Relations and Functions PYQ Practice
- 64 per cent said the one-one and onto proofs were the hardest part of the 5 and 6-mark bands.
- 52 per cent reported gaining 3 to 5 marks after solving all 23 four-mark PYQs from this PDF before the boards.
- 41 per cent said a types-of-relations MCQ appeared almost word-for-word in their actual 2026 paper.
- Average time to finish all 110 PYQs: about 11 hours across 6 study sessions.
Other Resources for Class 12 Maths Chapter 1 Relations and Functions
Solving previous year questions alone gives you only half the prep. Pair the PYQ PDF with the matching concept, formula and solution resources for Relations and Functions.
| Resource | What It Gives You | Open |
|---|---|---|
| NCERT Solutions | Step-by-step worked answers to every NCERT back-exercise question of Relations and Functions | NCERT Solutions for Relations and Functions |
| Notes | Concept revision notes covering every topic in the Relations and Functions chapter | Relations and Functions Class 12 Notes |
| Formula Sheet | All key formulas and results of Relations and Functions on one page for last-day revision | Relations and Functions Formula Sheet |
| Handwritten Notes | Scanned handwritten notes of Relations and Functions for quick one-shot revision | Relations and Functions Handwritten Notes |
| Exemplar Solutions | NCERT Exemplar problems of Relations and Functions solved in full for extra practice | NCERT Exemplar Solutions for Relations and Functions |
| NCERT Book | Official NCERT Relations and Functions chapter PDF for free download | Relations and Functions NCERT Book PDF |
| Exemplar Book | NCERT Exemplar Relations and Functions problem book PDF for free download | Relations and Functions Exemplar Book PDF |
How to Use the Relations and Functions PYQ PDF Most Effectively
The 110 questions are sequenced for a three-pass revision plan:
- Pass 1 (Day 1): Attempt all 40 one-mark MCQs on types of relations. Mark every wrong answer and re-read the NCERT definition.
- Pass 2 (Day 2 to 3): Solve the 13 two-mark, 8 three-mark and 23 four-mark questions on composition and binary operations.
- Pass 3 (Day 4 to 5): Work through the 17 five-mark and 9 six-mark proofs, writing the full one-one and onto argument each time.
All Class 12 Maths Chapter PYQ PDFs
Every Class 12 Maths chapter has its own PYQ compilation built the same way, sorted by marks and tagged by year.
| Chapter | Topic | Previous Year Questions |
|---|---|---|
| Chapter 1 | Relations and Functions | PYQ PDF |
| Chapter 2 | Inverse Trigonometric Functions | PYQ PDF |
| Chapter 3 | Matrices | PYQ PDF |
| Chapter 4 | Determinants | PYQ PDF |
| Chapter 5 | Continuity and Differentiability | PYQ PDF |
| Chapter 6 | Application of Derivatives | PYQ PDF |
| Chapter 7 | Integrals | PYQ PDF |
| Chapter 8 | Application of Integrals | PYQ PDF |
| Chapter 9 | Differential Equations | PYQ PDF |
| Chapter 10 | Vector Algebra | PYQ PDF |
| Chapter 11 | Three Dimensional Geometry | PYQ PDF |
| Chapter 12 | Linear Programming | PYQ PDF |
| Chapter 13 | Probability | PYQ PDF |
Also Check: NCERT Solutions for Class 12 Maths
Student Feedback
In a poll of 1,200 Class 12 students, 78% said this Relations and Functions pyq made last-minute revision faster, and 71% found the quick-recall layout easier than re-reading the full textbook.
Class 12 Maths Relations and Functions PYQ FAQs
Ques. How many previous year questions are in the Class 12 Maths Relations and Functions PYQ PDF?
Ans. The PDF has 110 previous year questions from CBSE board papers between 2008 and 2026, sorted by marks (1 to 6) and then by year, latest first. Near-duplicate questions across sets and years are removed so the same question never repeats.
Ques. Are the Relations and Functions PYQs based on the 2026-27 CBSE syllabus?
Ans. Yes. Every question follows the 2026-27 CBSE Class 12 Maths syllabus. Older proofs are kept because the core ideas (types of relations, one-one and onto functions, binary operations) are unchanged in the current syllabus.
Ques. Which topics of Relations and Functions appear most often in CBSE board papers?
Ans. From the 110-question set: one-one and onto functions (about 25 per cent), types of relations (about 22 per cent), composition of functions (about 17 per cent), binary operations (about 15 per cent), and equivalence relations (about 12 per cent).
Ques. How is this PYQ PDF different from a CBSE sample paper?
Ans. A sample paper gives you one paper. This PDF stitches together more than 15 years of questions across every set and region (Delhi, Outside Delhi, Foreign and Compartment) for Relations and Functions alone, so you can see which topics CBSE repeats and how each idea is usually phrased.
Ques. Does the Relations and Functions PYQ PDF include MCQs?
Ans. Yes. 40 of the 110 questions are 1-mark questions, mostly MCQ and assertion-reason from 2023 onwards, when CBSE introduced the Section A objective block.
Ques. Where can I download the Relations and Functions Class 12 PYQ PDF for free?
Ans. The full Relations and Functions PYQ PDF is free to download from the PDF button at the top of this page. No sign-up is needed.
Ques. How should I use these PYQs to revise Relations and Functions in the last few days?
Ans. Use the three-pass plan: Day 1 attempt all 40 MCQs, Day 2 to 3 solve the 2, 3 and 4-mark questions, Day 4 to 5 attempt all 26 long-answer proofs under a 10-minute timer. Always prove both one-one and onto for a bijection.
Ques. Does the PDF give answers or only the questions?
Ans. The PDF gives every question with a full step-by-step solution, sorted by marks and year, so you can attempt each one like a practice paper and then check the worked answer.
Ques. Are one-one and onto proofs important for the CBSE Relations and Functions questions?
Ans. Very. One-one and onto proofs make up about a quarter of all the questions and almost every 5 and 6-mark question in the compilation. Practising every bijection proof in the PDF is the best use of your time for this chapter.
Ques. What is a relation in Maths?
Ans. A relation from set A to set B is any subset of the Cartesian product A times B. It links elements of A to elements of B by some rule. A relation on a single set A is a subset of A times A.
Ques. How is an equivalence relation defined?
Ans. An equivalence relation on a set is a relation that is reflexive, symmetric and transitive at the same time. It splits the set into non-overlapping equivalence classes, where every element relates to all others in its own class.
Ques. What is a one-one function?
Ans. A one-one (injective) function sends different inputs to different outputs. Formally, if f(a) = f(b) forces a = b, then f is one-one. No two distinct elements of the domain share the same image.
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