Sets, Relations and Functions in JEE Main 2026 — Complete Overview
Sets, Relations and Functions is Unit 1 of the JEE Main Mathematics syllabus as prescribed by the National Testing Agency (NTA). It carries a weightage of 3–5% and typically contributes approximately 1 question(s) per paper. Classified as a Easy-difficulty chapter, Sets, Relations and Functions is a reliable source of guaranteed marks — missing questions from this chapter hurts your percentile because most other students answer them correctly.
The official NTA syllabus for Sets, Relations and Functions comprises 6 topics: Sets and their representation, power sets, types of sets, Union, intersection, complement, Venn diagrams, Relations: domain, codomain, range, and 3 more topics. Every topic listed in the NTA syllabus is examinable in JEE Main — NTA does not restrict questions to specific sub-topics within a chapter. Your preparation must cover all 6 official topics comprehensively to avoid losing marks from any corner of this chapter.
Strategically, Sets, Relations and Functions contributes meaningfully to your JEE Main score. Even 1 question per paper is 4 marks — and in a competitive exam where 1 mark can shift your percentile by 0.5–1 points, no chapter is optional.
JEE Main Mathematics has 14 chapters in total. Sets, Relations and Functions is Unit 1, which means it covers foundational concepts that underpin many later chapters. Strong understanding here accelerates learning across the rest of the syllabus.
In the JEE Main examination, the Mathematics section contains 25 questions: 20 Multiple Choice Questions (single correct answer, +4/–1 marking) and 5 Numerical Value Type questions (no negative marking, exact numeric answer). Questions from Sets, Relations and Functions can appear in either format. The NVT questions from this chapter often test a specific formula application or a precise calculation — making it even more critical to have all 4 key formulas memorised and practised in numerical contexts.
For JEE Main 2026 preparation, allocate time to Sets, Relations and Functions based on its difficulty and weightage. As an Easy chapter, 1–2 weeks of focused preparation — NCERT reading, formula memorisation, and 40–50 PYQs — is typically sufficient for 95%+ accuracy.
Topic-by-Topic Analysis — Sets, Relations and Functions (NTA JEE Main Syllabus)
A detailed breakdown of each official NTA topic within Sets, Relations and Functions — what NTA tests, how questions are framed, and how to master each sub-topic for JEE Main 2026.
1. Sets and their representation, power sets, types of sets
Sets and their representation, power sets, types of sets is an integral part of the Sets, Relations and Functions unit in JEE Main Mathematics. This sub-topic is explicitly listed in the NTA-prescribed syllabus, making it fully examinable in every JEE Main session. Questions on sets and their representation, power sets, types of sets in JEE Main test a combination of conceptual understanding and numerical ability — consistent with NTA's philosophy of assessing applied knowledge rather than rote memorisation.
In the JEE Main examination, questions involving sets and their representation, power sets, types of sets typically appear in three formats: (1) Direct formula application — testing whether students identify the correct formula and substitute values; (2) Conceptual MCQs — testing whether students understand the underlying principle and can eliminate wrong statements; (3) Multi-step problems — combining sets and their representation, power sets, types of sets with other Sets, Relations and Functions topics or adjacent chapters. Students who have practised 15–20 PYQs specifically on sets and their representation, power sets, types of sets will recognise the pattern immediately during the exam.
To master sets and their representation, power sets, types of sets for JEE Main 2026: begin with the NCERT Mathematics textbook's treatment of this concept — NCERT is the primary reference NTA uses when setting questions. For Easy chapters, NCERT combined with PYQ practice is fully sufficient. Pay special attention to the conditions under which concepts related to sets and their representation, power sets, types of sets are valid — NTA frequently frames trap questions where the standard approach fails due to a boundary condition or limiting case being violated.
2. Union, intersection, complement, Venn diagrams
Union, intersection, complement, Venn diagrams is an integral part of the Sets, Relations and Functions unit in JEE Main Mathematics. This sub-topic is explicitly listed in the NTA-prescribed syllabus, making it fully examinable in every JEE Main session. Questions on union, intersection, complement, venn diagrams in JEE Main test a combination of conceptual understanding and numerical ability — consistent with NTA's philosophy of assessing applied knowledge rather than rote memorisation.
In the JEE Main examination, questions involving union, intersection, complement, venn diagrams typically appear in three formats: (1) Direct formula application — testing whether students identify the correct formula and substitute values; (2) Conceptual MCQs — testing whether students understand the underlying principle and can eliminate wrong statements; (3) Multi-step problems — combining union, intersection, complement, venn diagrams with other Sets, Relations and Functions topics or adjacent chapters. Students who have practised 15–20 PYQs specifically on union, intersection, complement, venn diagrams will recognise the pattern immediately during the exam.
To master union, intersection, complement, venn diagrams for JEE Main 2026: begin with the NCERT Mathematics textbook's treatment of this concept — NCERT is the primary reference NTA uses when setting questions. For Easy chapters, NCERT combined with PYQ practice is fully sufficient. Pay special attention to the conditions under which concepts related to union, intersection, complement, venn diagrams are valid — NTA frequently frames trap questions where the standard approach fails due to a boundary condition or limiting case being violated.
3. Relations: domain, codomain, range
Relations: domain, codomain, range is an integral part of the Sets, Relations and Functions unit in JEE Main Mathematics. This sub-topic is explicitly listed in the NTA-prescribed syllabus, making it fully examinable in every JEE Main session. Questions on relations: domain, codomain, range in JEE Main test a combination of conceptual understanding and numerical ability — consistent with NTA's philosophy of assessing applied knowledge rather than rote memorisation.
In the JEE Main examination, questions involving relations: domain, codomain, range typically appear in three formats: (1) Direct formula application — testing whether students identify the correct formula and substitute values; (2) Conceptual MCQs — testing whether students understand the underlying principle and can eliminate wrong statements; (3) Multi-step problems — combining relations: domain, codomain, range with other Sets, Relations and Functions topics or adjacent chapters. Students who have practised 15–20 PYQs specifically on relations: domain, codomain, range will recognise the pattern immediately during the exam.
To master relations: domain, codomain, range for JEE Main 2026: begin with the NCERT Mathematics textbook's treatment of this concept — NCERT is the primary reference NTA uses when setting questions. For Easy chapters, NCERT combined with PYQ practice is fully sufficient. Pay special attention to the conditions under which concepts related to relations: domain, codomain, range are valid — NTA frequently frames trap questions where the standard approach fails due to a boundary condition or limiting case being violated.
4. Types of functions: one-one, onto, bijective
Types of functions: one-one, onto, bijective is an integral part of the Sets, Relations and Functions unit in JEE Main Mathematics. This sub-topic is explicitly listed in the NTA-prescribed syllabus, making it fully examinable in every JEE Main session. Questions on types of functions: one-one, onto, bijective in JEE Main test a combination of conceptual understanding and numerical ability — consistent with NTA's philosophy of assessing applied knowledge rather than rote memorisation.
In the JEE Main examination, questions involving types of functions: one-one, onto, bijective typically appear in three formats: (1) Direct formula application — testing whether students identify the correct formula and substitute values; (2) Conceptual MCQs — testing whether students understand the underlying principle and can eliminate wrong statements; (3) Multi-step problems — combining types of functions: one-one, onto, bijective with other Sets, Relations and Functions topics or adjacent chapters. Students who have practised 15–20 PYQs specifically on types of functions: one-one, onto, bijective will recognise the pattern immediately during the exam.
To master types of functions: one-one, onto, bijective for JEE Main 2026: begin with the NCERT Mathematics textbook's treatment of this concept — NCERT is the primary reference NTA uses when setting questions. For Easy chapters, NCERT combined with PYQ practice is fully sufficient. Pay special attention to the conditions under which concepts related to types of functions: one-one, onto, bijective are valid — NTA frequently frames trap questions where the standard approach fails due to a boundary condition or limiting case being violated.
5. Composition of functions, inverse of a function
Composition of functions, inverse of a function is an integral part of the Sets, Relations and Functions unit in JEE Main Mathematics. This sub-topic is explicitly listed in the NTA-prescribed syllabus, making it fully examinable in every JEE Main session. Questions on composition of functions, inverse of a function in JEE Main test a combination of conceptual understanding and numerical ability — consistent with NTA's philosophy of assessing applied knowledge rather than rote memorisation.
In the JEE Main examination, questions involving composition of functions, inverse of a function typically appear in three formats: (1) Direct formula application — testing whether students identify the correct formula and substitute values; (2) Conceptual MCQs — testing whether students understand the underlying principle and can eliminate wrong statements; (3) Multi-step problems — combining composition of functions, inverse of a function with other Sets, Relations and Functions topics or adjacent chapters. Students who have practised 15–20 PYQs specifically on composition of functions, inverse of a function will recognise the pattern immediately during the exam.
To master composition of functions, inverse of a function for JEE Main 2026: begin with the NCERT Mathematics textbook's treatment of this concept — NCERT is the primary reference NTA uses when setting questions. For Easy chapters, NCERT combined with PYQ practice is fully sufficient. Pay special attention to the conditions under which concepts related to composition of functions, inverse of a function are valid — NTA frequently frames trap questions where the standard approach fails due to a boundary condition or limiting case being violated.
6. Real-valued functions of real variable, algebra of functions
Real-valued functions of real variable, algebra of functions is an integral part of the Sets, Relations and Functions unit in JEE Main Mathematics. This sub-topic is explicitly listed in the NTA-prescribed syllabus, making it fully examinable in every JEE Main session. Questions on real-valued functions of real variable, algebra of functions in JEE Main test a combination of conceptual understanding and numerical ability — consistent with NTA's philosophy of assessing applied knowledge rather than rote memorisation.
In the JEE Main examination, questions involving real-valued functions of real variable, algebra of functions typically appear in three formats: (1) Direct formula application — testing whether students identify the correct formula and substitute values; (2) Conceptual MCQs — testing whether students understand the underlying principle and can eliminate wrong statements; (3) Multi-step problems — combining real-valued functions of real variable, algebra of functions with other Sets, Relations and Functions topics or adjacent chapters. Students who have practised 15–20 PYQs specifically on real-valued functions of real variable, algebra of functions will recognise the pattern immediately during the exam.
To master real-valued functions of real variable, algebra of functions for JEE Main 2026: begin with the NCERT Mathematics textbook's treatment of this concept — NCERT is the primary reference NTA uses when setting questions. For Easy chapters, NCERT combined with PYQ practice is fully sufficient. Pay special attention to the conditions under which concepts related to real-valued functions of real variable, algebra of functions are valid — NTA frequently frames trap questions where the standard approach fails due to a boundary condition or limiting case being violated.
Key Formulas for Sets, Relations and Functions — JEE Main 2026
These 4 formulas are the most frequently tested in JEE Main from Sets, Relations and Functions. Memorise each formula, understand what every symbol represents, and practise applying each one in 10+ different problem contexts.
Plain text: n(A∪B) = n(A) + n(B) - n(A∩B)
This formula from Sets, Relations and Functions is one of the 4 most-tested formulas in JEE Main Mathematics. Ensure you understand: (1) what each variable represents and its SI unit, (2) the conditions under which this formula applies, and (3) what happens at limiting cases. NTA regularly tests dimensionality and edge-case behaviour of formulas like this one.
Plain text: n(A∪B∪C) = n(A)+n(B)+n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C)
This formula from Sets, Relations and Functions is one of the 4 most-tested formulas in JEE Main Mathematics. Ensure you understand: (1) what each variable represents and its SI unit, (2) the conditions under which this formula applies, and (3) what happens at limiting cases. NTA regularly tests dimensionality and edge-case behaviour of formulas like this one.
Plain text: Number of subsets of set with n elements = 2ⁿ
This formula from Sets, Relations and Functions is one of the 4 most-tested formulas in JEE Main Mathematics. Ensure you understand: (1) what each variable represents and its SI unit, (2) the conditions under which this formula applies, and (3) what happens at limiting cases. NTA regularly tests dimensionality and edge-case behaviour of formulas like this one.
For Sets, Relations and Functions, the most effective formula memorisation technique is active recall: write out all 4 formulas from memory every morning for 7 consecutive days. On Day 1, you may forget 2–3 formulas. By Day 7, you will recall all of them perfectly under exam pressure. This is far more effective than passively reading formula sheets. Pair this with solving 2–3 problems per formula daily to build application speed alongside recall.
JEE Main Analysis — Sets, Relations and Functions (2019–2025 Data)
Analysis of JEE Main papers from 2019 to 2025 shows that Sets, Relations and Functions has appeared consistently across all sessions (January and April) and all shifts (Shift 1 and Shift 2). With an average of 1 question(s) per paper, this chapter contributes 4 marks assuming perfect accuracy. Across both January and April sessions of JEE Main, a student appearing in all sessions could face 4–8 questions from Sets, Relations and Functions — reinforcing why complete chapter preparation is essential.
The question pattern for Sets, Relations and Functions has evolved across JEE Main sessions. Between 2019 and 2021, NTA asked predominantly formula-based questions that rewarded formula memorisation. From 2022 onwards, questions have shifted toward application-oriented problems — testing whether students can apply concepts in unfamiliar or combined scenarios. For JEE Main 2026, NTA is expected to continue this trend toward application-based questions, making conceptual clarity more important than ever.
The Easy difficulty classification for Sets, Relations and Functions means that approximately 70–80% of JEE Main aspirants answer questions from this chapter correctly. Losing marks here hurts your percentile disproportionately — competitors who also prepared well will get these correct.
For JEE Main 2026, the recommended approach for Sets, Relations and Functions is to: first target 100% accuracy on the most-frequently tested sub-topics (Sets and their representation, power sets, types of sets and Union, intersection, complement, Venn diagrams), then systematically work through the remaining4 topics. Use HenceProve's JEE Main mock test platform to access all available PYQs from this chapter, filter by year, and track your improvement over time.
Year-wise Question Pattern — Sets, Relations and Functions in JEE Main
| Year | Jan Session | Apr Session | Most Tested Sub-topic |
|---|---|---|---|
| 2025 | 1 | 1 | Sets and their representation, power sets, types of sets |
| 2024 | 1 | 1 | Union, intersection, complement, Venn diagrams |
| 2023 | 1 | 1 | Relations: domain, codomain, range |
| 2022 | 1 | 1 | Types of functions: one-one, onto, bijective |
| 2021 | 1 | 1 | Composition of functions, inverse of a function |
| 2020 | 1 | 1 | Real-valued functions of real variable, algebra of functions |
| 2019 | 1 | 1 | Sets and their representation, power sets, types of sets |
The table above shows the approximate question count from Sets, Relations and Functions across JEE Main sessions from 2019 to 2025. The average has remained consistent at ~1 question(s) per paper, though individual sessions may vary by 1 question. The “Most Tested Sub-topic” column identifies which official NTA topics have appeared most frequently — these deserve proportionally more preparation time.
An important pattern from historical JEE Main data: topics that appeared less frequently in 2023–2024 often appear more prominently in 2025–2026 papers. NTA rotates sub-topic emphasis deliberately to prevent students from predicting questions based solely on the previous year's paper. This confirms that comprehensive preparation of all 6official topics is essential — you cannot safely skip any NTA-listed topic within Sets, Relations and Functions.
5 Common Mistakes in Sets, Relations and Functions — JEE Main 2026
Many students skip NCERT Mathematics and jump straight to reference books for Sets, Relations and Functions. This is a critical error. NTA frames JEE Main questions based on NCERT-level understanding. Students who haven't read NCERT carefully often fall for plausible-but-incorrect MCQ options that exploit subtle conceptual gaps. Read NCERT first — completely, not just highlighted portions — then move to reference books and PYQ practice.
Memorising the 4 key formulas from Sets, Relations and Functions is necessary but insufficient. NTA frequently asks "under what conditions does this formula apply?" and tests limiting cases and sign conventions. Students who know the derivation of each formula can answer these questions correctly without having memorised the specific edge case. Spend 10–15 minutes understanding each formula's derivation — this investment pays off for the entire exam.
JEE Main includes 5 NVT questions per subject, and Sets, Relations and Functions can contribute to these. NVT questions have no negative marking — making them high-value scoring opportunities. However, the exact numerical precision required differs from MCQ practice. Students who only practise MCQ formats often make unit conversion or rounding errors in NVT questions. Practise NVT questions from Sets, Relations and Functions separately to develop the right approach.
A significant fraction of wrong answers in Sets, Relations and Functions come from unit conversion errors and sign convention mistakes — not from conceptual misunderstanding. Students who understand the physics perfectly still lose marks because they didn't convert units or misapplied directional signs. Before solving any numerical from Sets, Relations and Functions, establish a clear coordinate system, list all given quantities with units, and convert everything to SI units before substituting into formulas.
Previous Year Questions are the most reliable indicator of JEE Main exam format. Students who solve all available PYQs from Sets, Relations and Functions develop familiarity with NTA's exact question style, making them faster and more accurate on exam day. Solve PYQs from 2019–2025 on HenceProve's chapter-wise test platform. When reviewing: focus not just on getting the right answer but on understanding why each wrong option is wrong — this builds genuine exam intuition that formula memorisation alone cannot provide.
How to Prepare Sets, Relations and Functions for JEE Main 2026 — 4-Step Strategy
Start with NCERT Mathematics — read the Sets, Relations and Functions chapter completely. Not skimming, not just solved examples — every paragraph, every theorem, every statement. NCERT's language is designed to reflect exactly what NTA expects students to know. Take notes on definitions, important principles, and the conditions under which each concept applies. Pay particular attention to: Sets and their representation, power sets, types of sets; Union, intersection, complement, Venn diagrams. After completing NCERT, read the corresponding chapter in your reference book (HC Verma / DC Pandey for Physics, O.P. Tandon for Chemistry, Arihant / Cengage for Mathematics) to reinforce your conceptual foundation with additional solved examples.
Create a dedicated formula sheet for Sets, Relations and Functions with all 4 key formulas. For each formula: (a) Write it in standard form, (b) Define every symbol with its SI unit, (c) Understand the derivation conceptually, (d) Write the conditions for the formula's validity, (e) Write one example problem using it. Test yourself daily by covering the formula sheet and writing all formulas from memory. By the end of Week 2, aim for instant recall of all 4 formulas without hesitation. Combine recall practice with 2–3 problems per formula per day to build application speed alongside memorisation.
With conceptual foundation and formula mastery established, solve Previous Year Questions from Sets, Relations and Functions. On HenceProve, access all available PYQs from this chapter across all JEE Main sessions (2019–2025). Target 60–80 PYQs at minimum. For each wrong answer: (a) Identify the exact error — conceptual, formula, or arithmetic, (b) Review the relevant concept or formula, (c) Solve 2–3 similar problems to reinforce the correct approach. Track your accuracy by sub-topic within Sets, Relations and Functions to identify which of the 6 official topics needs more attention. Achieve 90%+ PYQ accuracy before moving to mock tests.
Take chapter-specific mock tests on Sets, Relations and Functions using HenceProve's chapter-wise test feature. A 25–30 minute timed test reveals weaknesses that PYQ practice alone doesn't expose — particularly time management and exam-condition accuracy. After each mock test: (a) Analyse every wrong or uncertain answer in detail, (b) Update your formula sheet with any gaps discovered, (c) Re-read relevant NCERT sections for topics where mistakes persist. Repeat this mock test + revision cycle every 2 weeks until you consistently score 85%+ accuracy. In the final 4 weeks before JEE Main, revise your Sets, Relations and Functions formula sheet and notes every 3–4 days to maintain retention under heavy overall study load.
Best Books for Sets, Relations and Functions — JEE Main 2026
Choosing the right study material for Sets, Relations and Functions is critical for JEE Main preparation. Here are the most effective books for JEE Main Mathematics, with specific guidance on how to use each.
Comprehensive coverage of all JEE Mathematics topics with graded exercises and fully solved examples matching NTA patterns.
For Sets, Relations and Functions: Read this chapter first for conceptual clarity and worked examples before attempting PYQs.
Chapter-wise Arihant books are excellent for JEE Main-level practice. Each book covers one topic area with theory, solved examples, and PYQs.
For Sets, Relations and Functions: Use the chapter exercises to build problem-solving speed and accuracy on diverse question types.
Classic text for Coordinate Geometry and Trigonometry. Essential for chapters where NTA asks deeper conceptual questions.
For Sets, Relations and Functions: Reference for advanced problem types that NTA occasionally uses for Hard-level questions in this chapter.
Advanced calculus resource for strengthening limits, continuity, differentiation, and integration — the backbone of JEE Mathematics.
For Sets, Relations and Functions: Quick revision reference for formulas and key theorems before the exam.
For JEE Main (not JEE Advanced), NCERT is the foundation. Do not skip NCERT in favour of reference books. For Sets, Relations and Functions, follow this order: NCERT → PYQ practice on HenceProve → Reference book chapter → Mock tests. Do not attempt to read a reference book cover-to-cover — use only the Sets, Relations and Functions chapter until you have exhausted NCERT and PYQs.
Myths vs Facts — Sets, Relations and Functions in JEE Main
Clearing up common misconceptions helps you prepare more efficiently and avoid wasting preparation time on wrong strategies.