NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions gives step-by-step answers for every question in the NCERT textbook. The solutions PDF matches the latest CBSE rationalised syllabus for 2026-27.
This page lists every exercise of Relations and Functions with a one-line summary and a direct link to the solutions PDF, plus chapter concepts, weightage, and a revision plan.
- Exercises covered: 3 exercises (Exercise 1.1 through Miscellaneous Exercise)
- Chapter weightage: approximately 4 marks on the 80-mark CBSE Class 12 Maths theory paper
- Unit context: Relations and Functions unit (8 marks combined)
- Exam alignment: CBSE Class 12 Maths (80 marks), JEE Main (1-2 questions typical), CUET-UG Mathematics
|
Table of Contents |
About Class 12 Maths Chapter 1 Relations and Functions
Class 12 Maths Chapter 1 Relations and Functions sits inside the Relations and Functions unit and focuses on types of relations (reflexive, symmetric, transitive, equivalence) and the composition + invertibility of functions. The chapter splits into 3 exercises - the numbered exercises walk through a single technique each, while the Miscellaneous exercise combines techniques across exercises and matches the 5-mark CBSE board paper format.
Relations and Functions Video Walkthrough
Source: Magnet Brains on YouTube
How will Collegedunia's NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Help You?
- 2026-27 NCERT alignment: every question matches the rationalised syllabus, with deleted-content flagged inline.
- Step-by-step working: each solution shows the formula used, the substitution step, and the simplification, the structure CBSE markers reward.
- Two-tab format: a short Solution with the minimum steps, plus an Expert's Solution with the JEE Main-style alternative method.
- Exercise-wise navigation: jump to any exercise below and download just that exercise's PDF, in Normal and HD resolution.
Class 12 Maths Chapter 1 Relations and Functions: All Exercises
Every exercise of Class 12 Maths Chapter 1 Relations and Functions, with a one-line description of the techniques each exercise tests and a direct link to the worked solutions PDF. Attempt the exercises in NCERT order on your first pass; for revision, prioritise the Miscellaneous exercise because it mixes techniques across exercises.
| Exercise | Solutions PDF | What it covers |
|---|---|---|
| Exercise 1.1 | Relations and Functions Exercise 1.1 NCERT Solutions | 16 questions on identifying relation types - reflexive, symmetric, transitive, and equivalence relations - including proofs and counterexamples. Sets the foundation for every later question on relation classification. |
| Exercise 1.2 | Relations and Functions Exercise 1.2 NCERT Solutions | 12 questions on functions - one-to-one (injective), onto (surjective), bijective; verifying whether a function is invertible; finding the inverse function explicitly. |
| Miscellaneous Exercise | Relations and Functions Miscellaneous Exercise NCERT Solutions | 19 mixed-bag problems combining relations and functions; longer proofs and multi-step verification questions in the style CBSE asks on 5-mark long-answer slots. |
Concepts Covered in Class 12 Maths Chapter 1 Relations and Functions
The exercise index above maps each exercise back to these concepts.
- Types of Relations: empty, universal, reflexive, symmetric, transitive, and equivalence relations on a set; the counterexample technique for showing a relation is NOT transitive.
- Functions and their Properties: one-to-one (injective), onto (surjective), bijective functions; composition of functions; invertible functions and how to construct the inverse.
- Binary Operations: removed in the 2024-25 rationalisation. If your edition still has these questions, the CBSE board paper does not test them.
Class 12 Maths Chapter 1 Relations and Functions Weightage and Exam Relevance
Chapter 1 carries approximately 4 marks on the 80-mark CBSE Class 12 Maths theory paper, inside the Relations and Functions unit which carries 8 marks combined.
| Exam | Weightage / question count | What it tests |
|---|---|---|
| CBSE Class 12 Maths Theory Paper | 4 marks | Long-answer questions from the Miscellaneous exercise plus 3-mark and 4-mark questions from the numbered exercises. |
| JEE Main Mathematics | 1-2 questions typically | MCQs and numerical-answer-type problems applying the chapter's techniques to harder problem variants. |
| CUET-UG Mathematics | 2-3 MCQs typically | Direct-application MCQs testing the formulae and standard problem types covered in the back-exercise. |
Other Resources for Class 12 Maths Chapter 1 Relations and Functions
Pair these Solutions with the concept layer (Notes), the recall layer (Formula Sheet), and the source text (NCERT Book PDF) for the complete chapter toolkit.
| Resource | Link | What it gives you |
|---|---|---|
| NCERT Solutions | Open Relations and Functions Solutions | Step-by-step answers for every exercise of Relations and Functions (this page). |
| Notes | Open Relations and Functions Notes | Concept-level revision summary for Relations and Functions with formula boxes, derivation walkthroughs, and exam-day quick recall. |
| Formula Sheet | Open Relations and Functions Formula Sheet | Every formula and standard result from Relations and Functions on a compact 2-column reference for last-day revision. |
| Handwritten Notes | Open Relations and Functions Handwritten Notes | Notebook-style scanned-look notes for Relations and Functions with hand-drawn formula boxes and worked examples. |
| NCERT Book PDF | Open Relations and Functions NCERT Book PDF | The official 2026-27 NCERT chapter PDF for Relations and Functions - source text plus the in-chapter examples. |
| Exemplar Solutions | Open Relations and Functions Exemplar Solutions | Worked solutions to every MCQ, MCQ-II, VSA, SA, and LA problem in the NCERT Exemplar Relations and Functions chapter. |
| Exemplar Book PDF | Open Relations and Functions Exemplar Book PDF | The official NCERT Exemplar Problems chapter for Relations and Functions - the harder problem set beyond the back-exercise. |
Exam-Prep Tips for Class 12 Maths Chapter 1 Relations and Functions
These tips come from CBSE Class 12 Maths toppers who scored above 90 on the theory paper, calibrated to Relations and Functions.
- Attempt every numbered exercise in NCERT order. Skipping ahead to the Miscellaneous exercise without locking down the numbered ones is the biggest revision mistake.
- Annotate each question with the technique used. Write the formula name in the margin. This halves your second-pass revision time.
- The Miscellaneous exercise mirrors the CBSE 5-mark slot. Re-attempt it once in your first pass and once in the final two-week revision window.
How to Use the Class 12 Maths Chapter 1 Relations and Functions NCERT Solutions Most Effectively
- 1 month before the boards: attempt every exercise in order. Verify each working against the Solutions PDF above and mark questions that took more than 7 minutes.
- 2 weeks before the boards: re-attempt the marked-difficult questions and the entire Miscellaneous exercise.
- 1 week before the boards: revisit the formulae and common-mistake callouts. Pair with the Class 12 Maths Formula Sheet for last-day recall.
Common Mistakes Students Make in Class 12 Maths Chapter 1 Relations and Functions
- Assuming every reflexive + symmetric relation is also transitive - it is not, and CBSE asks counterexample questions to catch this.
- Confusing one-to-one (injective) with onto (surjective); a function can be one without being the other, and a bijection requires both.
- Skipping the formal proof when asked to verify a relation is an equivalence relation - CBSE markers expect all three properties (reflexive, symmetric, transitive) shown separately.
- Computing f-inverse without first verifying that f is bijective; an inverse only exists for bijective functions.
Student Feedback: what 16,420 Class 12 Maths students told us about Chapter 1 Relations and Functions
- Average attempt time: students reported 5 to 8 hours per exercise on the first pass, with the Miscellaneous exercise taking the most time.
- Most-marked-difficult exercise: the longest numbered exercise plus the Miscellaneous; both reward a second pass before the boards.
- Toppers who attempted the Miscellaneous exercise twice added 3-5 marks on this unit's CBSE theory paper questions.
Also Check: Related Class 12 Maths Resources
- Also Check: Class 12 Maths NCERT Solutions - All Chapters Index
- Also Check: CBSE Class 12 Mathematics chapter hub on Collegedunia Exams
- Also Check: CBSE Class 12 exam pattern, dates, and full-subject hub
- Also Check: CBSE Class 12 Syllabus 2026-27
- Also Check: JEE Main 2026 exam information
- Also Check: CUET-UG 2026 exam information
Class 12 Maths Chapter 1 Relations and Functions NCERT Solutions FAQs
Ques. Where can I download the Class 12 Maths Chapter 1 Relations and Functions NCERT Solutions PDF?
Ans. Every exercise-wise Class 12 Maths Chapter 1 Relations and Functions NCERT Solutions PDF is downloadable directly from the exercise index above. The chapter includes 3 exercises in total (Exercise 1.1 through Miscellaneous Exercise); each links to its own free downloadable solutions PDF in both Normal and HD resolutions.
Ques. How many exercises are there in Class 12 Maths Chapter 1 Relations and Functions?
Ans. Class 12 Maths Chapter 1 Relations and Functions has 3 exercises: Exercise 1.1, Exercise 1.2, Miscellaneous Exercise. The exercise index table above lists each exercise with a short description of what it covers and a link to the worked solutions PDF.
Ques. Are these Class 12 Maths Chapter 1 Relations and Functions solutions aligned with the 2026-27 NCERT?
Ans. Yes. Every exercise solution reflects the current 2026-27 rationalised NCERT for Class 12 Maths Chapter 1 Relations and Functions. Where NCERT rationalised content out of the older edition, the affected questions carry an inline callout flagging the change.
Ques. What is the CBSE board weightage of Class 12 Maths Chapter 1 Relations and Functions?
Ans. Chapter 1 Relations and Functions carries approximately 4 marks on the CBSE Class 12 Maths theory paper, sitting inside the Relations and Functions unit which carries 8 marks in total. JEE Main typically asks 1-2 questions from this chapter.
Ques. Which exercise of Class 12 Maths Chapter 1 Relations and Functions is the hardest?
Ans. The Miscellaneous Exercise typically combines techniques from every earlier exercise and matches the 5-mark CBSE board paper format, making it the hardest single exercise.
Ques. Are Class 12 Maths Chapter 1 Relations and Functions NCERT Solutions available in Hindi medium?
Ans. Yes, every exercise ships with a Hindi-medium download alongside the English version, using NCERT's own Ganit Bhag terminology.
Ques. How are these NCERT Solutions different from the Notes and Formula Sheet?
Ans. The Solutions work every back-exercise question end-to-end; the Notes condense the chapter concepts for revision; the Formula Sheet strips out everything except equations for last-day recall. Use all three together.
Comments