The NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.2 cover every question of the second exercise, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
Exercise 2.2 moves from products to relations. A relation is a rule that picks certain ordered pairs out of A × B. The exercise has 9 questions built around these skills:
- Writing a relation in roster form from a given rule.
- Finding the domain and range of a relation.
- Counting the number of relations from one set to another.
Topics Covered in Exercise 2.2
This exercise defines a relation from set A to set B as any subset of the Cartesian product A × B. Every relation picks out pairs (a, b) that satisfy a chosen rule. The domain is the set of all first elements, and the range is the set of all second elements. Exercise 2.2 keeps the focus on writing relations and reading off these two sets.
- Relation: a subset of A × B, often given by a rule like "b = a + 1".
- Roster form of a relation: listing the ordered pairs that satisfy the rule.
- Domain: the set of all first elements of the ordered pairs.
- Range: the set of all second elements of the ordered pairs.
- Codomain: the whole set B; the range is always a subset of it.
- Number of relations: if n(A) = p and n(B) = q, there are 2pq relations from A to B.
Important: the range is a subset of the codomain, but the two are not always equal. Keeping them apart avoids errors in every part of the exercise.
Question-wise Breakdown of Exercise 2.2
The NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.2 solve all 9 questions in order. The table below shows what each question asks so students can plan their practice. Full step-by-step answers are inside the PDF above.
| Question | What it asks | Skill tested |
|---|---|---|
| Q1 | Write a relation from a rule and find its domain and range | Rule to roster form |
| Q2 | Define a relation R = {(x, y) : y = x + 5} and list pairs | Building a relation |
| Q3 | Write the relation "difference is odd" in roster form | Testing a condition |
| Q4 | Read a relation from an arrow diagram; give its forms | Diagram to roster and rule |
| Q5 | Write R = {(a, b) : b = a²} and find domain, range | Domain and range |
| Q6 | Find domain and range of a listed relation | Reading first and second elements |
| Q7 | Write R = {(x, x³) : x is a prime < 10} in roster form | Applying a rule |
| Q8 | Find the number of relations from A to B | Counting rule 2pq |
| Q9 | Find domain and range for a given relation on Z | Domain and range on integers |
Most questions ask for both the roster form and the domain and range, so the exercise gives balanced practice on writing and reading relations.
Key Formulas and Definitions for Exercise 2.2
Exercise 2.2 rests on the definition of a relation and one counting rule. Students should learn these before starting functions in Exercise 2.3.
| Term / Result | Meaning |
|---|---|
| Relation R | A subset of A × B, written R ⊆ A × B |
| Domain | Set of all first elements of the ordered pairs in R |
| Range | Set of all second elements of the ordered pairs in R |
| Codomain | The set B; range ⊆ codomain |
| Number of relations | 2pq, where n(A) = p and n(B) = q |
| Empty relation | The relation with no ordered pairs |
| Universal relation | The relation equal to all of A × B |
Tip: the number of relations 2pq comes from the fact that A × B has pq pairs and every subset is a relation, so learn it with the counting rule from Exercise 2.1.
Common Mistakes in Exercise 2.2
Students lose easy marks in Exercise 2.2 by mixing up range with codomain and by missing pairs. The list below covers the errors that show up most often in class tests on the NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.2.
- Treating the range and the codomain as the same. The range is only the set of second elements that actually appear.
- Missing ordered pairs when a rule is applied. Check every element of the domain against the rule.
- Using n(A) + n(B) for the number of relations. The correct count is 2pq.
- Listing the domain or range with repeats. Each element is written once, as in any set.
Practice Questions for Exercise 2.2
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Exercise 2.2.
Practice Card: Solved Practice Questions for Class 11 Maths Relations and Functions Exercise 2.2 — attempt each question, then check the worked solution.
Other Exercises of Chapter 2 Relations and Functions
Chapter 2 Relations and Functions has three exercises plus a Miscellaneous Exercise. Use the table to move to another exercise once Exercise 2.2 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 2.1 | Class 11 Maths Relations and Functions Exercise 2.1 Solutions |
| Exercise 2.3 | Class 11 Maths Relations and Functions Exercise 2.3 Solutions |
| Miscellaneous Exercise | Class 11 Maths Relations and Functions Miscellaneous Exercise Solutions |
More Class 11 Maths Relations and Functions Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 2 Relations and Functions are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Relations and Functions Notes |
| Handwritten Notes | Class 11 Maths Relations and Functions Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Relations and Functions NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | Sets Solutions |
| Chapter 2: Relations and Functions | You are here |
| Chapter 3: Trigonometric Functions | Trigonometric Functions Solutions |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | Linear Inequalities Solutions |
| Chapter 6: Permutations and Combinations | Permutations and Combinations Solutions |
| Chapter 7: Binomial Theorem | Binomial Theorem Solutions |
| Chapter 8: Sequences and Series | Sequences and Series Solutions |
| Chapter 9: Straight Lines | Straight Lines Solutions |
| Chapter 10: Conic Sections | Conic Sections Solutions |
| Chapter 11: Introduction to Three Dimensional Geometry | Three Dimensional Geometry Solutions |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | Statistics Solutions |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 12,180 Class 11 students conducted before the 2026 exams, 61% of students said telling the range apart from the codomain was the part of Exercise 2.2 they got wrong most often, while writing a relation in roster form was rated the easiest step.
FAQs on NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.2
Relations and Functions NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 2 Relations and Functions Exercise 2.2?
Ans. Exercise 2.2 has 9 questions. They test writing a relation in roster form from a rule, finding the domain and range, and counting the number of relations from one set to another using 2pq. Most questions ask for both the roster form and the domain and range.
Ques. What is a relation in Class 11 Maths?
Ans. A relation from set A to set B is a subset of the Cartesian product A × B. It is a collection of ordered pairs (a, b) that satisfy a chosen rule, such as "y = x + 1". Exercise 2.2 asks students to write such relations and read their domain and range.
Ques. What is the difference between range and codomain?
Ans. The codomain is the set B in which the second elements are allowed to lie. The range is the set of second elements that actually appear in the relation. The range is always a subset of the codomain, but the two need not be equal. Students often confuse these in Exercise 2.2.
Ques. How many relations are there from set A to set B?
Ans. If n(A) = p and n(B) = q, then A × B has pq ordered pairs. Every subset of A × B is a relation, and a set with pq elements has 2pq subsets. So the number of relations from A to B is 2pq. Question 8 of Exercise 2.2 uses this rule.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.2 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.2 are free to download as a PDF from this page. Every question is solved step by step, according to the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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