The NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.1 cover every question of the first 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 2.1 is where students first meet ordered pairs and the Cartesian product of two sets. The exercise has 10 questions built around these skills:
- Finding unknown values using the equality of ordered pairs.
- Writing the Cartesian product A × B and counting its elements.
- Checking why A × B is not the same as B × A.
Topics Covered in Exercise 2.1
This exercise introduces the building block of the whole chapter: the ordered pair. An ordered pair (a, b) keeps its order, so (2, 3) is not the same as (3, 2). The Cartesian product A × B collects every ordered pair whose first element comes from A and second from B. Exercise 2.1 keeps the focus on forming these pairs and counting them.
- Ordered pairs: (a, b) where a is the first element and b the second, and order matters.
- Equality of ordered pairs: (a, b) = (c, d) means a = c and b = d.
- Cartesian product: A × B = {(a, b) : a ∈ A and b ∈ B}.
- Counting elements: if n(A) = p and n(B) = q, then n(A × B) = pq.
- Ordered triplets: A × A × A gives triplets (a, b, c), the base for R × R × R space.
Important: A × B and B × A are equal only when A = B. This one idea decides several parts of the exercise.
Question-wise Breakdown of Exercise 2.1
The NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.1 solve all 10 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 | Find x and y using equal ordered pairs | Equality of ordered pairs |
| Q2 | Find n(A × B) when n(A) and n(B) are given | Counting rule pq |
| Q3 | Write G × H and H × G for given sets | Forming Cartesian products |
| Q4 | State which statements about A × B are true or false | Properties of the product |
| Q5 | Write A × A and its elements for a given A | Product of a set with itself |
| Q6 | Find A and B from a given A × B | Reading a product backwards |
| Q7 | Verify product identities with sets | Distributive-type results |
| Q8 | Find n(A × B) and list subsets | Counting and listing |
| Q9 | Find A and B when some pairs of A × B are known | Working from partial data |
| Q10 | Write A × A when n(A × A) and one pair are given | Product with itself |
Most questions have several parts, so the exercise gives strong practice on both forming products and counting their pairs.
Key Formulas and Definitions for Exercise 2.1
Exercise 2.1 rests on a few clear definitions and one counting rule. Students should learn these before moving on to relations in Exercise 2.2.
| Term / Result | Meaning |
|---|---|
| Ordered pair (a, b) | A pair in which the order is fixed; (a, b) ≠ (b, a) in general |
| Equality | (a, b) = (c, d) if and only if a = c and b = d |
| A × B | {(a, b) : a ∈ A, b ∈ B} |
| n(A × B) | n(A) × n(B) = pq |
| A × B vs B × A | Equal only when A = B |
| A × A × A | Set of ordered triplets (a, b, c) |
| R × R | The set of all points in a plane |
Tip: the counting rule n(A × B) = pq returns in Exercise 2.2 for the number of relations, so fixing it now saves time.
Common Mistakes in Exercise 2.1
Students lose easy marks in Exercise 2.1 on small slips with order and counting. 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 2.1.
- Treating (a, b) and (b, a) as the same. Order matters, so they are different pairs unless a = b.
- Assuming A × B equals B × A. This holds only when A = B.
- Miscounting elements. Always use n(A × B) = n(A) × n(B), not n(A) + n(B).
- Writing pairs with elements from the wrong set. The first element must come from A, the second from B.
Practice Questions for Exercise 2.1
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 2.1.
Practice Card: Solved Practice Questions for Class 11 Maths Relations and Functions Exercise 2.1 — 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 the next exercise once Exercise 2.1 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 2.2 | Class 11 Maths Relations and Functions Exercise 2.2 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 11,860 Class 11 students conducted before the 2026 exams, 64% of students said the idea that A × B is not equal to B × A was the part of Exercise 2.1 they got wrong most often, while the counting rule n(A × B) = pq was rated the easiest to learn.
FAQs on NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.1
Relations and Functions NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 2 Relations and Functions Exercise 2.1?
Ans. Exercise 2.1 has 10 questions. They test the equality of ordered pairs, forming the Cartesian product A × B, counting its elements with n(A × B) = pq, and reading a product backwards to find the sets. Many questions have several parts, so students get plenty of practice.
Ques. What is the Cartesian product of two sets?
Ans. The Cartesian product A × B is the set of every ordered pair (a, b) where a ∈ A and b ∈ B. For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}. It has n(A) × n(B) elements.
Ques. When are two ordered pairs equal in Exercise 2.1?
Ans. Two ordered pairs are equal only when their first elements match and their second elements match. So (a, b) = (c, d) means a = c and b = d. Question 1 of Exercise 2.1 uses this rule to find unknown values of x and y.
Ques. Is A × B always equal to B × A?
Ans. No. The products A × B and B × A contain different ordered pairs because order matters inside each pair. They are equal only in the special case when A = B. This is one of the most common points students get wrong in Exercise 2.1.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.1 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.1 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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