NCERT Solutions Class 11 Maths Chapter 2 helps you understand Relations and Functions through step-by-step solutions covering ordered pairs, Cartesian products, domain and range, and different types of relations. You’ll learn how to identify reflexive, symmetric, and transitive relations, determine if a relation is a function, and solve problems on real-valued functions. These fundamental concepts are essential for calculus and advanced mathematics in Class 12.
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Download PDF (Free)NCERT Solutions Class 11 Maths Chapter 2 Relations and Functions – Complete Guide
NCERT Class 11 Chapter 2 on Relations and Functions introduces you to one of the most important topics in mathematics that connects algebra with real-world applications. This chapter carries 8 marks in the CBSE board examination and is considered of high importance as it lays the foundation for calculus and advanced mathematics in Class 12.
📊 CBSE Class 11 Maths Chapter 2 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 8 Marks |
| Unit Name | Sets and Functions |
| Difficulty Level | Medium |
| Importance | High |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 2-3 questions |
You will begin by understanding Cartesian products and ordered pairs, then progress to exploring different types of relations including reflexive, symmetric, transitive, and equivalence relations. The chapter then transitions into functions, where you’ll learn to identify whether a relation qualifies as a function, understand the crucial concepts of domain, co-domain, and range, and work with different types of functions such as one-one, onto, and bijective functions.
This chapter is particularly significant for CBSE board exams as it typically includes 2-3 questions ranging from MCQs (1 mark) to long answer questions (4-6 marks). You’ll encounter problems on identifying relations, finding domains and ranges, verifying function types, and solving real-life application problems. The graphical representation of functions is another critical skill you’ll develop, which directly connects to coordinate geometry.
Quick Facts – Class 11 Chapter 2
| 📖 Chapter Number | Chapter 2 |
| 📚 Chapter Name | Relations and Functions |
| ✏️ Total Exercises | 3 Exercises |
| ❓ Total Questions | 24 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
Mastering Relations and Functions is essential not just for board exams but also for competitive examinations like JEE and other entrance tests. The concepts you learn here will be extensively used in calculus, probability, and mathematical modeling. With focused practice of NCERT solutions and understanding the underlying principles, you’ll find this chapter both interesting and highly rewarding for your mathematical journey ahead.
NCERT Solutions Class 11 Maths Chapter 2 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| EXERCISE 2.1 | Complete step-by-step solutions for 10 questions | 📥 Download PDF |
| EXERCISE 2.2 | Complete step-by-step solutions for 9 questions | 📥 Download PDF |
| EXERCISE 2.3 | Complete step-by-step solutions for 5 questions | 📥 Download PDF |
Relations and Functions – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| Cartesian Product \(A \times B = \\{(a, b) | a \in A, b \in B\\}\) | Set of all ordered pairs where the first element is from set A and the second element is from set B. Note: Order matters! \(A \times B\) is generally not equal to \(B \times A\). If A has p elements and B has q elements, then \(A \times B\) has pq elements. | Finding all possible combinations between two sets. Often used in probability and relation problems. |
| Number of Relations \(2^{pq}\) | Total number of relations from a set A with p elements to a set B with q elements. Note: Each subset of \(A \times B\) defines a relation from A to B. | Problems asking for the total possible relations between two sets. |
| Domain of a Relation \(Domain = \\{a: (a, b) \in R\\}\) | Set of all first elements in the ordered pairs of a relation R. Note: Domain is a subset of the first set in the Cartesian product. | Finding the domain of a given relation defined as a set of ordered pairs. |
| Range of a Relation \(Range = \\{b: (a, b) \in R\\}\) | Set of all second elements in the ordered pairs of a relation R. Note: Range is a subset of the second set in the Cartesian product. | Finding the range of a given relation defined as a set of ordered pairs. |
| Codomain of a Relation Set B (where R is a relation from A to B) | The entire set B in which the second elements of the relation are chosen. Note: Range is always a subset of the codomain. | Identifying the codomain when a relation from A to B is given. |
| Function Definition For every \(x \in A\), there is a unique \(y \in B\) such that \((x, y) \in f\) | A relation f from A to B is a function if each element in A is mapped to exactly one element in B. Note: Vertical line test: If any vertical line intersects the graph more than once, it’s not a function. | Determining if a given relation is a function. |
| Domain of a Function Set of all possible input values (x) for which the function is defined. | Values of x that can be plugged into the function without causing undefined results (e.g., division by zero, square root of a negative number). Note: Careful with denominators being zero and values under square roots being negative. | Finding the allowed input values for a function, especially with fractions or square roots. |
| Range of a Function Set of all possible output values (y) that the function can produce. | The set of all f(x) values as x varies across the domain. Note: May require analyzing the function’s behavior or using calculus for more complex functions. | Finding the set of all possible output values of a function. |
| Identity Function \(f(x) = x\) | A function that returns the same value that was used as the argument. Note: The graph is a straight line passing through the origin with a slope of 1. | Simplifying expressions, understanding function composition. |
| Constant Function \(f(x) = c\) | A function that always returns the same constant value, regardless of the input. Note: The graph is a horizontal line. | Modeling situations where the output is always the same. |
| Modulus Function \(f(x) = |x| = \begin{cases} x, & \text{if } x \geq 0 \\ -x, & \text{if } x < 0 \end{cases}\) | Returns the absolute value of x, always non-negative. Note: The graph is V-shaped, symmetric about the y-axis. | Dealing with distances, inequalities involving absolute values. |
| Signum Function \(f(x) = sgn(x) = \begin{cases} 1, & \text{if } x > 0 \\ 0, & \text{if } x = 0 \\ -1, & \text{if } x < 0 \end{cases}\) | Returns 1 if x is positive, 0 if x is zero, and -1 if x is negative. Note: The graph is a step function. | Analyzing the sign of a value, switching between positive and negative values. |
| Greatest Integer Function \(f(x) = [x]\) | Returns the greatest integer less than or equal to x. Note: Also known as the floor function. [3.7] = 3, [-2.3] = -3 | Rounding down to the nearest integer, dealing with step functions. |
| Composition of Functions \( (f \circ g)(x) = f(g(x)) \) | Applying function g first, then applying function f to the result. Note: Order matters! \(f \circ g\) is generally not equal to \(g \circ f\). | Combining two functions, finding the output of a nested function. |
Frequently Asked Questions – NCERT Class 11 Maths Chapter 2
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