Subject specialists have created NCERT Solutions for Class 11 Maths Chapter 2:Relations and functions, which include thorough solutions for reference. All of the questions from the textbook’s exercises are answered here. Students can use these answers to help them prepare for their exams. The **NCERT Solutions for Class 11** provide useful solutions for improving conceptual knowledge.

The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving **NCERT Solutions for Class 11 Maths**. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 11 pupils perform well in upcoming competitive exams.

The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.

**NCERT Solutions for Class 11 Maths Chapter 2- Relations and Functions**

The topic explained in Chapter 2 Relations & Functions for Class 11 are listed below:

**2.1 Introduction**

The concept discussed in chapter Relations and Functions is explained in this section.

The relation between the total number of students and their respective height is shown in terms of the set of ordered-pair numbers. In general ordered-pair numbers are written like (x, y). Such that x is the domain of the relation, which contains the set of all elements of x and y is the range of the relation which contains the set of all elements of y.

**2.2 Cartesian Product of Sets**

In this section, students learn about the product of the cartesian coordinate system and also about the ordered pairs with the help of a real-life model, its representation and some worked examples.

Let us suppose chocolates have four shapes, two flavours, and five colours.

S :={circle, triangle, trapezoidal, oval}

F :={orange, vanilla}

C :={red, blue, pink, white, purple}

S:={circle, triangle,trapezoidal, oval}, F:={orange, vanilla},C:={red, blue, pink, white, purple}

be the four shapes, two flavours, and five colours respectively. Therefore, the set of manufactured chocolates is the triple cartesian product S×F×C and consists of 4⋅2⋅5=40 elements. Hence, if the manager has to sell the given set of chocolates then they have to prepare the room for 40 heaps.

**2.3 Relations**

In this section, the definitions of domain and co-domain are given, and also the mapping of set A to set B is explained with the help of solved problems.

The concept of mapping a particular phone number to the respective person to whom the phone number belongs is a relation. Here the relation is — phone number to person.

**2.4 Functions**

In this section, image and preimage are explained, and also functions, visualization of functions, when the relation is known as function are explained with the help of examples.

Since the height of any person, is determined by the femur bone length. Therefore, it is an example of the function.

**2.4.1 Some functions and their graphs**

In this section, the types of functions and their graphical representations are shown. The types of functions are as follows.

Identity function

Constant function

Polynomial function

Rational functions

The Modulus function

Signum function

Greatest integer function

**2.4.2 Algebra of real functions**

In this section, the algebraic operations on functions are explained.

Addition of two real functions

Subtraction of a real function from another

Multiplication by a scalar

Multiplication of two real functions

The quotient of two real functions

**The number of questions available in the exercises of Chapter 2 is listed below: **

Exercise 2.1 Solutions 10 Questions

Exercise 2.2 Solutions 9 Questions

Exercise 2.3 Solutions 5 Questions

Miscellaneous Exercise On Chapter 2 Solutions 12 Questions

**Key Features of NCERT Solutions for Class 11 Maths Chapter 2- Relations and Functions**

- When the two elements are grouped in a particular order then it is known as an ordered pair.
- The cartesian product of the two sets A and B is A × B, such that A × B = {(a, b): a ∈ A, b ∈ B}.
- The relation R from a set A to a set B is always a subset of its cartesian product A × B. It explains the relation between the first element and second element, x, and y of the ordered pairs in the cartesian product A × B.
- In a relation R, the image of an element x is given by an element y, such that (x, y) ∈ R.
- The set of all the first elements in the ordered pairs in a relation R is the domain of R.
- The set of all the second elements in the ordered pairs in a relation R is the range of R.
- The function A from set A to set B is a special kind of relation R, for which every x element of set A has one and only one image y in set B. It is written as f: A→B, such that f(x) = y.
- In a function, the range is the set of images.
- A real function is always the set of real numbers or one of its subsets can be both its domain and its range.

Here, the students learn about the basic concepts that are covered in the NCERT Solutions for Class 11 Maths modules which help them to enhance knowledge in their area of work. The recent update in the term-wise CBSE Syllabus 2021-22 ensures that the content covered is beneficial for the students to go ahead in their respective streams in the future. It helps the student to understand the concept of Relations and Functions in-depth as it covers most of the portion in the question paper. Before solving any real-world applications and also problems, the concept should be learned thoroughly.

**Frequently Asked Questions on NCERT Solutions for Class 11 Maths Chapter 2**

- How to find which relation is a function in Chapter 2 of NCERT Solutions for Class 11 Maths?
- Explain the basic steps for the Cartesian product of sets in NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions?
- What is the meaning of relations in Chapter 2 of NCERT Solutions for Class 11 Maths?

**1. How to find which relation is a function in Chapter 2 of NCERT Solutions for Class 11 Maths? **

From the definition, a function relates an element from a domain to only one element of the range. With the help of a graph, any function is said to be a relation when any vertical line drawn on a graph cuts the x-axis only once. The method of finding whether a relation is a function or not by the graph is known as the vertical line test. It can also be found with the help of different formulas.

**2. Explain the basic steps for the Cartesian product of sets in NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions?**

To understand the basic concepts for solving a question based on the Cartesian product of sets, students should go through the first exercise of this chapter. To solve the problem quickly, solve examples before each exercise are given to the students. When the students solve the problems from the NCERT textbook then their conceptual understanding will enhance, with the help of which they will perform better in their first term examination.

**3. What is the meaning of relations in Chapter 2 of NCERT Solutions for Class 11 Maths? **

Relations R is the collection of ordered pairs which has one element from each set. Sometimes a function is considered as a relation but the conceptual idea of both are different. From the NCERT Solutions of Class 11 Maths Chapter 2, the students learn and analyze the proper definition of the relations as per the syllabus of the term – I CBSE for the session 2021-22. Also, the examples given in the solutions will help students in solving the problems based on relations.