NCERT Exemplar Solutions for Class 11 Maths Chapter 2 – Relations and Functions

Subject specialists have created NCERT Exemplar Solutions for Class 11 Maths Chapter 2, which includes 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 Exemplar Solutions for Class 11 provide useful solutions for improving conceptual knowledge and preparing for exams like JEE.

2.1 Introduction

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

The relation between the total number of students and their respective heights 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 flavors, and five colors.

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, and 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 Exemplar 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.

Frequently Asked Questions

How to find which relation is a function in Chapter 2 of NCERT Exemplar 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.

Explain the basic steps for the Cartesian product of sets in NCERT Exemplar 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.

What is the meaning of relations in Chapter 2 of NCERT Exemplar 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 Exemplar 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.

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