The NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions are solved in detail in the pdf given below. All the problems in the exercises are solved in the pdf given below, which enables the student to prepare for the exam and ace it. The NCERT Solutions are prepared by the most experienced teachers in the education industry making the explanation of each solution simple and understandable. This solution helps Class 11 students to master the concept of Relations and Functions.

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## NCERT Solutions for Class 11 Maths Chapter 2- Relations And Functions

The following ideas of Chapter 2 Relations & Functions for Class 11 are given elaborately.

**2.1 Introduction**

This section introduces the concepts covered in the chapter Relations and Functions

The combination of the register number of the student and his corresponding height is a relationship, which can be written as a set of ordered-pair numbers. Ordered-pair numbers are expressed as (x,y). The set of all elements of x is called the domain of the relation and the set of all elements of y is called the range of the relation.Â

**2.2 Cartesian Product of Sets**

This section defines the cartesian product and ordered pairs by giving a real-life model, its representation and some worked examples.

Lindt chocolates come in five shapes, three flavours and in six colours.

C :={circle, triangle, rectangle, rhombus, square}

N :={orange, vanilla, peach}

S :={red, blue,pink, white, yellow, purple}

C:={circle, triangle, rectangle, rhombus, square}, N:={orange, vanilla, peach}, S:={red, blue, pink, white, yellow, purple}

be the five shapes, three flavours and six colours respectively. Then the set of all chocolates to be manufactured in the triple cartesian product CÃ—NÃ—S and consists of 5â‹…3â‹…6=90elements. As a manager, to sell this set of chocolates would have to make room for 90 heaps.

**2.3 Relations**

This section explains the mapping of set A to set B with a few solved problems. Definitions of domain and codomain are also introduced.

The idea of mapping a particular phone number to the respective person to whom the number belongs to. Thatâ€™s a relation â€” from phone number to person.

**2.4 Functions**

This section covers functions, visualisation of functions, how is a relation said to be a function with a few examples. Meaning of image & preimage.Â

The height of a person can be determined by the length of his femur bone. Hence, it is an example of a function.

2.4.1 Some functions and their graphs

This section talks about different types of functions and their graphical representation. Some of the types of functions are listed below.

- Identity function
- Constant function
- Polynomial function
- Rational functions
- The Modulus function
- Signum function
- Greatest integer function

2.4.2 Algebra of real functions

This section includes the algebraic operations on functions.

- 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

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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

## NCERT Solutions for Class 11 Maths Chapter 2- Relations And Functions

- The two elements which are grouped in particular order are termed as ordered pair.Â
- Cartesian product A Ã— B of two sets A and B is given by A Ã— B = {(a, b): a âˆˆ A, b âˆˆ B}
- Relation R from a set A to a set B is a subset of the cartesian product A Ã— B obtained by explaining the relationship between the first element x and the second element y of the ordered pairs in A Ã— B.
- The image of an element x under a relation R is given by y, where (x, y) âˆˆ R.
- The domain of R is the set of all first elements of the ordered pairs in a relation R.
- The range of a relation R is the set of all second elements of the ordered pairs in a relation R.
- Function A from a set A to a set B is a specific type of relation for which every element x of set A has one and only one image y in set B. We write f: Aâ†’B, where f(x) = y.
- The range of the function is the set of images.
- A real function has the set of real numbers or one of its subsets both as to its domain and as its range.

Basics Maths are covered in these modules to help students move ahead in their area of work. The NCERT syllabus ensures that the content covered is apt for the students to move ahead in their respective streams in the future. A student needs to understand the concept of Relations and Functions as it is the main chunk in the question paper. Before solving real-world applications and problems, the concept has to be learned thoroughly.Â

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