# Important Questions Class 11 Maths Chapter 2

## Important Questions for CBSE Class 11 Mathematics Chapter 2 – Relations and Functions

Extramarks’ Important Questions Class 11 Mathematics Chapter 2 covers the main topics of Chapter 2 “Relations and Functions” Class 11 Mathematics. To ensure that these questions are in line with the most recent CBSE Syllabus, subject matter experts regularly review and update these questions. Extramarks recommends that students carefully review these questions to ensure that they have a firm grasp of the material before exams.

The topics covered in CBSE Chapter 2 “Relations and Functions” of Class 11 Mathematics are as follows –

2.1 Introduction

2.2 Cartesian Products of Sets

2.3 Relations

2.4 Functions

2.4.1 Some functions and their graphs

2.4.2 Algebra of real functions

### Access Important Questions for Class 11 Mathematics Chapter 2- Relations and Functions

Students can use the link to view the list of Class 11 Mathematics Chapter 2 Important Questions. Here is a sample of the Important Questions from Chapter 2 Class 11 Mathematics.

Q1. If (a – 1, b + 5) = (2, 3), find a and b.

Ans: Given (a – 1, b + 5) = (2, 3),

Then,

a –1 = 2

b + 5 = 3

Therefore,

a = 3

b = – 2

Q2. If A = {1, 3, 5} and B = {2, 3},

• Find A × B

Ans: The Cartesian Product of sets implies that if the two sets are non-empty sets, then they will be ordered pairs. Therefore, the Cartesian product of A and B is the set of ordered pairs (a, b), so that a A, b B, is represented by A × B.

Hence, A × B = {(1, 2), (1, 3), (3, 2), (3, 3), (5, 2), (5, 3)}

• Find B × A

Ans: Since B × A is the cartesian product set of B and A, where b B, a A, and (b, a) B × A are all positive integers, we get

B × A = {(2, 1), (2, 3), (2, 5), (3, 1), (3, 3), (3, 5)}

Q3. A real function f is defined by f(x) = 2x − 5. Then the value of f(−3) is

(a) 0

(b) 1

(c) -11

(d) none of the above

Ans: Given, f(x) = 2x – 5

Substituting x = -3, we get:

= – 6 – 5

= –11

Therefore, the correct answer is (c).

Q1. Calculate the domain and range of f(x) = |2x-3|-3.

Ans. The function is given as f(x)=|2x -3|-3.

No value of x exists for which f(x) is unbounded. Therefore, the set of all real numbers R is the domain of the function f(x).

Note that f(x)≥ -3 since |2x – 3|≥0.

Consequently, [3, ∞] is the range of the function f(x).

Q2. Determine the domain and range of the function f(x) = x21-x2

Ans: Given, f(x) = x21-x2

Note that 1 + x2 ≠ 0. The function is therefore defined for all real numbers.

As a result, the set of all real numbers R is the domain of the function f(x).

Rewrite the given function now by assuming that f(x)=y.

y = x21-x2

⇒ y + x2y = x2

x2 (1-y) = y

x2= y1-y

x = y1-y, which is valid if y1-y ≥ 0,

i.e., if y (1 – y) ≥ 0,

i.e., if -y (y – 1) ≥ 0,

i.e., if y ≥ 0 and y – 1 < 0, since y should not be 1.

i.e., if 0 ≤ y ≤ 1.

Hence, the range of the function f(x) is (0, 1).

Q3. Let the function f(x) = x2 for all x ∈ X, where X = {-2, -1, 0, 1, 2, 3} define f: X 🡪 Y. Express the relation f in roaster form. Mention if f is a function.

Ans: Given, f: X 🡪 Y.

f(x) = x2, for all x X = {-2, -1, 0, 1, 2, 3} and Y = {0, 1, 4, 7, 9, 10}

Then, f(-2) = (-2)2=4

f(-1) = (-1)2=1

f(0) = 02 = 0

f(1) = 12 = 1

f(2) = 22 = 4

f(3) = 32 = 9

Therefore, f = {(-2, 4), (-1,1), (0,0), (1,1), (2,4), (3,9)}

Since each of the element in X has the distinct image in Y, so f is a function.

### 6 Marks Answers and Questions

Q1. Prove that [f (x)]3 = f(x3) + 3f (1x) if f(x) = x1x

Ans: Given, f(x) = x1x.

When x is substituted for 1x in the given function, we get,

f(1x) = 1x-x …(1)

Therefore, |f(x)|= (x1x)3

= x31x3 – 3 × x × 1x (x1x)

= x31x3 – 3 (x1x)

= x31x3 + 3 (x1x)

By applying equation (1), f (x3) + 3f (1x).

Q2. Let F: x 🡪 5x2+2, x R define the function f. Then:

• Find the image of 3 under f

Ans: Given, f(x) = 5x2 + 2.

Substituting x = 3 in the function, we get:

f(3) = 5(3)2 + 2

= 5(9) + 2

= 47

Thus, the image of 3 under f is 47.

• Find f(3) × f(2)

Ans: Given f(x) = 5x2 + 2.

By substituting x = 2, we get:

f(2) = 5(2)2+2

= 5(4) + 2

= 22.

By substituting x = 3, we get:

f(3) = 5(3)2 + 2

= 5(9) + 2

= 47.

Therefore, f(3) × f(2) = 47 × 22 = 1034

• Find x such that f(x) = 22

Ans: Given f(x) = 5x2 + 2.

By substituting f(x) = 22, we get:

22 = 5x2 + 2

⇒ 5x2= 20

x2= 4

x = 2,2

The values of x are – 2, 2.

Q3. The formula to convert xоC to Fahrenheit units is the function f(x)=9x5 + 32. Calculate:

• f(0)

Ans: Given f(x)= 9x5 + 32

By substituting x = 0, we get

f(0) = 9(0)5 + 32

= 32

Therefore, 0оC = 32оF.

• f(-10)

Ans: Given f(x)= 9x5 + 32

By substituting x = -10, we get

f(-10) = 9(-10)5 + 32

= 905+32

=14

Therefore, -10оC = 14оF.

• The value of x when f(x) = 212.

Ans: Given f(x)= 9x5 + 32

By substituting f(x) = 212, we get:

212 = 9x5 + 32

9x5=212-32

⇒ 9x = 5 × (180)

x = 100

Therefore, 212 оF = 100оC

### Class 11 Mathematics Chapter 2 Important Questions of Relations and Functions

The Following are the Important Topics:

• An overview of relations and functions.
• Definition of a cartesian product of sets with examples.
• Definition of a Relation.
• Definition of a Function.
• Domain and Range.
• Representation of a relation.
• Function as a
• Special kind of relation.
• Correspondence.
• Relations – Types and Definitions.
• Functions – Types and Definitions.
• Equal functions.
• Real functions.
• Domains of a real function.
• Standard real functions with graphs.
• Operations on real functions.

Mathematics Chapter 2 – Relations and Functions

What is the Relation?

In Mathematics, a relation describes the relationship between two distinct sets of data. If more than two non-empty sets are taken into consideration, the relationship between them will be determined if there is a connection between their items.

What is a Function?

In Mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

A function is typically represented by the notation f(x), where x represents the input.In general, a function is represented as y = f(x).

Domain and Range

The term “domain” describes a collection of input values, whereas the “graph domain” refers to all the input values displayed on the x-axis.

The range is the collection of output values displayed on the y-axis.

For example

 x y 1 3 2 3 2 5 -4 3

In the given relation set, the range is 3, 3, 5, 2, whereas the domain is 1, 2, 2, -4.

Types of Relations

There are 8 main types of relations which include:

• Empty Relation – When there is no relationship between any two elements of a set, the relation is said to be empty (or void).
• Equivalence Relation – An equivalence relation is one that is transitive, symmetric, and reflexive at the same time.
• Identity Relation – Each element of a set solely maps to itself in an identity relation.
• Inverse Relation – When a set contains elements that are inverse pairs of another set, this is known as an inverse relation.
• Reflexive Relation – A reflexive relation is a relationship between elements of a set where each element is related to the others in the set. In other words, every component of the set has an image that is a reflection of itself.
• Symmetric Relation – A symmetric relation is a connection between two or more elements in which, if the first element is related to the second, the second element is also in a similar way connected to the first element.
• Transitive Relation – Transitive relations are binary relations that are defined on a set such that if the first element is linked to the second element and the second element is connected to the third member of the set, then the first element must be related to the third element.
• Universal Relation – Every component of a set is associated with each other in a universal (full relation) type of relation.

Types of Functions

Given below are a few functions. There are other additional functions, including algebraic functions.

• Injective Function (One to One Function) – When there is a mapping for a range for each domain between two sets, this is known as an injective function or one to one function.
• Surjective Function (Onto Function) – When more than one element is mapped from domain to range, the function is said to be surjective or to be an onto function.
• Polynomial Function – The term “polynomial function” refers to a function made out of polynomials.
• Inverse Function – Functions  that can invert another function are known as inverse functions.

Some Functions in Algebra

The main algebraic functions include

• Linear Function

A linear function is a polynomial function of degree zero or one with a graph that is a straight line.

A polynomial function with one or more variables and a second-degree maximum is referred to as a quadratic function.

• Inverse Function

A function that can reverse into another function is known as an inverse function. In other words, the inverse of a function “f” will take y to x if the function “f” takes x to y.

• Constant Function

A constant function is one whose value is the same regardless of the input value.

• Identity Function

A function is said to be an identity function if it consistently returns the same value that it received as an input. In other words, if f is identity, then f(x)=x is true for all values of x.

• Modulus Function

A function that provides an absolute value for a number or variable is known as a modulus function. It is also described as an absolute value function. The function’s output is always positive, regardless of the input.

• Even and Odd Functions

Functions that meet particular symmetry relations when taking additive inverses are even and odd functions. They play a significant role in many fields of mathematical analysis, particularly in the power series and Fourier series theories.

• Periodic Function

A function that repeats its values at regular intervals is said to be periodic.

• Composite Function

Typically, a composite function is a function contained within another function. The composition of a function is performed by substituting one function for another.

• Signum Function

A special mathematical function called the signum function is used to determine the sign of a real number.

How to Determine Whether a Function Is a Relationship

• It is possible to graphically determine whether a relation is a function.
• The X values or input values can be examined.
• The output values of Y can be verified.
• The relation becomes a function if each of the input values is unique, and it ceases to be a relation if the values are replicated.

Why are Relations and Functions Class 11 Important Questions useful?

Extramarks has provided Chapter 2 Class 11 Mathematics Important Questions here. Solutions are provided in detail, covering every step so that students can easily understand the concept. These questions cover all the important topics of Relation and Functions. Students can practise them to score well in Class 11.

• This chapter covers fundamental concepts such as sets, relations, and functions that are crucial for advanced concepts such as linear algebra, calculus, and so on. As a result, students must carefully examine these concepts with precise points.
• These important questions come with solutions. With these step-by-step answers, students can clear up any confusion they may have about relationships and functions.

These Mathematics Class 11 Chapter 2 Important Questions will also broaden students’ preparation. Aside from learning the suggested questions, they will also learn how to properly compile answers and thus score higher in the exams.

Q.1

Let R be a relation on set N of natural numbers defined by R = {(a, b) : ab = 10, a ? N, b ? N}, then range of R is

1. {1, 2, 5, 8, 10}.
2. {(1,2), (2,5), (1,10)}.
3. { 10, 5, 2, 1}.
4. {2, 5, 10}.

Marks:1

Ans

R = {(1,10), (2,5), (5,2), (10,1)}.

Range is the set of second components of the ordered pairs, therefore the range is {10, 5, 2, 1}.

Q.2

If n(A) = 4 and n(A × B) = 28, then n(B) is equal to

Marks:1

Ans

Since we know, n(A × B) = n(A) × n(B)

28 = 4 × n(B)

n(B) = 7

Q.3

Express the following functions as a sets of ordered pairs and determine their ranges?(a)?f?:?A?R,  fx?=?x2+1, where?A?=?-1,0,2,4?(b)?g?:?A?N, gx?=?2x, where?A=x:x?N,x?10

Marks:1

Ans

A We have, f(-1)=(-1)2+1=2, f0=02+1,f(2) = 22+1 = and f 4=42+1=17  f={x, fx):xA} = {(-1,2),(0,1),(2,5),(4,17)} Hence,

Range off={2,1,5,17} b We have, A={1,2,3,,10}.

Therefore,g1=2—1=2, g2=2—2=4,  g3=2—3=6,g4=2—4=8, g5=2—5=10, g6=2—6=12,g7=2—7=14, g8=2—8=16, g9=2—9=18,

g10=2—10=20g={x, gx):xA}={(1,2),(2,4),(3,6),(10,20)} Range of g = g(A) = {g(x):xA} ={2,4,6,8,10,12,14,16,18,20}

Q.4

Find?the?domain?of?function fx?=?x49?x2.

Marks:4

Ans

We know that all the values ofxfor which functionis defined is called domain.fx=x49-x2For function to be defined,49-x2>0x2-49<0x2-72<0x-7x+7<0x>-7andx<7-7<x<7x-7,7Hence, the domain of the given function is-7,7.

Q.5

Let f = {(1,1), (2,3), (0, ?1), (?1, ?3)} be a linear function from Z into Z. Find f(x).

Marks:4

Ans

Since f is a linear function,

Therefore, let us suppose f(x) = mx + c (1)

Also, since (1, 1), (0, 1) R,

f (1) = m + c = 1 (2)

and f (0) = c = 1.

On putting the value of c in (2), we get

m 1 = 1

m = 2

On putting the value of c and m in (1), we get

f(x) = 2x 1.

## Please register to view this section

### 1. What relations can be identified as a function?

A function, by definition, can relate  each element present in a domain to a single element present in the range. Any vertical line that a pupil draws on a graph can only make one pass through the x-axis. Vertical line tests and other formulas can be used to identify relations derived from functions.

### 2. What is a "relation"?

A relation is a subset of the ordered pairings in the cartesian product set A x B. A subset is obtained by establishing a relationship between the first and second elements of A x B.The Roster form or builder form can both display the relation. An arrow diagram may also be used to visually illustrate it. The domain and range of a relation R are the sets of all first and second elements, respectively.

### 3. What key ideas are discussed in Chapter 2 of the Class 11 Mathematics?

In Chapter 2 of Class 11 Mathematics, students will learn about relations, functions, cartesian products of sets, and ordered pairs. Students should comprehend the fundamental ideas of relationships and functions presented in the chapter as they are important from the exam point of view. For a better comprehension of the key ideas, students can refer to the Extramarks’ Class 11 Mathematics Chapter 2 Notes. Students may access these notes from the website at their convenience.

### 4. How are the Class 11 Mathematics Chapter 2 Notes beneficial?

Extramarks Class 11 Chapter 2 Mathematics Notes are thorough and cover the most recent CBSE and NCERT syllabus. All of the topics from the NCERT Class 11 Mathematics Chapter 2 are covered in these notes. Students can access these notes anytime from the website for a quick review of the chapter.

One of the best strategies is to refer to the revision notes after thoroughly reading the chapter. Students can improve their exam results by using the Relations And Functions Chapter 2 Mathematics Notes from Extramarks.