# Important Questions for CBSE Class 12 Maths Chapter 1 – Relations and Functions 2023-24

## Important Questions for CBSE Class 12 Maths Chapter 1 – Relations and Functions

Maths is an important subject in Class 12 board exams. With the right practice and study materials, students can prepare well and score more. Having said that, Extramarks has prepared important questions chapter-by-chapter for Class 12 Maths.

Class 12 Maths has 13 chapters in total, and the most important questions and frequently asked questions can be found on the Extramarks official website. These questions are picked by subject matter experts.

You can also find CBSE Class 12 Maths Important Questions Chapter-by-Chapter Important Questions here:

### CBSE Class 12 Maths Important Questions

Sr No Chapter No Chapter Name
1 Chapter 1 Relations and Functions
2 Chapter 2 Inverse Trigonometric Functions
3 Chapter 3 Matrices
4 Chapter 4 Determinants
5 Chapter 5 Continuity and Differentiability
6 Chapter 6 Application of Derivatives
7 Chapter 7 Integrals
8 Chapter 8 Application of Integrals
9 Chapter 9 Differential Equations
10 Chapter 10 Vector Algebra
11 Chapter 11 Three Dimensional Geometry
12 Chapter 12 Linear Programming
13 Chapter 13 Probability

## Marking Scheme of Relation And Function Class 12 Questions

Different sets of questions are included in Chapter 1 of Class 12 Maths Relations and Functions. There are 1-mark, 2-mark, 3-mark, 4-mark, and 5 mark questions, as well as other questions based on the latest CBSE curriculum for the current session.

## CBSE Class 12 Maths Important Questions Chapter Wise

Important Questions at Extramarks covers the following important concepts from Class 12 Maths chapters from which questions are likely to appear on the final exam:

### Chapter 1: Relations and Functions

• Theory of Relations and Functions
• Binary Operations

### Chapter 2: Inverse Trigonometric Functions

• Trigonometric Functions and its inverse

### Chapter 3: Matrices

• Introduction and Concept of Matrix
• Operations of Matrices
• Transpose of a Matrix
• Symmetric Matrix and Inverse of a Matrix by Elementary Operations

### Chapter 4: Determinants

•  Properties and Expansion of Determinants
• Inverse of a Matrix
• Application of Determinants and Matrix

### Chapter 5: Continuity and Differentiability

• Continuity and Differentiability

### Chapter 6: Application of Derivatives

• Increasing-Decreasing Functions
• Rate Measure Approximations
• Maxima and Minima
• Tangents and Normals

### Chapter 7: Integrals

• Integrals and Types of Integrals

### Chapter 8: Application Of Integrals

• NCERT Problems and Solutions

### Chapter 9: Differential Equation

• Formation of Differential Equations
• Solution of Different Kinds of Differential Equations

### Chapter 10: Vector Algebra

• Algebra of Vectors
• Dot and Cross Products

### Chapter 11: Three Dimensional Geometry

• Direction Lines
• Direction Cosines
• Plane

### Chapter 12: Linear Programming

• NCERT Problems and Solutions

### Chapter 13: Probability

• Conditional Probability
• Probability Distribution
• Independent Events
• Bayes Theorem

## Relations And Functions Class 12 Important Questions

Important Questions from Relationship and Function Class 12 Maths are provided to assist students to achieve more marks in the Class 12 Board Maths examination. Let us first review the fundamental concepts covered in Maths Chapter 1 Class 12. This chapter on Relations and Functions introduces the concepts of relations, functions and binary operations.

### Introduction to Relation

The definition of “relation” in the English language, which states that two objects or quantities are linked if there is a discernible connection or link between the two objects or values, serves as the basis for the idea of “relation” in Maths.

To better understand the concept of relation, consider two sets A and B. A relation R from Set A into Set B is the subset of A×B. The relationship can be further classified into three types:

• Symmetric Relation
• Reflexive Relation
• Transitive Relation

### Introduction to Function

A function is defined in the mathematical domain as a relation between two sets, with each component in set 1 linking to a component in set 2. To put it simply, if “f” is a function from A to B, then every component in set B is an image of a component in set A. The various types of functions are as follows:

• One to One function
• One to Many functions
• Onto function
• One to one Correspondence

## Class 12 Maths Chapter 1 Important Questions with Solutions – Relations and Functions

Students can examine the Class 12 Maths Chapter 1 Important Questions with answers in this section. All of the Relations and Functions Class 12 Important Questions that were frequently asked in previous board examinations are provided here.

1. Determine f(f(x)), if f: R → R is described by f(x) = x2 − 3x + 2.
2. Given:

F(x) = x² − 3x + 2.

To determine the function: f{f(x)}

F {f(x)} = f(x)2 − 3f(x) + 2.

= (x² – 3x + 2)² – 3(x² – 3x + 2) + 2

After applying the formula (a-b + c) ²= a² + b² + c² -2ab +2ac-2ab, we obtain

= (x²)² + (3x)² + 2²– 2x² (3x) + 2x²(2) – 2x²(3x) – 3(x² – 3x + 2) + 2

Now, after substituting the values, we get

= x4 + 9x² + 4 – 6×3 – 12x + 4x² – 3x² + 9x – 6 + 2

= x4 – 6×3 + 9x² + 4x² – 3x² – 12x + 9x – 6 + 2 + 4

Simplifying the expression, we obtain,

F {f(x)} = x4 – 6×3 + 10x² – 3x

## NCERT Based Relations and Functions Class 12 Important Questions with Solutions

NCERT Important Questions for Class 12 Maths is a valuable resource for Class 12 students preparing for upcoming board exams. The Extramarks Class 12 Maths Chapter 1 Important Questions cover problem questions and concepts from very important topics from the chapter Relations and Functions. This list of questions will also give them an idea of the types of questions expected in the Class 12 exam.

## Important Questions Relations And Functions Class 12 Based On Latest Syllabus

Students will find Relations and Functions in Class 12 Important Questions based on the most recent CBSE Board syllabus here. Some of these questions are discussed below:-

1. Discuss whether the following functions described on X are one-one onto or bijective functions given X = 1,1. You can choose from the following options:

(i)            g(x) =  |x|

(ii)          f(x) = x/2

(iii)          (iii) h(x) = x |x|

(iv)         (iv) k(x) = x2

1. (ii) g(x) is neither bijective nor one-one.

(ii) f(x) is a one-one function but not bijective.

(iii) h(x) is both one-one and bijective.

(iv) k(x) is neither bijective nor one-one.

1. Let R be a relation defined on the natural number set N. Determine the relation’s domain and range. Check to see if R is symmetric, reflexive, and/or transitive.

R = {x, y}: x∈N, y∈N, 2x + y = 41}

The range of the relation is 1,3, 5, 7,….., 39.

The domain of the relation R is 1, 2, 3, 4, 5, 6, 7,…., 20.

R is neither symmetric, reflexive, nor transitive.

## Use and Benefits of Important Questions Of Relation And Function Class 12

Students studying for the upcoming Class 12 Board Exam will find the above questions extremely useful, even for last-minute revision. These questions were created and compiled with the CBSE Class 12 Maths revised syllabus and examination pattern in mind. In addition to the Important Questions of Chapter 1 Maths Class 12, there are important questions from the other twelve chapters.

## Latest Important Questions on Relations and Functions Class 12

Class 12 Maths Relations and Functions important questions are available on the website. The additional questions for practice from the CBSE Class 12 examination include questions from previous years’ exams of previous years as well as questions provided by and other private and government schools in India affiliated with the CBSE, New Delhi.

Q.1

$\begin{array}{l}\mathrm{Let}\text{}\mathrm{f}:\text{}\left\{2,\text{}3,\text{}4,\text{}5\right\}\text{}\text{}\left\{3,\text{}4,\text{}5,\text{}9\right\}\text{}\mathrm{and}\\ \mathrm{g}:\text{}\left\{3,\text{}4,\text{}5,\text{}9\right\}\text{}\text{}\left\{7,\text{}11,\text{}15\right\}\text{}\mathrm{be}\text{}\mathrm{functions}\text{}\mathrm{defined}\text{}\mathrm{as}\\ \mathrm{f}\left(2\right)\text{}=\text{}3,\text{}\mathrm{f}\left(3\right)\text{}=\text{}4,\text{}\mathrm{f}\left(4\right)\text{}=\text{}\mathrm{f}\left(5\right)\text{}=\text{}5\text{}\mathrm{and}\text{}\mathrm{g}\left(3\right)\text{}=\text{}\mathrm{g}\left(4\right)\text{}=\text{}7\text{}\mathrm{and}\\ \mathrm{g}\left(5\right)\text{}=\text{}\mathrm{g}\left(9\right)\text{}=\text{}11,\text{}\mathrm{then}\text{}\mathrm{gof}\left(5\right)\text{}\mathrm{equals}\text{}\mathrm{to}\end{array}$

Option –

11

7

5

3

11

7

5

3

Ans.

11

Exp –

(gof)(5) = g(f(5))
= g(5)      [Since f(5) = 5  (given)]
= 11.        [Since g(5) = 11 (given)]

Q.2

Option –

{-13, 13}.

{-12, 12}.

{-11, 11}.

{-9, 9}.

Ans.

Q.3

Ans.

Q.4

Option –

Ans –

Q.5

Show that the Relation R on the set A = {x  Z : 0  x  12}, given by R = {(a, b) : |a – b| is a multiple of 4} is an equivalence relation.

Option –

R = {(a, b) : |a – b| is a multiple of 4}, where a, b A ={x Z : 0  x  12} = {0, 1, 2, …, 12}.

Reflexivity: For any a  A, |a – a| = 0, which is a multiple of 4.

(a, a)  R, for all a A.

So, R is reflexive.

Symmetry: Let (a, b)  R. Then,

(a, b)  R

|a – b| is a multiple of 4
|a – b| = 4k for some k  N
|b – a| = 4k for some k  N
(b, a)  R

So, R is symmetric.

Transitive: Let (a, b)  R and (b, c)  R. Then,
|a – b| is a multiple of 4 and |b – c| is a multiple of 4
|a – b| = 4k and |b – c| = 4m for some k, m  N
a – b = ± 4k and b – c = ± 4m
a – c = ± 4k ± 4m
a – c is a multiple of 4
|a – c| is a multiple of 4
(a, c)  R

So, R is transi

Ans –

R = {(a, b) : |a – b| is a multiple of 4}, where a, b ˆˆ A ={x Z : 0 ‰¤ x ‰¤ 12} = {0, 1, 2, …, 12}.

Reflexivity: For any a ˆˆ A, |a – a| = 0, which is a multiple of 4.

(a, a) ˆˆ R, for all a ˆˆ A.

So, R is reflexive.

Symmetry: Let (a, b) ˆˆ R. Then,

(a, b) ˆˆ R

|a – b| is a multiple of 4
|a – b| = 4k for some k ˆˆ N
|b – a| = 4k for some k ˆˆ N
(b, a) ˆˆ R

So, R is symmetric.

Transitive: Let (a, b) ˆˆ R and (b, c) ˆˆ R. Then,
|a – b| is a multiple of 4 and |b – c| is a multiple of 4
|a – b| = 4k and |b – c| = 4m for some k, m ˆˆ N
a – b = ± 4k and b – c = ± 4m
a – c = ± 4k ± 4m
a – c is a multiple of 4
|a – c| is a multiple of 4
(a, c) ˆˆ R

So, R is transitive.

Hence, R is an equivalence relation.