Important Questions for CBSE Class 12 Maths Chapter 1 - Relations and Functions 2024-25

Chapter 1 of Class 12 Mathematics Relations and Functions contains different sets of questions. The questions include 1 mark, 2 mark, 3 marks, 4 marks and 5 marks questions and other questions according to the latest CBSE curriculum for the current session

CBSE Class 12 Maths Important Questions Chapter Wise

Below are the chapters with important concepts from which questions are likely to come in the final exam. You need not spend enough time gathering Class 12 Maths Chapter 1 Important Questions and other chapters. You can master them following the important questions Maths Class 12 link. Refer below for the chapters:

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 (Not in the current syllabus)

• 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 (Not in the current syllabus)

Chapter 7: Integrals

• Integrals and Types of Integrals

Chapter 8: Application Of Integrals

• Applications in finding the area circles

• 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

Chapter 12: Linear Programming

• Feasible and infeasible regions (unbounded)

• NCERT Problems and Solutions

Chapter 13: Probability

• Conditional Probability

• Probability Distribution

• Independent Events

• Bayes Theorem

Relations And Functions Class 12 Important Questions

Important Questions of Relation and Function Class 12 are provided for you to fetch good marks in the Class 12 Board Maths examination. Here, we are going to discuss Class 12 Maths Ch 1 Important Questions with Solutions. Before that, let's learn the basic concepts covered in Maths Chapter 1 Class 12. Chapter 1 of Relations and Functions covers the concept of relations, functions and binary operations.

Introduction to Relation

To understand the concept of relation, let’s take into account two sets A and B. Then a relation R from Set A into Set B is described as the subset of A × B. The relation can further be categorized into 3 different types, such as:

• Symmetric Relation

• Reflexive Relation

• Transitive Relation

Introduction to Function

In the mathematical domain, a function is described as a relation between two sets, in which every component in the set 1 links to the component in set 2. Simply to say, if “f” is a function from A to B, then every component in set B is the image of a component in set A. The various forms of functions are:

• One to One function

• One to Many functions

• Onto function

• One to one Correspondence

Important Questions Of Relation And Function Class 12 With Solution

Go through the solved problems of Class 12 Maths Chapter 1 Important Questions in this section. Here, all the Relations and Functions Class 12 Important Questions are given that are frequently asked in the previous board examinations.

Example:

If f: R → R is described by f(x) = x2 − 3x + 2, determine f(f(x)).

Solution:

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

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, substituting the values, we get

= x4 + 9x² + 4 – 6x3 – 12x + 4x² – 3x² + 9x – 6 + 2

= x4 – 6x3 + 9x² + 4x² – 3x² – 12x + 9x – 6 + 2 + 4

Simplify the expression, we obtain,

F {f(x)} = x4 – 6x3 + 10x² – 3x

NCERT Based Relations And Functions Class 12 Important Questions

Class 12 Maths NCERT Exemplar is quite a crucial resource for 12th board students preparing for upcoming board examinations. Vedantu has given NCERT based Exemplar Problems Solutions Class 12. Problem Questions and concepts from very important topics from NCERT Exemplar Class 12 are covered in Class 12 Maths Ch 1 Important Questions offered by Vedantu. This list of questions will also help you have an idea about the type of questions as well as technique to answer in your Class 12th examination.

Important Questions Relations And Functions Class 12 Based On Latest Syllabus

Here, you will find Relations and Functions in Class 12 Important Questions that are based on the latest syllabus issued by the CBSE Board. Let’s see what type of questions you will face in your final Class 12 Maths examination.

Q1: Let X = [-1,1] , then, discuss if the following functions described on X are one-one onto or bijective functions. You have the following options:

(i)            g(x) =  |x|

(ii)          f(x) = x/2

(iii)          (iii) h(x) = x |x|

(iv)         (iv) k(x) = x²

Answer:

(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. 

Q2. Each of the Given Below Explains a Relation of n

(i)            X is greater than y, x, y ∈ N

(ii)          (x + y) = 10 x, y ∈ N

(iii)         Xy is the square of an integer x, y ∈ N

(iv)         (x + 4y) = 10 x, y ∈ N

Identify which of the above-mentioned relations are reflexive, transitive and symmetric.

Answer:

(i)            R is neither symmetric nor reflexive but transitive

(ii)          R is neither transitive nor reflexive but symmetric

(iii)         R is all symmetric, reflexive as well as transitive

(iv)         R is neither reflexive nor symmetric  but transitive

Q3. Let m = {1, 2, 3,4,5 ...,9} and R be the relation in M × m described by (m , n) R (o , p) if m + p = n + o for (m , n), (o , p) in m × m Prove that R is an equivalence relation and also get the equivalent class [(2, 5)].

Answer: The equivalence class consisting of [(2, 5)] is provided as {(1, 4), (2, 5), (3, 6), (4, 7), (5, 8), (6, 9)}.

Q4.  Let R be a relation described on the set of natural numbers N. Determine the domain and range of the relation. Also check whether R is symmetric, reflexive and/or transitive.

R = {x, y}: x ∈ N, y ∈ N, 2x+y = 41}

Answer: 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 nor reflexive and not even transitive.

Benefits of Important Questions of Relation and Function Class 12

The students preparing for the upcoming Class 12th Board exam 2024 will find the above questions quite helpful even for the last minute preparation. These questions are formulated and collected taking into account the CBSE Class 12th Mathematics Examination 2024 revised syllabus and pattern. In addition to Important Questions of Chapter 1 Maths Class 12, you will find other twelve chapters’ important questions. All these solved questions along with answer keys are based on the NCERT textbook, sample papers and previous year papers. For other chapters of Class 12 Mathematics, you can subscribe to Vedantu or check the links mentioned on the official website.

Latest Important Questions Of Chapter 1 Maths Class 12 Free PDF Download

Class 12 Mathematics Relations and Functions important questions are available for PDF download for annual examination preparation. The additional questions for practice from CBSE Class 12th examination are collected includes questions being asked in previous year exams, as well as questions provided by and other private and government schools in India affiliated to CBSE, New Delhi. 

Important Related Links for CBSE Class 12 Maths