case study questions class 12 maths chapter 1

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Class 12 Maths Case Study Questions

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Class 12 Maths question paper will have 1-2 Case Study Questions. These questions will carry 5 MCQs and students will attempt any four of them. As all of these are only MCQs, it is easy to score good marks with a little practice. Class 12 Maths Case Study Questions are available on the myCBSEguide App and Student Dashboard .

Why Case Studies in CBSE Syllabus?

CBSE has introduced case study questions in the CBSE curriculum recently. The purpose was to make students ready to face real-life challenges with the knowledge acquired in their classrooms. It means, there was a need to connect theories with practicals. Whatsoever the students are learning, they must know how to apply it in their day-to-day life. That’s why CBSE is emphasizing case studies and competency-based education .

Case Study Questions in Maths

Let’s have a look over the class 12 Mathematics sample question paper issued by CBSE, New Delhi. Question numbers 17 and 18 are case study questions.

Focus on concepts

If you go through each MCQ there, you will find that the theme/case study is common but the questions are based on different concepts related to the theme. It means, that if you have done ample practice on the various concepts, you can solve all these MCQs in minutes.

Easy Questions with a Practical Approach

The difficulty level of the questions is average or say easy in some cases. On the other hand, you get four options to choose from. So, you get two levels of support to get full marks with very little effort.

Practice Questions Regularly

Most of the time we feel that it’s easy and neglect it. But in the end, we have to pay for this negligence. This may happen here too. Although it’s easy to score good marks on the case study questions if you don’t practice such questions, you may lose your marks. So, we suggest students should practice at least 30-40 such questions before writing the board exam.

12 Maths Case-Based Questions

We are giving you some examples of case study questions here. We have arranged hundreds of such questions chapter-wise on the myCBSEguide App. It is the complete guide for CBSE students. You can download the myCBSEguide App and get more case study questions there.

Case Study Question – 1

• A is a diagonal matrix
• A is a scalar matrix
• A is a zero matrix
• A is a square matrix
• If A and B are two matrices such that AB = B and BA = A, then B 2 is equal to

Case Study Question – 2

• 4(x 3  – 24x 2   + 144x)
• 4(x 3 – 34x 2   + 244x)
• x 3  – 24x 2   + 144x
• 4x 3  – 24x 2   + 144x
• Local maxima at x = c 1
• Local minima at x = c 1
• Neither maxima nor minima at x = c 1
• None of these

Case Study Questions Matrices -1

Answer Key:

Case Study Questions Matrices – 2

Read the case study carefully and answer any four out of the following questions: Once a mathematics teacher drew a triangle ABC on the blackboard. Now he asked Jose,” If I increase AB by 11 cm and decrease the side BC by 11 cm, then what type of triangle it would be?” Jose said, “It will become an equilateral triangle.”

Again teacher asked Suraj,” If I multiply the side AB by 4 then what will be the relation of this with side AC?” Suraj said it will be 10 cm more than the three times AC.

Find the sides of the triangle using the matrix method and  answer the following questions:

• (a) 3  ×  3

Case Study Questions Determinants – 01

DETERMINANTS:  A determinant is a square array of numbers (written within a pair of vertical lines) that represents a certain sum of products. We can solve a system of equations using determinants, but it becomes very tedious for large systems. We will only do 2 × 2 and 3 × 3 systems using determinants. Using the properties of determinants solve the problem given below and answer the questions that follow:

Three shopkeepers Ram Lal, Shyam Lal, and Ghansham are using polythene bags, handmade bags (prepared by prisoners), and newspaper envelopes as carrying bags. It is found that the shopkeepers Ram Lal, Shyam Lal, and Ghansham are using (20,30,40), (30,40,20), and (40,20,30) polythene bags, handmade bags, and newspapers envelopes respectively. The shopkeeper’s Ram Lal, Shyam Lal, and Ghansham spent ₹250, ₹270, and ₹200 on these carry bags respectively.

• (b) Shyam Lal
• (a) Ram Lal

Case Study Questions Determinants – 02

Case study questions application of derivatives.

• R(x) = -x 2  + 200x + 150000
• R(x) = x 2  – 200x – 140000
• R(x) = 200x 2  + x + 150000
• R(x) = -x 2  + 100 x + 100000
• R'(x) > 0
• R'(x) < 0
• R”(x) = 0
• (a) -x 2  + 200x + 150000
• (a) R'(x) = 0
• (c) 257, -63

Case Study Questions Vector Algebra

• tan−1⁡(5/12)
• tan−1⁡(12/3)
• (b) 130 m/s
• (a)  tan−1⁡(5/12)
• (b) 170 m/s

More Case Study Questions

These are only some samples. If you wish to get more case study questions for CBSE class 12 maths, install the myCBSEguide App. It has class 12 Maths chapter-wise case studies with solutions.

12 Maths Exam pattern

Question Paper Design of CBSE class 12 maths is as below. It clearly shows that 20% weightage will be given to HOTS questions. Whereas 55% of questions will be easy to solve.

• No. chapter-wise weightage. Care to be taken to cover all the chapters
• Suitable internal variations may be made for generating various templates keeping the overall weightage to different forms of questions and typology of questions the same.

Choice(s): There will be no overall choice in the question paper. However, 33% of internal choices will be given in all the sections

12 Maths Prescribed Books

• Mathematics Part I – Textbook for Class XII, NCERT Publication
• Mathematics Part II – Textbook for Class XII, NCERT Publication
• Mathematics Exemplar Problem for Class XII, Published by NCERT
• Mathematics Lab Manual class XII, published by NCERT

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Class 12 Maths: Case Study Based Questions PDF Download

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You must practice some good Case Study questions of Class 12 Maths to boost your preparation to score 95+% on Boards. In this post, you will get Case Study Questions of All Chapters which will come in CBSE Class 12 Maths Board Exams.

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

We have provided here Case Study questions for the Class 12 Maths exams. You can read these chapter-wise Case Study questions. Prepared by subject experts and experienced teachers. The answer key is also provided so that you can check the correct answer for each question. Practice these questions to score well in your Board Final exams.

We are providing Case Study questions for class 12 Biology based on the latest syllabi. There is a total of 13 chapters included in CBSE class 12 Maths exams. Students can practice these questions for concept clarity and score better marks in their exams.

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CBSE Class 12th – MATHS : Chapterwise Case Study Question & Solution

CBSE will ask two Case Study Questions in the CBSE class 12 maths questions paper. Question numbers 15 and 16 are case-based questions where 5 MCQs will be asked based on a paragraph. Each theme will have five questions and students will have a choice to attempt any four of them.

Case Study Based Questions for Class 12 Maths

Class 12 Physics Case Study Questions Class 12 Chemistry Case Study Questions Class 12 Biology Case Study Questions Class 12 Maths Case Study Questions

Books for Class 12 Maths

Strictly as per the new term-wise syllabus for Board Examinations to be held in the academic session 2022-23 for class 12 Multiple Choice Questions based on new typologies introduced by the board- Stand-Alone MCQs, MCQs based on Assertion-Reason Case-based MCQs. Include Questions from CBSE official Question Bank released in April 2022 Answer key with Explanations What are the updates in the book: Strictly as per the Term wise syllabus for Board Examinations to be held in the academic session 2022-23. Chapter-wise -Topic-wise Multiple choice questions based on the special scheme of assessment for Board Examination for Class 12th.

Class 12 Maths Syllabus 2022-23

Unit-i: relations and functions.

1. Relations and Functions (15 Periods)

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.

2. Inverse Trigonometric Functions (15 Periods)

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.

Unit-II: Algebra

1. Matrices (25 Periods)

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Oncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

2. Determinants 25 Periods

Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

Unit-III: Calculus

1. Continuity and Differentiability (20 Periods)

Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, 𝑙𝑖𝑘𝑒 sin −1  𝑥 , cos −1  𝑥 and tan −1  𝑥, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives.

2. Applications of Derivatives (10 Periods)

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as reallife situations).

3. Integrals (20 Periods)

Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.

Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

4. Applications of the Integrals (15 Periods)

Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)

5. Differential Equations (15 Periods)

Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:

Unit-IV: Vectors and Three-Dimensional Geometry

1. Vectors (15 Periods)

Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.

2. Three – dimensional Geometry (15 Periods)

Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines.

Unit-V: Linear Programming

1. Linear Programming (20 Periods)

Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit-VI: Probability

1. Probability 30 (Periods)

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of random variable.

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Case Study Questions for Class 12 Maths PDF Download

We have provided here Case Study questions for the Class 12 Maths for board exams. You can read these chapter-wise Case Study questions. These questions are prepared by subject experts and experienced teachers. The answer key is also provided so that you can check the correct answer for each question. Practice these questions to score well in your final exams.

CBSE 12th Standard CBSE Maths question papers, important notes, study materials, Previous Year questions, Syllabus, and exam patterns. Free 12th Standard CBSE Maths books and syllabus online. Important keywords, Case Study Questions, and Solutions.

Class 12 Maths Case Study Questions

CBSE Class 12 Maths question paper will have case study questions too. These case-based questions will be objective type in nature. So, Class 12 Maths students must prepare themselves for such questions. First of all, you should study NCERT Textbooks line by line, and then you should practice as many questions as possible.

Chapter-wise Solved Case Study Questions for Class 12 Maths

Class 12 students should go through important Case Study problems for Maths before the exams. This will help them to understand the type of Case Study questions that can be asked in Grade 12 Maths examinations. Our expert faculty for standard 12 Maths have designed these questions based on the trend of questions that have been asked in last year’s exams. The solutions have been designed in a manner to help the grade 12 students understand the concepts and also easy to learn solutions.

Books for Class 12 Maths

Strictly as per the new term-wise syllabus for Board Examinations to be held in the academic session 2022-23 for class 12 Multiple Choice Questions based on new typologies introduced by the board- Stand-Alone MCQs, MCQs based on Assertion-Reason Case-based MCQs. Include Questions from CBSE official Question Bank released in April 2022 Answer key with Explanations What are the updates in the book: Strictly as per the Term wise syllabus for Board Examinations to be held in the academic session 2022-23. Chapter-wise -Topic-wise Multiple choice questions based on the special scheme of assessment for Board Examination for Class 12th.

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Chapter 1 Class 12 Relation and Functions

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Get NCERT Solutions for Chapter 1 Class 12 Relation and Functions. Solutions of all questions and examples are given. 

In this Chapter, we study

• What a Relation is, Difference between relations and functions and finding relation
• Then, we define Empty and Universal Relation and take some examples
• We study different relations and check if they are reflexive, transitive, symmetric using different questions
• Questions on finding number of relations are solved. These are important questions and can come in the exams
• Then, we define Functions and do examples to check if it is a function or not. 
• We prove functions one-one & onto , one-one is also called injective ; onto is also called surjective and both one-one and onto is called bijective
• Then, we find Composite functions - fog and gof ... and also what is domain and range of fog and gof  
• Then we prove Composite functions one-one and onto
• We learn what is an inverse of a function,  check if a function has inverse or not and find an inverse
• Then, we do some proof questions with inverse of
• We learn about Binary Operations
• And check whether they are commutative or associative
• We also find Identity Element in a Binary Operation
• And then, find its inverse

Besides providing, NCERT Solutions of Chapters , we also provide Sample Papers and Important Questions

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Concept wise.

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NCERT Solutions Class 12 Maths Chapter 1 Relations and Functions

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions describes all the fundamental concepts covered in this most important algebraic topic. The mathematical term relation is drawn from the English word relation that implies two objects or quantities have a recognizable connection. Students have already studied the notion of relations, functions, domain, co-domain, and range in class 11. Chapter 1 of class 12 maths further elaborates the types of relations, functions, composition of functions, invertible functions, and binary operations. By learning through NCERT Solutions Class 12 Maths Chapter 1, students will get well-versed with all these topics and their applications.

Some of the types of relations explained in this chapter are empty relation, universal relation, symmetric relation, and transitive relation. An empty relation is also known as a void relation and is defined as a set in which there exists no relationship between the elements. With the regular practice of Class 12 Maths NCERT Solutions Chapter 1, students will quickly gain a deep understanding of Relations and their types. To learn and practice with NCERT Solutions Chapter 1 Relation and Functions, download the exercises provided in the links below.

• NCERT Solutions Class 12 Maths Chapter 1 Ex 1.1
• NCERT Solutions Class 12 Maths Chapter 1 Ex 1.2
• NCERT Solutions Class 12 Maths Chapter 1 Ex 1.3
• NCERT Solutions Class 12 Maths Chapter 1 Ex 1.4
• NCERT Solutions Class 12 Maths Chapter 1 Miscellaneous Exercise

NCERT Solutions for Class 12 Maths Chapter 1 PDF

Students often juggle the study material during exams that result in poor scores. It is essential to wisely choose the right resource to pave the way to exam success. NCERT Solutions for Class 12 Maths are meticulously formulated by subject matter experts to support and promote the understanding of Relations, Functions, and their types. To practice with these solutions, click on the links of the pdf file given below.

☛ Download Class 12 Maths NCERT Solutions Chapter 1 Relations and Functions

NCERT Class 12 Maths Chapter 1   Download PDF

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

The concept of functions was first introduced in the 17th century and has evolved over a long period of time. The definition of function known to us presently was given after set theory was developed by Georg Cantor (1845-1918). NCERT solutions Class 12 Maths Chapter 1 Relations and Functions are comprehensive guides that efficiently impart the complete knowledge of relations and functions. These resources are competent to strengthen the key skills required to study all topics in detail and also practice relations and functions worksheets . To practice the exercise-wise NCERT Solutions Class 12 Maths Relations and Functions, try the links given below.

• Class 12 Maths Chapter 1 Ex 1.1 - 16 Questions
• Class 12 Maths Chapter 1 Ex 1.2 - 12 Questions
• Class 12 Maths Chapter 1 Ex 1.3 - 14 Questions
• Class 12 Maths Chapter 1 Ex 1.4 - 13 Questions
• Class 12 Maths Chapter 1 Miscellaneous Ex - 19 Questions

☛ Download Class 12 Maths Chapter 1 NCERT Book

Topics Covered: The topics covered in NCERT Solutions Class 12 Maths Chapter 1 are types of relations, types of functions , representation of functions, the composition of functions , invertible function , and binary operations.

Total Questions: Class 12 Maths Chapter 1 Relations and Functions has 55 questions in 4 exercises along with 19 extra questions provided in a miscellaneous exercise. These problems are mostly short answer types and multiple choices that are based on types of relations and functions, their compositions as well as binary operations.

List of Formulas in NCERT Solutions Class 12 Maths Chapter 1

The topic of relations and functions is majorly focused on learning terms, definitions, theorems, and properties. NCERT Solutions Class 12 Maths Chapter 1 elaborates all these essential concepts using illustrations. Some of the important concepts defined in these NCERT Solutions are quite helpful for excellent exam preparation. This topic is also used in the next chapter as a basis for inverting trigonometric functions . Thus, students must have a good grasp of all the procedures, definitions, and formulas outlined in this lesson as they will be used further also. Kids can gain a deep understanding of these by referring to the details provided in NCERT Solutions for Class 12 Maths Chapter 1.

• Symmetric relation: A Symmetric relation R in X satisfies a certain relation as (a, b) ∈ R implies (b, a) ∈ R.
• Reflexive relation: A Reflexive relation R in X can be given as: (a, a) ∈ R; for all ∀ a ∈ X.
• Transitive relation: A Transitive relation R in X can be given as (a, b) ∈ R and (b, c) ∈ R, thereby implying (a, c) ∈ R.
• Equivalence relation: Equivalence relation R in X is a relation that shows all the reflexive, symmetric, and transitive relations.
• Injective Function: A function f: X → Y is one-one/injective; if f(x 1 ) = f(x 2 ) ⇒ x 1 = x 2 ∀ x1 , x 2 ∈ X.
• Subjective Function: A function f: X → Y is onto/surjective; if given any y ∈ Y, ∃ x ∈ X such that f(x) = y.

FAQs on NCERT Solutions Class 12 Maths Chapter 1

What is the importance of ncert solutions for class 12 maths chapter 1 relations and functions.

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions are developed by experienced professionals and field experts to promote a deep understanding of concepts. These solutions are framed after thorough research and are well structured in a suitable manner to enhance the topic-wise learnability of relations and functions. Practicing with these resources will help students to strategize effectively for exams.

What are the Important Topics Covered in Class 12 Maths NCERT Solutions Chapter 1?

Chapter 1 Relations and Functions of class 12 Maths fairly covers all the important topics and subtopics in four comprehensive exercises. The important topics covered in the NCERT Solutions Class 12 Maths Chapter 1 are types of relations, types of functions, the composition of functions, invertible functions, and binary operations. The set of problems provided in these solutions are proficient at enhancing the problem-solving skills of students. The primary goal of these solutions is to help kids score well in the Class 12 exams. With the help of these valuable resources, it becomes pretty convenient to prepare for various competitive exams.

Do I Need to Practice all Questions Provided in NCERT Solutions Class 12 Maths Relations and Functions?

The questions included in NCERT Solutions Class 12 Maths Relations and Functions are well-framed to facilitate thorough conceptual understanding. By practicing all questions available in these solutions, students can easily master the fundamentals of Relations and Functions and their applications. These solutions help in getting well-versed with the terms and theorems related to Relations and Functions.

How Many Questions are there in Class 12 Maths NCERT Solutions Chapter 1 Relations and Functions?

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions has 55 questions in 4 exercises. The practice of these exercises is useful in attaining a clear understanding of this topic, including important terms, definitions, theorems, and concepts based on Relations and Functions. The easy-to-understand format of these solutions is proficient for acquiring a sound understanding of the types of Relations and Functions.

What are the Important Formulas in NCERT Solutions Class 12 Maths Chapter 1?

NCERT Solutions Class 12 Maths Chapter 1 explains the concept of Relations and Functions. Some of the important concepts described in these solutions are based on understanding the types of relations, types of functions, the composition of functions, and their boolean operations. These concepts are covered in detail with the help of examples and illustrations. This chapter requires students to concentrate more on theory rather than formulas.

Why Should I Practice NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions?

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions is a competent learning resource that offers complete guidance and practice of core concepts for higher-level studies. These solutions cover the whole syllabus of CBSE Class 12 Maths Chapter 1 to provide comprehensive learning of all topics. The format of these solutions is simple and easy for students to grasp all complex concepts. Regular practice of these resources will ensure the best results in exams.

NCERT Solutions for Class 12 Maths Chapter 1 – Relations and Functions

Ncert solutions for class 12 maths chapter 1 – relations and functions pdf.

NCERT Solutions for Class 12 Maths Chapter 1 – Relations and Functions includes all the questions provided in NCERT Books prepared by Mathematics expert teachers as per CBSE NCERT guidelines from Mathongo.com. To download our free pdf of Chapter 1 – Relations and Functions Maths NCERT Solutions for Class 12 to help you to score more marks in your board exams and as well as competitive exams.

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CBSE Case Study Questions for Class 12 Maths Matrices Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 12 Maths Matrices  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 12 Maths Matrices PDF

Mcq set 1 -, mcq set 2 -, checkout our case study questions for other chapters.

• Chapter 1 Relations and Functions Case Study Questions
• Chapter 2 Inverse Trigonometric Functions Case Study Questions
• Chapter 4 Determinants Case Study Questions
• Chapter 5 Continuity and Differentiability Case Study Questions

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

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NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

NCERT solutions for Class 12 Maths Chapter 1 Relations and Functions in Hindi and English Medium revised and updated for academic year 2023-24. As per new NCERT textbook there are only three exercises (including miscellaneous) in class 12th Maths chapter 1. Earlier there were five, rest two are deleted from the syllabus now.

Class 12 Maths Chapter 1 Solutions in English Medium

• Class 12 Maths Exercise 1.1 in English
• Class 12 Maths Exercise 1.2 in English
• 12th Maths Chapter 1 Miscellaneous Exercise

Class 12 Maths Chapter 1 Solutions in Hindi

• Class 12 Maths Exercise 1.1 in Hindi
• Class 12 Maths Exercise 1.2 in Hindi

Class XII Mathematics all exercises including miscellaneous are in PDF Hindi & English Medium along with NCERT Solutions Apps free download. Download assignments based on Relations and functions and Previous Years Questions asked in CBSE board, important questions for practice as per latest CBSE Curriculum.

NCERT solutions for Class 12 Maths Chapter 1 all exercises are given to free download in PDF. NCERT Books as well as Solutions are available in English Hindi Medium. Ask your doubts in Maths, Physics and other subjects, NIOS Board admission query and CBSE Board information through Discussion Forum . NCERT Solutions and Offline apps are based on latest CBSE Syllabus.

Class 12 Maths Chapter 1 Study Material

• Class 12 Maths NCERT Book Chapter 1
• Class 12 Maths Revision Book Chapter 1
• Class 12 Maths Revision Book Answers
• Download Class 12 Maths Assignment 1
• Download Class 12 Maths Assignment 2
• Download Class 12 Maths Assignment 2 Answers
• Download Class 12 Maths Assignment 3
• Download Class 12 Maths Assignment 4
• Class 12 Maths NCERT Solutions
• Class 12 all Subjects NCERT Solutions

Important Terms related to Chapter 1

Before studying this lesson, you should know:

• Concept of set, types of sets, operations on sets
• Concept of ordered pair and cartesian product of set.
• Domain, co-domain and range of a relation and a function

Let A and B be two sets. Then a relation R from Set A into Set B is a subset of A × B. Types of Relations

• Reflexive Relation
• Symmetric Relation
• Transitive Relation

Equivalence Relation

A relation R on a set A is said to be an equivalence relation on A iff

• it is reflexive
• it is symmetric
• it is transitive

Let f be a function from A to B. If every element of the set B is the image of at least one element of the set A i.e. if there is no unpaired element in the set B then we say that the function f maps the set A onto the set B. Otherwise we say that the function maps the set A into the set B. Functions for which each element of the set A is mapped to a different element of the set B are said to be one-to-one.

A function can map more than one element of the set A to the same element of the set B. Such a type of function is said to be many-to-one. A function which is both one-to-one and onto is said to be a bijective function.

Important Questions on 12th Maths Chapter 1

Determine whether each of the following relation are reflexive, symmetric and transitive: relation r in the set a = {1, 2, 3… 13, 14} defined as r = {(x, y): 3x – y = 0}.

A = {1, 2, 3 … 13, 14} R = {(x, y): 3x − y = 0} ∴ R = {(1, 3), (2, 6), (3, 9), (4, 12)} R is not reflexive since (1, 1), (2, 2) … (14, 14) ∉ R. Also, R is not symmetric as (1, 3) ∈ R, but (3, 1) ∉ R. [3(3) − 1 ≠ 0] Also, R is not transitive as (1, 3), (3, 9) ∈ R, but (1, 9) ∉ R. [3(1) − 9 ≠ 0] Hence, R is neither reflexive, nor symmetric, nor transitive.

Show that the relation R in the set R of real numbers, defined as R = {(a, b): a ≤ b²} is neither reflexive nor symmetric nor transitive.

R = {(a, b): a ≤ b²} It can be observed that (1/2,1/2)∉R, since, 1/2>(1/2)² ∴ R is not reflexive. Now, (1, 4) ∈ R as 1 (1.5)² = 2.25 ∴ (3, 1.5) ∉ R ∴ R is not transitive. Hence, R is neither reflexive, nor symmetric, nor transitive.

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b): b = a + 1} is reflexive, symmetric or transitive.

Let A = {1, 2, 3, 4, 5, 6}. A relation R is defined on set A as: R = {(a, b): b = a + 1} ∴ R = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)} We can find (a, a) ∉ R, where a ∈ A. For instance, (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) ∉ R ∴ R is not reflexive. It can be observed that (1, 2) ∈ R, but (2, 1) ∉ R. ∴ R is not symmetric. Now, (1, 2), (2, 3) ∈ R but, (1, 3) ∉ R ∴ R is not transitive. Hence, R is neither reflexive, nor symmetric, nor transitive.

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Let A = {1, 2, 3}. A relation R on A is defined as R = {(1, 2), (2, 1)}. It is clear that (1, 1), (2, 2), (3, 3) ∉ R, ∴ R is not reflexive. Now, as (1, 2) ∈ R and (2, 1) ∈ R, then R is symmetric. Now, (1, 2) and (2, 1) ∈ R, however, (1, 1) ∉ R, ∴ R is not transitive. Hence, R is symmetric but neither reflexive nor transitive.

Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y): x and y have same number of pages} is an equivalence relation.

Set A is the set of all books in the library of a college. R = {x, y): x and y have the same number of pages} Now, R is reflexive since (x, x) ∈ R as x and x has the same number of pages. Let (x, y) ∈ R ⇒ x and y have the same number of pages. ⇒ y and x have the same number of pages. ⇒ (y, x) ∈ R ∴ R is symmetric. Now, let (x, y) ∈R and (y, z) ∈ R. ⇒ x and y and have the same number of pages and y and z have the same number of pages. ⇒ x and z have the same number of pages. ⇒ (x, z) ∈ R ∴ R is transitive. Hence, R is an equivalence relation.

Show that the relation R in the set A of points in a plane given by R = {(P, Q): Distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all point related to a point P ≠ (0, 0) is the circle passing through P with origin as centre.

R = {(P, Q): Distance of point P from the origin is the same as the distance of point Q from the origin} Clearly, (P, P) ∈ R since the distance of point P from the origin is always the same as the distance of the same point P from the origin. ∴ R is reflexive. Now, Let (P, Q) ∈ R. ⇒ The distance of point P from the origin is the same as the distance of point Q from the origin. ⇒ The distance of point Q from the origin is the same as the distance of point P from the origin. ⇒ (Q, P) ∈ R, ∴ R is symmetric. Now, Let (P, Q), (Q, S) ∈ R. ⇒ The distance of points P and Q from the origin is the same and also, the distance of points Q and S from the origin is the same. ⇒ The distance of points P and S from the origin is the same. ⇒ (P, S) ∈ R ∴ R is transitive. Therefore, R is an equivalence relation. The set of all points related to P ≠ (0, 0) will be those points whose distance from the origin is the same as the distance of point P from the origin. In other words, if O (0, 0) is the origin and OP = k, then the set of all points related to P is at a distance of k from the origin. Hence, this set of points forms a circle with the centre as the origin and this circle passes through point P.

Show that the relation R defined in the set A of all polygons as R = {(P1, P2): P1 and P2 have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?

R = {(P1, P2): P1 and P2 have same the number of sides} R is reflexive, Since (P1, P1) ∈ R, as the same polygon has the same number of sides with itself. Let (P1, P2) ∈ R. ⇒ P1 and P2 have the same number of sides. ⇒ P2 and P1 have the same number of sides. ⇒ (P2, P1) ∈ R, ∴ R is symmetric. Now, Let (P1, P2), (P2, P3) ∈ R. ⇒ P1 and P2 have the same number of sides. Also, P2 and P3 have the same number of sides. ⇒ P1 and P3 have the same number of sides. ⇒ (P1, P3) ∈ R ∴ R is transitive. Hence, R is an equivalence relation. The elements in A related to the right-angled triangle (T) with sides 3, 4, and 5 are those polygons which have 3 sides (Since T is a polygon with 3 sides). Hence, the set of all elements in A related to triangle T is the set of all triangles.

Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2): L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.

R = {(L1, L2): L1 is parallel to L2} R is reflexive as any line L1 is parallel to itself i.e., (L1, L1) ∈ R. Now, let (L1, L2) ∈ R. ⇒ L1 is parallel to L2 ⇒ L2 is parallel to L1. ⇒ (L2, L1) ∈ R ∴ R is symmetric. Now, let (L1, L2), (L2, L3) ∈ R. ⇒ L1 is parallel to L2. Also, L2 is parallel to L3. ⇒ L1 is parallel to L3. ∴ R is transitive. Hence, R is an equivalence relation. The set of all lines related to the line y = 2x + 4 is the set of all lines that are parallel to the line y = 2x + 4. Slope of line y = 2x + 4 is m = 2 It is known that parallel lines have the same slopes. The line parallel to the given line is of the form y = 2x + c, where c ∈ R. Hence, the set of all lines related to the given line is given by y = 2x + c, where c ∈ R.

Let f: {1, 3, 4} → {1, 2, 5} and g: {1, 2, 5} → {1, 3} be given by f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}. Write down gof.

The functions f: {1, 3, 4} → {1, 2, 5} and g: {1, 2, 5} → {1, 3} are defined as f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}. gof(1) = g[f(1)] = g(2) = 3 [as f(1) = 2 and g(2) = 3] gof(3) = g[f(3)] = g(5) = 1 [as f(3) = 5 and g(5) = 1] gof(4) = g[f(4)] = g(1) = 3 [as f(4) = 1 and g(1) = 3] ∴ gof = {(1, 3), (3, 1), (4, 3)}

Show that the function f: R → R given by f(x) = x³ is injective.

f: R → R is given as f(x) = x³. For one – one Suppose f(x) = f(y), where x, y ∈ R. ⇒ x³ = y³ … (1) Now, we need to show that x = y. Suppose x ≠ y, their cubes will also not be equal. ⇒ x³ ≠ y³ However, this will be a contradiction to (1). ∴ x = y Hence, f is injective.

What is the core motive of chapter 1 Relations and Functions of 12th standard Maths?

The core motive of chapter 1 (Relations and Functions) of 12th standard Maths is to teach students the following things:

• Empty relation is the relation R in X given by R = φ ⊂ X × X.
• Universal relation is the relation R in X given by R = X × X.
• Reflexive relation R in X is a relation with (a, a) ∈ R ∀ a ∈ X.
• Symmetric relation R in X is a relation satisfying (a, b) ∈ R implies (b, a) ∈ R.
• Transitive relation R in X is a relation satisfying (a, b) ∈ R and (b, c) ∈ R implies that (a, c) ∈ R.
• Equivalence relation R in X is a relation which is reflexive, symmetric and transitive.
• A function f: X → Y is one-one (or injective) if f(x₁) = f(x₂) ⇒x₁ = x₂ ∀ x₁, x₂∈ X.
• A function f: X → Y is onto (or surjective) if given any y ∈ Y, ∃ x ∈ X such that f(x) = y.
• A function f: X → Y is one-one and onto (or bijective), if f is both one-one and onto.
• The composition of functions f: A → B and g: B → C is the function gof: A → C given by gof(x) = g(f(x)) ∀ x ∈ A.
• A function f: X → Y is invertible if and only if f is one-one and onto.
• Given a finite set X, a function f: X → X is one-one (respectively onto) if and only if f is onto (respectively one-one). This is the characteristic property of a finite set. This is not true for infinite set.
• A binary operation ∗ on a set A is a function ∗ from A × A to A.
• An element e ∈ X is the identity element for binary operation ∗: X × X → X, if a ∗ e = a = e ∗ a ∀ a ∈ X.
• An element a ∈ X is invertible for binary operation ∗: X × X → X, if there exists b ∈ X such that a ∗ b = e = b ∗ a where, e is the identity for the binary operation ∗. The element b is called inverse of a and is denoted by a^(–1).
• An operation ∗ on X is commutative if a ∗ b = b ∗ a ∀ a, b in X.
• An operation ∗ on X is associative if (a ∗ b) ∗ c = a ∗ (b ∗ c) ∀ a, b, c in X.

What should be revised before starting chapter 1 of 12th standard Maths?

Before starting chapter 1 (Relations and Functions) of 12th standard Maths, students should revise chapter 2 (Relations and Functions) of grade 11th Maths. Chapter 2 of class 11th Maths works as a base for chapter 1 of class 12th Maths.

Does chapter 1 of grade 12th Maths has any miscellaneous exercise?

Yes, chapter 1 of grade 12th Maths has a miscellaneous exercise. There are five exercises in chapter 1 of class 12th Maths, and the last exercise is the miscellaneous exercise of chapter 1 of grade 12th Maths.

Is NCERT chapter 1 of 12th Standard Maths short or lengthy?

Chapter 1 of 12th standard Maths is lengthy. There are five exercises in this chapter. In the first exercise, there are 6 examples (examples 1 to 6) and 16 questions. The second exercise contains eight examples (examples 7 to 14) and 12 questions. The last (Miscellaneous) exercise has 11 examples (examples 41 to 51) and 19 questions. So, there are good examples and just a little questions in chapter 1 of class 12th Maths.

Are there any theorems in chapter 1 of class 12th Maths?

Yes, there are two theorems in chapter 1 of class 12th Maths. Both the theorems are nice and easy. Proofs of these theorems are short and easy. Students can easily understand the proofs of these theorems.

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• Class 12 Maths
• Chapter 1: Relations Functions

Important Questions For Class 12 Maths Chapter 1 - Relations and Functions

Important Questions for Class 12 Maths Chapter 1 – Relations and functions are provided here for the students to score good marks in the class 12 board Maths examination. Here, all the important problems are covered as per the NCERT book. By practising and going through the important questions, students can get the confidence to solve the problems easily and efficiently. Get the class 12 Maths important questions for all the chapters at BYJU’S.

Here, we are going to discuss the important questions in class 12 chapter 1 – Relations and functions with solutions. Before that, let us learn the basic concepts covered in class 12 Maths chapter 1. In relations and functions chapter 1, it covers the concept of relations, functions and binary operations.

What is the Relation?

Let us consider two sets A and B. Then a relation R from Set A into Set B is defined as the subset of A × B. The relation can be classified into three different types, such as:

• Reflexive Relation
• Symmetric Relation
• Transitive Relation

What is a Function?

A function is defined as the relation between two sets, in which every element in set 1 is associated with the elements in set 2. In other words, if  “f” is a function from A to B, then every element in set B is the image of an element in set A.  The different types of functions are:

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

Also, check:

• Important 4 Marks Questions for CBSE Class 12 Maths
• Important 6 marks Questions for CBSE Class 12 Maths

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

Go through the solved problems given below. Here, all the important questions for class 12 chapter 1 maths problems are given. The problems given here are frequently asked in the previous board examinations. Practice these problems well and solve the practice problems provided here.

Q.1:   Show that the Signum Function f: R → R, given by

Check for one to one function:

For example:

Since, the different elements say f(1), f(2) and f(3), shows the same image, then the function is not one to one function.

Check for Onto Function:

For the function,f: R →R

In this case, the value of f(x) is defined only if x is 1, 0, -1

For any other real numbers(for example y = 2, y = 100) there is no corresponding element x.

Thus, the function “f” is not onto function.

Hence, the given function “f” is neither one-one nor onto.

Q.2:  If f: R → R is defined by f(x) = x 2 − 3x + 2, find f(f(x)).

Given function:

f(x) = x 2 − 3x + 2.

To find f(f(x))

f(f(x)) = f(x) 2 − 3f(x) + 2.

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

By using the formula (a-b+c) 2 = a 2 + b 2 + c 2 -2ab +2ac-2ab, we get

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

Now, substitute the values

= x 4 + 9x 2 + 4 – 6x 3 – 12x + 4x 2 – 3x 2 + 9x – 6 + 2

= x 4 – 6x 3 + 9x 2 + 4x 2 – 3x 2 – 12x + 9x – 6 + 2 + 4

Simplify the expression, we get,

f(f(x)) = x 4 – 6x 3 + 10x 2 – 3x

Q.3:  Let A = N × N and * be the binary operation on A defined by (a, b) * (c, d) = (a + c, b + d). Show that * is commutative and associative. Find the identity element for * on A, if any.

Check the binary operation * is commutative :

We know that, * is commutative if (a, b) * (c, d) = (c, d) * (a, b) ∀ a, b, c, d ∈ R

L.H.S =(a, b) * (c, d)

=(a + c, b + d)

R. H. S = (c, d) * (a, b)

Hence, L.H.S = R. H. S

Since (a, b) * (c, d) = (c, d) * (a, b) ∀ a, b, c, d ∈ R

* is commutative (a, b) * (c, d) = (a + c, b + d)

Check the binary operation * is associative :

We know that * is associative if (a, b) * ( (c, d) * (x, y) ) = ((a, b) * (c, d)) * (x, y) ∀ a, b, c, d, x, y ∈ R

L.H.S =  (a, b) * ( (c, d) * (x, y) ) =  (a+c+x, b+d+y)

R.H.S =  ((a, b) * (c, d)) * (x, y) = (a+c+x, b+d+y)

Thus, L.H.S = R.H.S

Since (a, b) * ( (c, d) * (x, y) ) = ((a, b) * (c, d)) * (x, y) ∀ a, b, c, d, x, y ∈ R

Thus, the binary operation * is associative

Checking for Identity Element:

e is identity of * if (a, b) * e = e * (a, b) = (a, b)

where e = (x, y)

Thus, (a, b) * (x, y) = (x, y) * (a, b) = (a, b) (a + x, b + y)

= (x + a , b + y) = (a, b)

Now, (a + x, b + y) = (a, b)

Now comparing these, we get:

x = a -a = 0

Next compare: b +y = b

y = b-b = 0

Since A = N x N, where x and y are the natural numbers. But in this case, x and y is not natural number. Thus, the identity element does not exist.

Therefore, operation * does not have any identity element.

Q.4:  Let f : N → Y be a function defined as f (x) = 4x + 3, where, Y = {y ∈ N: y = 4x + 3 for some x ∈ N}. Show that f is invertible. Find the inverse.

Checking for Inverse:

f(x) = 4x + 3

Let f(x) = y

x = (𝑦 − 3)/4

Let g(y) = (𝑦 − 3)/4

where g: Y → N

Now find gof:

gof = g(f(x))

= g(4x + 3) = [(4𝑥 + 3) − 3]/4

= [4𝑥 + 3 − 3]/4

Now find fog:

fog= f(g(y))

=4[(𝑦 − 3)/4] +3

= y – 3 + 3

Thus, gof = I N and fog = I y ,

Hence, f is invertible

Also, the Inverse of f = g(y) = [𝒚 – 3]/ 4

Q. 5:  Let A = R {3} and B = R – {1}. Consider the function f: A →B defined by f (x) = (x- 2)/(x -3). Is f one-one and onto? Justify your answer.

f (x) = (x- 2)/(x -3)

Checking for one-one function:

f (x 1 ) = (x 1 – 2)/ (x 1 – 3)

f (x 2 ) = (x 2 -2)/ (x 2 -3)

Putting f (x 1 ) = f (x 2 )

(x 1 -2)/(x 1 -3)= (x 2 -2 )/(x 2 -3)

(x 1 -2) (x 2 – 3) = (x 1 – 3) (x 2 -2)

x 1 (x 2 – 3)- 2 (x 2 -3) = x 1 (x 2 – 2) – 3 (x 2 – 2)

x 1 x 2 -3x 1 -2x 2 + 6 = x 1 x 2 – 2x 1 -3x 2 + 6

-3x 1 – 2x 2 =- 2x 1 -3x 2

3x 2 -2x 2 = – 2x 1 + 3x 1

Hence, if f (x 1 ) = f (x 2 ), then x 1 = x 2

Thus, the function f is one-one  function.

Checking for onto function:

f (x) = (x-2)/(x-3)

Let f(x) = y such that y B i.e. y ∈ R – {1}

So, y = (x -2)/(x- 3) y(x -3) = x- 2

xy -3y = x -2

xy – x = 3y-2

x (y -1) = 3y- 2

x = (3y -2) /(y-1)

For y = 1, x is not defined But it is given that. y ∈ R – {1}

Hence, x = (3y- 2)/(y- 1) ∈ R -{3} Hence, f is onto.

Practice Problems for Class 12 Maths Chapter 1

• Show that the function f: R → R is given by f(x) = x 3 is injective.

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Let f: {1, 3, 4} → {1, 2, 5} and g: {1, 2, 5} → {1, 3} be given by f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}. Write down gof.

For more important questions on class 12 Maths chapters, register with BYJU’S – The Learning App and download the app to solve all the problems with ease.

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CBSE Case Study Class 12

While preparing for the board exams, students are being judged on different levels of skills, such as writing, reading, etc. CBSE Case Study Class 12 questions are one of them that helps in assessing critical thinking.

The Central Board of Secondary Education will be asking the case study questions in the Class 12 board examination. Therefore, here on this page, we have provided the CBSE Case Study Class 12 for Maths, Physics, Chemistry, Biology and other subjects. Our subject matter experts have prepared Case Study questions so that Apart from the basic standard questions, students can have a variety of problems to solve. 

Just like MCQs, and other written types questions CBSE Case Study Class 12 questions will impact the overall performance of a student. Therefore for the convenience of the students we have provided the download links here, so that they can easily access the Class 12 Case Study.

Download Subject Wise CBSE Case Study Class 12 Question and Answers PDF 

There are three different streams in class 12th: Science, Arts & Commerce. And all these streams have a variety of subjects therefore, here our subject experts have crafted the Subject Wise Case Study For Class 12. Download Subject Wise CBSE Case Study Class 12 Question and Answers PDF from the below given links.

CBSE Case Study Questions Class 12 for Maths

To learn how to answer CBSE Case Study Class 12 maths questions, it would be a good choice to refer to the separate set of questions in PDF. CBSE Case Study Questions for Class 12 Maths can be quite useful and helpful in understanding how the board will prepare the case based questions for maths. 

The Maths Case studies are distributed into different chapters as per the prescribed syllabus of maths. Each and every chapter contains several number of case studies problems which enable the learners to gain in-depth knowledge in the subject.

The maths case study questions of class 12 are usually based on the formula. If any student wants to get a good score in maths case studies then they have to be well versed with a set of formulas as per the chapters and topics. Case Study Class 12 Maths can be downloaded here on this website for free of cost.

Case Study Questions Class 12 Chapter 1 Relations And Functions

Case Study Questions Class 12 Chapter  3 Matrices

Case Study Questions Class 12 Chapter  4 Determinants

Case Study Questions Class 12 Chapter  5 Continuity And Differentiability

Case Study Questions Class 12 Chapter  6 Application Of Derivatives

Case Study Questions Class 12 Chapter  8 Application Of Integrals

Case Study Questions Class 12 Chapter  9 Differential Equations

Case Study Questions Class 12 Chapter  10 Vector Algebra

Case Study Questions Class 12 Chapter  11 Three Dimensional Geometry

Case Study Questions Class 12 Chapter  12 Linear Programming

Case Study Questions Class 12 Chapter  13 Probability

CBSE Case Study Questions Class 12 for Physics

CBSE Class 12 Physics Case Study for different chapters can be interesting to solve. Class 12th physics case studies generally contain descriptive paragraphs and 4 to 5 different questions are given based on the paragraph. Students are required to read the paragraph thoroughly and understand them as well as observe the given data and information to answer the Class 12 Case Study Questions for Physics. 

In order to solve those questions students are required to have a better understanding of the basic level of physics concepts too, so make sure to use Class 12 Revision Notes of Physics. 

Case Study Questions Class 12 Chapter 1 Electric Charges and Fields

Case Study Questions Class 12 Chapter 2 Electrostatic Potential And Capacitance

Case Study Questions Class 12 Chapter 3 Current Electricity

Case Study Questions Class 12 Chapter 4 Moving Charges And Magnetism

Case Study Questions Class 12 Chapter 5 Magnetism And Matter

Case Study Questions Class 12 Chapter 6 Electromagnetic Induction

Case Study Questions Class 12 Chapter 7 Alternating Current

Case Study Questions Class 12 Chapter 8 Electromagnetic Waves

Case Study Questions Class 12 Chapter 9 Ray Optics & Optical Instruments

Case Study Questions Class 12 Chapter 10 Wave Optics

Case Study Questions Class 12 Chapter 11 Dual Nature Radiation & Matter

Case Study Questions Class 12 Chapter 12 Atoms

Case Study Questions Class 12 Chapter 13 Nuclei

Case Study Questions Class 12 Chapter 14 Semiconductor Electronics - Materials, Devices & Simple Circuits

CBSE Case Study Questions Class 12 for Chemistry

Students opted for Science stream will have to study CBSE Case Study Class 12 Chemistry. The given PDF of CBSE Class 12 Case Study Questions for Chemistry will enable the students to practice tons of questions on a regular basis. It will help them to revise the chemistry questions and its syllabus frequently. The Case study questions allow students to think more creative and find the answers in the quickest way possible. Links to download the PDF file of Class 12 Chemistry Case Study are given here.

Case Study Questions Class 12 Chapter 1 The Solid State

Case Study Questions Class 12 Chapter  2 Solutions

Case Study Questions Class 12 Chapter  3 Electrochemistry

Case Study Questions Class 12 Chapter  4 Chemical Kinetics

Case Study Questions Class 12 Chapter  5 Surface Chemistry  

Case Study Questions Class 12 Chapter  7 The p-Block Elements

Case Study Questions Class 12 Chapter  8 The d- and f-Block Elements

Case Study Questions Class 12 Chapter  9 Coordination Compounds

Case Study Questions Class 12 Chapter  10 Haloalkanes And Haloarenes

Case Study Questions Class 12 Chapter 11 Alcohols, Phenols And Ethers

Case Study Questions Class 12 Chapter  12 Aldehydes. Ketones & Carboxylic Acids

Case Study Questions Class 12 Chapter  13 Amines

Case Study Questions Class 12 Chapter 14 Biomolecules

CBSE Case Study Questions Class 12 for Biology

There are lots of chapters in class 12 Biology from which Class 12 Case Study Questions can be framed. Going through such types of questions help the students to assess their understanding level in the topics discussed in NCERT Class 12 Biology Books. By practicing the Class 12 Case Study Questions for Biology students will be very confident to ace the board exam. Also the Biology case study will be very useful for the NEET exam preparation.

Doing a regular practice of Class 12 Biology Case Study questions is a great way to score higher marks in the board exams as it will help students to develop a grip on the concepts. 

Case Study Questions Class 12 Chapter 2 Sexual Reproduction in Flowering Plants

Case Study Questions Class 12 Chapter 3 Human Reproduction

Case Study Questions Class 12 Chapter 4 Reproductive Health

Case Study Questions Class 12 Chapter 5 Principles of Inheritance & Variation

Case Study Questions Class 12 Chapter 6 Molecular Basic of Inheritance

Case Study Questions Class 12 Chapter 8 Human Health And Diseases

Case Study Questions Class 12 Chapter 10 Microbes in Human Welfare

Case Study Questions Class 12 Chapter 11 Biotechnology - Principles & Processes

Case Study Questions Class 12 Chapter 12 Biotechnology And Its Applications

Case Study Questions Class 12 Chapter 13 Organisms And Populations

Case Study Questions Class 12 Chapter 15 Biodiversity And Conversation

Case study types of questions are generally descriptive that helps to gather more information easily so, it is kinda easy to answer. However, our subject matter experts have given the solutions of all the CBSE Case Study Class 12 Biology questions.

Passage Based Class 12 Case Study Questions in PDF

CBSE Class 12 Case studies are known as Passage Based Questions. These types of problems usually contain a short/long paragraph with 4 to 5 questions. 

Students can easily solve Passage Based Class 12 Case Study Questions by reading those passages. By reading the passage students will get the exact idea of what should be the answers. Because the passage already contains some vital information or data. However a better understanding of the basic concepts that can be learned from the NCERT Class 12 Textbooks will aid in solving the Case based questions or passage based questions.

How to Download CBSE Case Study of Class 12?

Follow the below given simple steps to know how to download CBSE Case Study of Class 12:-

• Open Selfstudys website in your browser
• Go to the navigation menu that look like this
• Now, click on CBSE and then Case Study respectively
• A new page will open, where you have to click on “Class 12”
• Now, you are ready to select the subject for which you want to download the case study questions.

How to Solve Case Study Based Questions of Class 12?

There are very simple methods that a student should keep in mind while solving CBSE Case Study Class 12 for any subject:

• Read each line of paragraph carefully and pay attention to the given data/numbers. Often questions are framed according to the highlighted data of the passage.
• Since case study questions are often framed in Multiple choice questions, students should have the knowledge of elimination methods in MCQs.
• Having a good understanding of the topics that are discussed in CBSE Class 12 Books are ideal to Solve Case Study Based Questions of Class 12.

Features Of Class 12 Case Study Questions And Answers PDF

The three most noticeable features of Class 12 Case Study Questions And Answers Pdf are -

• It Is Free To Use:  Keeping in mind the need of students and to help them in doing Self Study, our team has made all the PDF of CBSE Case Study Class 12 free of cost.
• Answers Are Given:  Not only the PDFs are free provided but answers are given for all the questions of CBSE Case Study Class 12. 
• PDF Can Be Downloaded Or Viewed Online:  Many students don’t like to download the PDFs on their device due to the shortage of storage. Therefore, CBSE Class 12 Case Study questions are made available here in online format, so that students can view them online. However, through the Selfstudys app, a learner can download the PDFs too.

Benefits of Using CBSE Class 12 Case Study Questions and Answers

The CBSE Class 12 Case Study Questions and Answers can help a student in several ways:

• In Exam Preparation:  Those who go through the CBSE Case Study Class 12 will find support during the exam preparation as case based questions are also asked in the CBSE Class 12 Board examination. 
• Help in brushing up the previous learnings:  No matter how brilliant you are, you have to revise the studied topics time and again to keep them refreshed. And in this task, the CBSE Class 12 Case Study Questions and Answers can help a lot.
• To develop the critical thinking:  Able to analyse information and make an objective judgement is a skill that is known as critical thinking. A student of class 12 can use CBSE Case Study Class 12 with answers to develop critical thinking so that they can make better decisions in their life and in the board examination.

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CBSE Class 12 Biology Exam 2024: Download FREE Important Questions PDF

Cbse 12th important questions biology: the cbse class 12 biology exam 2024 is on march 19. there is not much time left for students to search for important resources and prepare for the exam. thus, check out this article to get all the important questions in one place, along with other important resources like mind maps and revision notes. .

Types of Questions Asked in CBSE Class 12 Biology Board Exam

The CBSE Class 12 Biology exam covers many topics and asks questions in different ways to see if you understand them. Here's what kinds of questions you might get:

• Multiple Choice Questions (MCQs): These are questions where you have to pick the right answer from a few choices. They check if you know basic facts.
• Assertion-Reasoning: These questions see if you can think about and understand information. You're given a statement and a reason for it. You have to decide if both are true or if the statement is true but the reason isn't a good explanation.
• Fill in the blanks: These questions test if you know important words and ideas. You get a sentence with a space, and you have to fill in the missing word or phrase. These are the types of questions which are rarely asked in CBSE 12 Biology papers. If you will find any FIB questions, those will be in the form of MCQs.
• Very short answer questions: These ask for short explanations or just one-word answers, like defining something quickly.
• Short answer questions: These need a bit more explaining. You might have to give examples or describe something in more detail, like drawing a picture or explaining how something works.
• Essay type questions: These ask you to show how well you really understand something and if you can explain it clearly. They might want you to talk about a topic, look at an experiment, think about how a biological idea can be used, or suggest ways to solve problems in biology.
• Case-based questions: These give you a story or situation about biology. You have to read it carefully, use what you know, and answer questions about it.

CBSE Class 12 Biology Important Questions

To get more relevant information, check the links below:

• CBSE Class 12 Biology Previous Year Question Papers with Solutions PDF Download
• CBSE Class 12 Syllabus 2023-24 PDF (All Subjects)
• CBSE Class 12 Deleted Syllabus (All Subjects)
• CBSE Class 12 Previous Year Papers with Solution PDF Download
• CBSE Class 12 Additional Practice Questions
• CBSE Class 12 Sample Paper 2023-24 with Solution and Additional Practice Questions
• Important MCQs for CBSE Class 12 Biology, All Chapters
• CBSE Class 12 NCERT Biology Revised Textbook PDF
• CBSE Class 12 NCERT Biology Solutions
• CBSE Class 12 Biology Chapter-wise notes
• CBSE Class 12 Date Sheet 2024
• CBSE Competency Based Questions 2023-24
• CBSE Class 12 Additional Practice Questions 2024

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