case study questions class 12 maths chapter 1

• Relations and Functions Class 12 Case Study Questions Maths Chapter 1

Last Updated on July 29, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 12 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 12 maths. In this article, you will find case study questions for CBSE Class 12 Maths Chapter 1 Relations and Functions. It is a part of Case Study Questions for CBSE Class 12 Maths Series.

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Case Study Questions on Relations and Functions

Passage 1: Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1, 2, 3, 4, 5, 6}. Let A be the set of players while B be set of all possible outcomes. A = {S, D}, B = {1, 2, 3, 4, 5, 6}

Based on the above information answer the following:

(i) Let R : B –> B be defined by R = {(x, y) : y is divisible by x} is (a) Reflexive and transitive but not symmetric (b) Reflexive and symmetric but not transitive (c) Not reflexive but symmetric and transitive (d) Equivalence

Difficulty Level: Medium

Ans. Option (a) is correct.

(ii) Raji wants to know the number of functions from A to B. How many number of functions are possible? (a) 6 2 (b) 2 6 (c) 6! (d) 2 12

(iii) Let R be a relation on B defined by R = {(1, 2), (2, 2), (1, 3), (3, 4), (3, 1), (4, 3), (5, 5)}. Then R is (a) Symmetric (b) Reflexive (c) Transitive (d) None of these three

Ans. Option (d) is correct.

(iv) Raji wants to know the number of relations possible from A to B. How many numbers of relations are possible? (a) 6 2 (b) 2 6 (c) 6! (d) 2 12

(v) Let R : B –> B be defined by R = {(1, 1), (1, 2), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}, then R is (a) Symmetric (b) Reflexive and Transitive (c) Transitive and symmetric (d) Equivalence

Ans. Option (b) is correct.

Matrices Class 12 Case Study Questions Maths Chapter 3

Inverse trigonometric functions class 12 case study questions maths chapter 2, topics from which case study questions may be asked.

• Definition of Relation
• Domain & Range of a Relation
• Types of Relations from One Set to Another Set
• Types of Intervals
• Types of Functions
• Algorithm to Check for Surjectivity of a Function

A relation R, from a non-empty set A to another non-empty set B is mathematically as a subset of A × B. Equivalently, any subset of A × B is a relation from A to B.

A relation from A to B is also called a relation from A into B.

Case study questions from the above given topic may be asked.

Frequently Asked Questions (FAQs) on Relations and Functions Case Study

Q1: what is a case study question in mathematics.

A1: A case study question in mathematics is a problem or set of problems based on a real-life scenario or application. It requires students to apply their understanding of mathematical concepts to analyze, interpret, and solve the given situation.

Q2: How should students tackle case study questions in exams?

A2: To tackle case study questions effectively, students should: Read the problem carefully: Understand the scenario and identify the mathematical concepts involved. Break down the problem: Divide the case study into smaller parts to manage the information better. Apply relevant formulas and theorems: Use the appropriate mathematical tools to solve each part of the problem.

Q3: Why are case study questions included in the Class 12 Maths curriculum?

A3: Case study questions are included to bridge the gap between theoretical knowledge and practical application. They help students see the relevance of what they are learning and prepare them for real-life situations where they may need to use these mathematical concepts.

Q4: What is a relation in mathematics?

A4: In mathematics, a relation is a set of ordered pairs, typically defined between two sets. If set A has elements a1, a2, and a3, and set B has elements b1, b2, and b3, a relation R from set A to set B is a subset of the Cartesian product A × B, consisting of ordered pairs (a, b) where ‘a’ belongs to A and ‘b’ belongs to B.

Q5: What is a function? How is it different from a relation?

A5: A function is a special type of relation where every element in the domain (set A) is associated with exactly one element in the codomain (set B). In other words, for every ‘a’ in A, there is only one ‘b’ in B such that (a, b) is in the relation. While all functions are relations, not all relations are functions.

Q6: What are the types of functions?

A6: Functions can be categorized into several types, including: One-to-one function (Injective): Each element of the domain is mapped to a unique element of the codomain. Onto function (Surjective): Every element of the codomain is mapped by at least one element of the domain. One-to-one and onto function (Bijective): A function that is both injective and surjective. Constant function: Every element of the domain is mapped to the same single element of the codomain.

Q7: What is the domain and range of a function?

A7: The domain of a function is the set of all possible input values (x-values) for which the function is defined. The range is the set of all possible output values (y-values) produced by the function.

Q8: What is the vertical line test?

A8: The vertical line test is a graphical method to determine if a relation is a function. If a vertical line intersects the graph of a relation at more than one point, then the relation is not a function. This is because a function can only have one output value for each input value.

Q9: How do you determine if a function is one-to-one?

A9: To determine if a function is one-to-one, check that each element in the domain maps to a unique element in the codomain. Mathematically, a function f(x) is one-to-one if f(a) = f(b) implies a = b for all elements a and b in the domain.

Q10: What is the composition of functions?

A10: The composition of functions is the process of applying one function to the results of another. If you have two functions, f and g, the composition (f ∘ g)(x) is defined as f(g(x)). This means you first apply g to x, then apply f to the result of g(x).

Q11: What are inverse functions?

A11: An inverse function reverses the operation of the original function. If f is a function, its inverse f^(-1) satisfies the condition that f(f^(-1)(x)) = x and f^(-1)(f(x)) = x for all x in the domain of f^(-1) and f, respectively. Inverse functions exist only for bijective functions.

Q12: Are there any online resources or tools available for practicing relations and functions case study questions?

A12: We provide case study questions for CBSE Class 12 Maths on our  website . Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit  Physics Gurukul  website. they are having a large collection of case study questions for all classes.

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Class 12 Maths Case Study Questions

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Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

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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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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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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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

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Case Study Questions for Class 12 Maths Chapter 1 Relations and Functions

• Last modified on: 1 year ago
• Reading Time: 4 Minutes

Question 1:

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1, 2, 3, 4, 5, 6}. Let A be the set of players while B be set of all possible outcomes. A = {S, D}, B = {1, 2, 3, 4, 5, 6}

Based on the above information answer the following:

(i) Let R : B –> B be defined by R = {(x, y) : y is divisible by x} is (a) Reflexive and transitive but not symmetric (b) Reflexive and symmetric but not transitive (c) Not reflexive but symmetric and transitive (d) Equivalence

(ii) Raji wants to know the number of functions from A to B. How many number of functions are possible? (a) 6 2 (b) 2 6 (c) 6! (d) 2 12

(iii) Let R be a relation on B defined by R = {(1, 2), (2, 2), (1, 3), (3, 4), (3, 1), (4, 3), (5, 5)}. Then R is (a) Symmetric (b) Reflexive (c) Transitive (d) None of these three

(iv) Raji wants to know the number of relations possible from A to B. How many numbers of relations are possible? (a) 6 2 (b) 2 6 (c) 6! (d) 2 12

(v) Let R : B –> B be defined by R = {(1, 1), (1, 2), (2, 2)(3, 3), (4, 4), (5, 5), (6, 6)}, then R is (a) Symmetric (b) Reflexive and Transitive (c) Transitive and symmetric (d) Equivalence

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CBSE Case Study Questions for Class 12 Maths Relations and Functions Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 12 Maths Relations and Functions  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 Relations and Functions PDF

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

• Chapter 2 Inverse Trigonometric Functions Case Study Questions
• Chapter 3 Matrices 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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• CBSE Class 10

CBSE Class 10 Maths Chapter 13 Statistics Competency-Focused Practice Questions With Answer Key 2024-25: Download For Free

Cbse class 10 maths chapter 13 practice questions 2025: this article provides the cbse class 10 competency-focused practice questions of maths chapter 13 statistics with answer key. download for free for 2025 board examination..

CBSE 2024-25 Competency Based Questions With Answers: As a means to reform  curriculum methodologies, the Central Board of Secondary Education (CBSE) has designed and released the competency-focused practice questions for the students of class 10-12. The questions have been released on, cbseacademic.nic.in. 

In this article we have provided the CBSE Class 10 Mathematics Chapter 13 Statistics competency-focused questions along with the answer key. For the convenience of students, we have given the questions for download in pdf format. Students can download the questions from volume 4 as well as volume 2 for extra practice. As a part of the assessments, students get to practice a mix of multiple choice questions and free response questions. 

What are Competency-Based Practice Questions?

Competency-focused practice questions are questions designed specifically to test conceptual understanding and application of concepts. They aim to encourage students to practice learning by doing. The idea behind designing the competency-based questions is to develop higher order skills such as analysis, critical thinking and problem solving in students. 

CBSE Class 10 Maths Chapter 13 Competency Based-Questions 

Multiple choice questions.

Q:1 The chart below shows the marks obtained by students of sections A and B of grade 10. The results are recorded in groups as follows:

Based on the above information, two statements are given below - one labelled Assertion (A) and the other labelled Reason (R). Read the statements carefully and choose the option that correctly describes statements (A) and (R).

Assertion (A): The median mark of section A is equal to the median mark of section B. 

Reason (R): The cumulative frequency of the median class and the preceding class are the same for both the sections.

1. Both (A) and (R) are true and (R) is the correct explanation for (A). 

2. Both (A) and (R) are true but (R) is not the correct explanation for (A). 

3. (A) is true but (R) is false.

 Study the given information and answer the questions that follow.

The game of cricket is a bat and ball game played between two teams, each consisting of 11 players. The length of a match is determined by the total number of balls bowled by both the teams. 

Shown below is a histogram for the number of matches that were finished in or less than 200 balls. 

(Note: Round all calculations to two decimal places.)

Q:2 Shown below is an ogive for the given data.

Which of the following can be determined from the above graph? 

i) Least number of balls bowled in a match.

ii) The number of matches with 80 balls bowled. 

iii) The total number of matches played with less than 200 balls bowled.

1. only ii) 

2. only iii) 

3. only i) and ii) 

4. only ii) and iii)

Q:3 Ankit used the given data and found the mean number of balls bowled in each match as 105.33 balls. 

Which of the following is definitely true?

1. Mean number of balls bowled cannot be a decimal. 

2. Mean number of balls bowled can be a decimal and 105.33 balls is the actual mean. 

3. 105.33 balls is an approximate mean as the exact number of matches with the number of balls bowled is not known.

Free Response Questions

Q:5 Shown below is the frequency polygon. It represents the performance of all participating countries in a question in an international assessment, TIMSS 2011.

If Japan's performance was 43%, did it perform better or worse than the average performance? Show your work.

Q:6 A football match is 90 minutes long and is divided into 15 minute intervals to collect data, like 0-15, 15-30, so on. 

All goals scored in a football match between Brazil and Serbia at FIFA 2022 were in the 60-75 minute interval. 

What is the mode of this data? Show your work. 

(Note: Any extra time to be ignored.)

Q:7 The median of the following distribution is 35. Some of the entries in the table are missing.

Find the value A. Show your steps.

Q:8 The graph below shows the number of goals scored upto a given minute-mark in all football matches in FIFA World Cup 2022.

Find the approximate minute in the 90-minute game before which about 50% of the goals in FIFA World Cup 2022 were scored. Show your work. 

Tips to Prepare for CBSE Class 10 Mathematics Examination

1. Mathematics is a subject that demands regular practice. It is important that students practice as much as they can. Practice the questions given at the end of each chapter. Note the points where you get stuck during solving questions. 

2. Students should prepare an effective study plan and give time to all topics on the basis of their strengths and weaknesses. Don’t let your bias towards your favourite chapter affect the time-table. The schedule should also have time for revision. 

3. Students should solve the problems from CBSE Class 10 subject textbook to clear the concepts and strengthen understanding. While solving problems, students should make it a habit to show rough work clearly which will help them in the examination as well. 

CBSE Video Courses for Class 10 Students 

Class 10 students can study effectively for the exams with the help of video courses prepared by the subject matter experts. These video courses will explain the concepts in a simple and interactive manner which will help learners to understand clearly. 

CBSE Class 10 Video Courses 

Also, check

CBSE Class 10 Syllabus 2024-25: Download Latest and Revised FREE PDFs

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Probability Notes: Definition, Types, Formulas, Applications and More

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Sequence and Series: Formula, Definition & Concepts

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CBSE 12th Standard Maths Subject Relations and Functions Case Study Questions With Solution 2021

By QB365 on 21 May, 2021

QB365 Provides the updated CASE Study Questions for Class 12 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

QB365 - Question Bank Software

12th Standard CBSE

Final Semester - June 2015

Case Study Questions

A relation R on a set A is said to be an equivalence relation on A iff it is (a) Reflexive i.e..,  \((a, a) \in R \ \forall \ a \in A\) (b) Symmetric i.e.,  \((a, b) \in R \Rightarrow(b, a) \in R \ \forall \ a, b \in A\)   (c) Transitive i.e.,  \((a, b) \in R\)  and  \((b, c) \in R \Rightarrow(a, c) \in R\ \forall\ a, b, c \in A\)   Based on the above information, answer the following questions. (i) If the relation R = {(1, 1), (1, 2), (1, 3), (2,2), (2, 3), (3,1), (3, 2), (3, 3)} defined on the set A = {1, 2, 3}, then R is

(ii) If the relation R = {(1, 2), (2,1), (1, 3), (3, I)} defined on the setA = {1, 2, 3}, then R is

 (iii) If the relation R on the set N of all natural numbers defined as R = {(x, y) : y = x + 5 and x < 4}, then R is

(iv) If the relation R on the set A = {1, 2, 3, , 13, 14}defined as R = {(x, y) : 3x - y = 0}, then R is

Consider the mapping  \(f: A \rightarrow B\)  is defined by  \(f(x)=\frac{x-1}{x-2}\)  such that f is a bijection.  Based on the above information, answer the following questions. (i) Domain of f is

(ii) Range of f is

(iii) If g:  \(R-\{2\} \rightarrow R-\{1\}\)  is defined by g(x) = 2f(x) - I, then g(x) in terms of x is

(iv) The function g defined above, is

(v) A function J(x) is said to be one-one iff

*****************************************

Cbse 12th standard maths subject relations and functions case study questions with solution 2021 answer keys.

(i) (a) :  Clearly (1, 1), (2, 2), (3, 3),  \(\in\)  R. So, R is reflexive on A. Since,  \((1,2) \in R \text { but }(2,1) \notin R\)  So, R is not symmetric on A. Since,  \((2,3), \in R\)  and  \((3,1) \in R\)  but  \((2,1) \notin R\)  .So, R is not transitive on A. (ii) (b) : Since, (1,1), (2, 2) and (3, 3) are not in R. So, R is not reflexive on A. Now,  \((1,2) \in R \Rightarrow(2,1) \in R\)   and  \((1,3) \in R \Rightarrow(3,1) \in R\)   So, R is symmetric Clearly, \((1,2) \in R \text { and }(2,1) \in R \text { but }(1,1) \notin R\)   So, R is not transitive on A. (iii) (c) :  We have,  \(R=\{(x, y): y=x+5 \text { and } x<4\}\)  ,where  \(x, y \in N\)  . \(\therefore R=\{(1,6),(2,7),(3,8)\}\)   Clearly, (1, 1), (2, 2) etc. are not in R. So, R is not reflexive. Since,  \((1,6) \in R\)  but  \((6,1) \notin R\)  So, R is not symmetric.  Since,  \((1,6) \in R\)  R and there is no order pair in R which has 6 as the first element. Same is the case for (2, 7) and (3, 8). So, R is transitive. (iv) (d) : We have,R = {(x, y) : 3x - y = 0}, where  \(x, y \in A=\{1,2, \ldots \ldots, 14\}\)  . \(\therefore\)  R = {(I, 3), (2, 6), (3, 9), (4, 12)} Clearly, \((1,1) \notin R\)  So, R is not reflexive on A. Since,  \((1,3) \in R\)  but  \((3,1) \notin R\)  .So, R is not symmetric on A. Since,  \((1,3) \in R\)  and  \((3,9) \in R\)   but   \((1,9) \notin R\)  So, R is not transitive on A. (v) (d) : Clearly, (1, 1), (2, 2), (3, 3) ∈  R. So, R is reflexive on A. We find that the ordered pairs obtained by interchanging the components of ordered pairs in R are also in R. So, R is symmetric on A. For  \(1,2,3 \in A\)   such that (1, 2) and (2, 3) are in Rimplies that (1, 3) is also, in R. So, R is transitive on A. Thus, R is an equivalence relation.

(i) (a) : For f(x) to be defined  \(x-2 \neq 0\)  i.e., \(x \neq 2\)   \(\therefore\)  Domain of f = R - {2} (ii) (b) : Let y =J(x), then  \(y=\frac{x-1}{x-2}\)   \(\Rightarrow x y-2 y=x-1 \Rightarrow x y-x=2 y-1 \Rightarrow x=\frac{2 y-1}{y-1}\)   Since,   \(x \in R-\{2\}\) ,therefore  \(y \neq 1\) Hence, range of f = R-{1}  (iii) (d):  We have,g(x) = 2f(x) - 1 \(=2\left(\frac{x-1}{x-2}\right)-1=\frac{2 x-2-x+2}{x-2}=\frac{x}{x-2}\) (iv) (a) : We have,  \(g(x)=\frac{x}{x-2}\)  , Let   \(g\left(x_{1}\right)=g\left(x_{2}\right) \Rightarrow \frac{x_{1}}{x_{1}-2}=\frac{x_{2}}{x_{2}-2}\)     \(\Rightarrow x_{1} x_{2}-2 x_{1}=x_{1} x_{2}-2 x_{2} \Rightarrow 2 x_{1}=2 x_{2} \Rightarrow x_{1}=x_{2}\)   Thus,  \(g\left(x_{1}\right)=g\left(x_{2}\right) \Rightarrow x_{1}=x_{2}\)   Hence, g(x) is one-one. (v) (c) 

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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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