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CBSE Class 12 Maths Case Study Questions With Solutions

CBSE Class 12 Mathematics Case Study Questions are introduced this year in the updated CBSE Board Exam Pattern. According to that this year the candidates need to prepare for the case study problems along with the questions that are legacy of CBSE Board.

In Class XIIth Mathematics Case Study Questions there are problems based on Objective types of questions, Assertions and Reason, and cae based problems. These problems have the intention to examine the students' overall understanding of the subject. If you are preparing for the Maths board exam then this is the right place for you. 

Here, we have provided the complete set of CBSE class 12 maths case study questions With Solutions. These are developed by the subject matter expert. If you want to score good marks in the board papers then you should practice these Case based problems. It is absolutely free of cost. 

Download PDF CBSE Class 12 Maths Case Study From the Given links. It is in chapter wise format.

Class 12th Mathematics Important Formulas, MCQ, Case-Based, Assertion and Reason

Class 12th maths case study.

In class 12th Maths Case Study the questions are based on the real world scenarios. A passage filled with information or data is provided to the students. On the basis of that paragraph upto 5 questions are developed which should be answered by the students. To answer them they need to read the passage carefully and then pay attention to the given data to solve such questions.

These types of problems are generally known as case based questions which can be only solved by referring to the given paragraph.

Class 12 Maths Important Formulas

Knowing about the Maths Important Formulas is a crucial part of solving the Maths questions. Formulas help in solving the problems more efficiently and faster. Therefore the PDF file that we have provided here consists of all the basics and Important formulas of maths. It will help in revisions and solving the questions more accurately and easily.

Every chapter has its own topics and formulas so the PDF has been divided into chapter wise format. And if you access them from this place then you will be able to get all the formulas and other questions separately.

Class 12 Maths Assertion and Reason MCQs

Class 12th Maths Assertion and Reason MCQs PDF with Solutions are also given here. It is the most important part of Case Study Questions because scoring good marks in this section is not that much hard. If your basic concepts are clear. Because most of the time such types of questions are directly prepared by referring to the concepts.

Furthermore, the assertion and reason MCQs are solved by applying the distinct approaches. For instance, to answer these questions first candidates need to verify the Assertion (Statement) and then the reason if both are correct, then learners need to verify whether both statement and reason support each other or not.

There are a total of 5 sections in CBSE Class 12 Maths Questions Term 1. Section A contains 1 mark, Section B contains 2 marks, Section C contains 3 marks, Section D contains 4 marks and the last Section E contains 5 marks. A total of 5 questions are given in these sections.

No, In Term 1 exam there will be a total of 5 questions in each case study of class 12 maths, out of which 4 are compulsory to solve.

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  • Class 12th /

Business Studies Class 12 Case Studies

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  • Updated on  
  • Feb 12, 2021

Business Studies Class 12 Case Studies

The Central Board of Secondary Examination [CBSE] carries out periodic changes frequently in the structure of syllabus and question pattern across different commerce subjects . With more and more questions being added which aim to evaluate concept-application, analysis and interpretation, the prevalent practice of theoretical learning is being done away with. The inclusion of Business Studies class 12 case studies is a step in this direction. Further, the vast nature of syllabus in the subject makes this way testing much more practical in place of merely listing and rewriting. Here, we present a full-fledged guide on how to tackle these case studies questions in a way that can get you better scores.

This Blog Includes:

Overview & structure, what is a case study, business studies class 12 case studies: examples, how to solve case studies in business studies class 12.

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Business studies broadly encompass ‘Principles and Functions of Management’ which deal with management, its nature, elements, theories and application as well as ‘Business Finance and Marketing’ which concerns financial markets , marketing management and consumer protection. Before taking a look at the Business Studies Class 12, take a look at the pattern of the paper is as follows:

Note: Case studies are not separate sections or parts. They can be asked as all across the above-mentioned sections.

In particular, case studies are based on real-life scenarios which concern business-related situations. This involves, for instance, cases wherein a person starts a business concern, problems faced in its management, a unique set of circumstances encountered and a host of other different situations. The students are required to correlate concepts in management and solve questions based on their understanding of such concepts. Identification of a particular aspect of Business Management is also a highly used testing criterion.

Here are a few examples of case study questions you can expect to see in the Class 12 Business Studies paper based on official CBSE Question Paper 2020:

Umang Gupta is the Managing Director of Denver Ltd. The company had established a good name for itself and had been doing well. It was known for the timely completion of orders. The Production Manager, Ms Kanta was efficiently handling the processing of the order and had a team of fourteen motivated employees working under her. Everything was going on well. Unfortunately, she met with an accident. Umang knew that in the absence of Ms Kanta, the company may not be able to meet the deadlines. He also knew that not meeting the deadlines may lead to customer dissatisfaction with the risk of loss of business and goodwill. So, he had a meeting with his employees in which accurate the speedy processing of orders was planned. Everybody agreed to work as a team because the behaviour of Umang Gupta was positive towards the employees of the organisation. Hence everyone put in extra time and efforts and the targets were met on time. Not only this, Umang visited Ms Kanta and advised her to take sufficient rest. 1. Identify the leadership style of Umang Gupta and draw a diagram depicting the style. 2. State any two values highlighted by the behaviour of Umang Gupta. (CBSE, Delhi 2017)

Indian Youth Organisation (IYO) organised a visit of its members to an old age home to inculcate the habit of social work among them. The visit revealed that the living conditions of the inmates of the old age home were not hygienic. So, the IYO members decided to clean the premises. During their cleanliness drive, they realised that the old age home also required pest control. But some of the inmates of old age home were reluctant about it because they believed that the pest control might create health problems for them. IYO, therefore, decided to provide ethical, safe and odourless pest control. They showed to the inmates of old age home a pamphlet of the proposed pest control product which promised easy, inexpensive and long-lasting pest control. The inmates happily agreed and the pest control was carried out. It worked for a fortnight but to their dismay, the effect started wearing off. IYO contacted the pest control company which kept on postponing their visit. After waiting for a month, IYO filed a cased in the consumer court. The consumer court was satisfied with the genuineness of the complaint and issued necessary directions to the pest control company. 1. State the six directions that might have been issued by the court. 2. Also, identify any two values that are being communicated by IYO to society. (CBSE, Delhi 2017)

ABC Ltd is a consumer appliance company established in 1992. With its effort of quality maintenance, it has established a competent name in the market for its products. In its efforts of specialisation, it has set up different departments of finance, sales, manufacturing, technical services and maintenance services. As the spaces of operation have risen along with soaring consumer demand, ABD Ltd came to resolution to alter its current principle of management in order to meet varying requirements of the environment.  Write the specific general principle of management the company intends to modify to meet the changing requirements.

Gold Land Pvt. Ltd. is a wheat-producing company. Daily 5000 bags of wheat weighing 10 kg each are produced here. In comparison to the previous year, this ere has been less number of bags produced on a per-day basis. The number is around 4500 which is less than the target of 5000 set by the company. The company however has been able to reduce the costs involved in comparison to last year’s spending on the production and packaging of each bag. The quality of bags has also been up to the mark. Identify the concept of management ignored here.

A floor manager of a mall is a very good manager as he utilizes all the functions of management to minimize the cost of maintenance of his area. He directs all the staff members under him to follow the targets and advises them to put their efforts in the direction of the achievement of these targets. Under his guidance, the employees admit that they learn a lot and are able to meet their targets. This has led to an increase in their salaries. Identify the importance of management highlighted above.

A bank named ‘Dhan Sangraha Karta’ allows the Kapoor family to deposit their money time and again in it. It gives a definite return to this family which is in the form of interest. To get this interest the money stored in the household of Kapoor family gets entry into this bank. Nearby there is a stock exchange, Mr Rajan Kapoor, who is the head of the family, goes there and buys securities. He says that in this way more return in earned by him on his saved money though the risk is also there. 1. Identify the process in the above case performed by the bank and the stock exchange. 2. What are the roles of the bank and the stock exchange with respect to each other? 3. Name a condition for the bank to perform its role in this process. 4. Name a condition for the stock market to perform its role in this process.

To make the sports day of the school successful the Headmaster of the school divided all the activities into task groups each dealing with a specific area like holding of the event, the arrangement of medals, refreshments etc. Each group was placed under the overall supervision of a senior teacher. The physical education teacher was made responsible for holding different events, the home science teacher for refreshments and the Maths teacher for medals. Identify the function of management performed by the Headmaster in doing so.

Exploring Class 12 notes? Don’t Forget to Check Out Our Exclusive Guide on CBSE Accountancy Class 12 !

RTVB Technologies Ltd. entered the gaming market via its launch of a comprehensive gaming brand name that focused on gaming consoles, games and other accessories. This was done after careful consideration of changing consumer needs and market trends. While its products are expensive, they are of high quality as well as eco-friendly. Their efforts were to differentiate their product from the existing items available in the market and devoted significant efforts, time and money in the creation of the brand name as without this they can only focus on awareness for generic products and can never be sure of sale of products. After some time, their efforts led to a positive growth in demand of products and parallelly as the customers liking also grew, the higher price was no longer a buyer. Over time, the company’s gaming brand became regarded as a status symbol owing to its impressive quality and consumers by using them felt a sense of pride. I. What is RTVB Ltd.’s marketing management philosophy? II. In the above case, describe the benefits of branding to the marketeers.

Note: You can access more Business Studies Class 12 Case Studies here .

Since they aim to analyze the student’s understanding of business studies and management studies, the case studies in Class 12 can be intricate and complex ones to comprehend. But there are many ways to easily solve them and grasp the concepts covered under Business Studies. We have enlisted some of the best tips and tricks you can utilise to crack the case studies in Business Studies Class 12:

Read NCERT Books for Business Studies thoroughly and go through all the topics covered in each chapter. NCERT books can be your best buddy in exploring the nuances of business and management as they describe the essential topics in a simpler and uncomplicated manner. Once you have read all the chapters given in NCERT as well as the case studies under each chapter then move towards studying with reference books.

While solving case studies for Business Studies Class 12, understand the question carefully and highlight all the key aspects mentioned that seem important. This can vary from the changes brought forward by a business firm to a decision that led to something important or the beliefs and philosophies an enterprise started with. Highlight all the key pointers and then start drafting the answers.

If the question asks an analysis of a certain aspect of a decision or management, it’s better to write down all the key pointers elucidating the pros and cons of the issue you are asked to analyse . Once you have the pointers, you can write down the answer easily.

Don’t write lengthy answers and try to make them concise and insightful . Adhere to the word limit provided and draft a comprehensive answer accordingly.

Some questions might explicitly mention the topic from the syllabus for Business Studies Class 12 such as “analyse the step taken by ______ Manager as per the Functions of Management”. You can use this as a hint to answer the question as per the concepts covered under the Functions of Management in the syllabus. Look out for such hints in the question on case studies as they can help you draft an impressive and high-scoring answer.

While preparing for the class 12 examinations, one can make use of the following resources:

  • Case Studies Mentor in Business Studies Class- XII by Alka Dhawan
  • Case Studies in Business Studies by Tapan Pathak for CBSE Class 12 by Tapan Pathak
  • Business Studies with Case Studies for Class-XI by Sandeep Garg
  • Business Studies for Class 12 – Question-Answer Bank by MeriPustak
  • CBSE Class 12 Business Studies-Case Studies by Shiv Das
  • Oswaal CBSE Question Bank Class 12 Business Studies Book by Oswaal Books
  • Business Studies for Class 12 by RK Singla
  • All In One Business Studies CBSE class 12 2019-20 (Old Edition) by Arihant Experts
  • ABD’s Business Studies – Mastering Case Studies – (Class XII) (2019-2020) by Neeru Sethi

It requires a solid grasp over business and management concepts to tackle Business Studies Class 12 Case Studies. If you are planning to pursue a degree in Business after class 12, take assistance of our team of experts at Leverage Edu and we’ll help you find a suitable course and university thus gearing you up for a successful future ahead.

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myCBSEguide

  • Class 12 Economics Case...

Class 12 Economics Case Study Questions

Table of Contents

myCBSEguide App

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.

In this article, we will discuss how to download CBSE class 12 Economics Case Study Questions from the myCBSEguide App and our Student Dashboard for free. For the students appearing for class 12 board exams from the commerce/ humanities stream, Economics is a very lucrative and important subject. It is a very high-scoring subject that aids the students to increase their percentile and excel in academics.

The exam is divided into 2 parts:

  • Macro Economics
  • Indian Economics Development

12 Economics Case Study Questions

CBSE introduced case-based questions for class 12 in the year 2021-22 to enhance critical thinking in students. CBSE introduced a few changes in the question paper pattern to enhance and develop analytical and reasoning skills among students. Sanyam Bharadwaj, controller of examinations, CBSE quoted that the case-based questions would be based on real-life situations encountered by students.

The purpose was to drift from rote learning to competency and situation-based learning. He emphasized the fact that it was the need of the hour to move away from the old system and formulate new policies to enhance the critical reasoning skills of students. Introducing case study questions was a step toward achieving the goals of the National Education Policy (NEP) 2020.

What is a Case Study Question?

As part of these questions, the students would be provided with a comprehensive passage, based on which analytical questions will have to be solved by them. The students will have to read the given passage thoroughly before attempting the questions. In The current examination cycle (2021-22), case-based questions have a weightage of around 20%.

Types of Case Study Questions in Economics

CBSE plans to increase the weightage of such questions in the following years, so as to enhance the intellectual and analytical abilities of the students. Case-based questions are predominantly of 3 types namely:

  • Inferential

Local questions

Local questions can be easily solved as the answers are there in the given passage itself.

Global Questions

For Global questions, the students will have to read the passage in depth, analyze it and then solve it.

Inferential questions

Inferential questions are the ones that would require the student to have complete knowledge of the topic and could be answered by application of the concepts. The answers to such questions are tricky and not visible in the given passage, though the passage would highlight the concept on which the questions would be asked by CBSE.

HOTS Questions in Class 12 Economics

Personally, the concept of case-based questions is not new since CBSE has always included questions based on Higher Order Thinking Skills (HOTs). Though now we will have an increased percentage of such questions in the question paper.

Advantages of Case-based Questions

Class 12 Economics has two books and CBSE can ask Case study questions from any of them. Students must prepare themselves for both the books. They must practice class 12 Economics case-based questions as much as possible.

Case study questions:

  • Enhance the intellectual and analytical abilities of the students.
  • Provide a complete and deeper understanding of the subject.
  • Inculcate intellectual reasoning and scientific temperamental in students.
  • Help students retain knowledge for a longer time.
  • Would definitely help to discard the concept of memorizing insanely and cramming without a factual understanding of the content.
  • The questions would help to terminate the existing system of education in India that promotes rote learning.

Sample case study questions (Economics) class 12

Here are some case study questions for CBSE class 12 Economics. If you wish to get more case study questions and other related study material, download the myCBSEguide App now. You can also access it through our Student Dashboard.

Case Study 1

Keeping in view the continuing hardships faced by banks in terms of social distancing of staff and consequent strains on reporting requirements, the Reserve Bank of India has extended the relaxation of the minimum daily maintenance of the CRR of 80% for up to September 25, 2020. Currently, CRR is 3% and SLR is 18.50%.

“As announced in the Statement of Development and Regulatory Policies of March 27, 2020, the minimum daily maintenance of CRR was reduced from 90% of the prescribed CRR to 80% effective the fortnight beginning March 28, 2020 till June 26, 2020, that has now been extended up to September 25, 2020,” said the RBI.

Q.1 The full forms of CRR and SLR are:

  • Current Reserve Ratio and Statutory Legal Reserves
  • Cash Reserve Ratio and Statutory Legal Reserves
  • Current Required Ratio and Statutory Legal Reserves
  • Cash Reserve Ratio and Statutory Liquidity Ratio (ans)

Q.2 What will be the value of the money multiplier?

  • None of these

Q.3 SLR implies:

  • a) Certain percentage of the total banks’ deposits has to be kept in the current account with RBI
  • b) Certain percentage of net total demand and time deposits have to be kept by the bank themselves (ans)
  • c) Certain percentage of net demand deposits has to be kept by the banks with RBI
  • d) None of the above

Q.4 Decrease in CRR will lead to __.

  • a) fall in aggregate demand in the economy
  • b) rise in aggregate demand in the economy (ans)
  • c) no change in aggregate demand in the economy
  • d) fall in the general price level in the economy

Case Study 2

An important lesson that the COVID-19 pandemic has taught the policymakers in India is to provide greater impetus to sectors that make better allocation of resources and reduce income inequalities. COVID-19 has also taught a lesson that in crisis the population returns to rely on the farm sector. India has a large arable land, but the farm sector has its own structural problems. However, directly or indirectly, 50 percent of the households still depend on the farm sector. Greater support to MSMEs, higher public expenditure on health and education and making the labour force a formal employee in the economy are some of the milestones that the nation has to achieve.

One of the imminent reforms to be done in the country is labour reforms. Labour laws are outmoded in India, and some of these date back to the last century.

India’s complex labour laws have been blamed for keeping manufacturing businesses small and hindering job creation. Industry hires labour informally because of complex laws and that is responsible for low wages.

  • Which types of structural problems are faced by the agricultural sector?
  • “It is necessary to create employment in the formal sector rather than in the informal sector.’’ Defend or refute the given statement with valid argument.
  • Hired labour comes in …………………. (Informal organisation / formal organisation)
  • What do you mean by MSMEs?

Case Study 3

People spend to acquire information relating to the labour market and other markets like education and health. This information is necessary to make decisions w.r.t investment in human capital and its efficient utilization. Thus, expenditure incurred for acquiring information relating to the labour market and other markets is also a source of human capital formation.

Q1. Which of the following is the source of human capital formation in India?

  • Acquiring information
  • All of these (ans)

Q2. Education provides

  • Private benefit
  • Social benefit
  • Both 1) and 2) (ans)

Q3. __ persons contribute more to the growth of an economy.

Q4. Training given by a company to its employees is generally__________

  • Investment (ans)
  • Social wastage
  • Both 1) and 2)

Tips to Solve Case Study Questions in Economics

Let’s understand how you can solve case study questions in class 12 Economics. The two books are Macroeconomics and Indian Economic Development.

  • Read the passage thoroughly
  • Can follow a reversal pattern, especially macroeconomics questions, i.e. read questions first and then look for the answers in the passage.
  • In case the question asked is about Indian Economic Development, read the passage very carefully as most of the answers would be hidden in the passage itself.
  • Macro Economics questions will be more application-based and would test your conceptual clarity.
  • Answer briefly and precisely.

Important Chapters – Economics Case Study Questions

Following are some of the very important topics that need to be prepared very thoroughly under CBSE class 12 Economics. We expect that CBSE will certainly ask case-based questions from these chapters.

  • National income and its aggregates
  • Government budget
  • Current challenges faced by the Indian economy

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thanks for your information, dont forget to visit airlangga university website https://www.unair.ac.id/mahasiswa-unair-dan-y20-indonesia-diskusikan-isu-resesi-ekonomi/

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Important CBSE Class 12 Case Study Based Questions 2023 for History Exam Tomorrow

History important case study questions for cbse class 12: practice important case study/source based questions from essential themes of cbse class 12 history. these source-based questions are important for the upcoming cbse class 12 history board exam 2023..

Atul Rawal

CBSE Class 12 History Exam 2023: Source-Based Questions  

FROM JOHN MARSHALL, Mohenjo-Daro, and the Indus Civilization, 1931.

Sixteen skeletons of people with the ornaments that they were wearing when they died were found in the same part of Mohenjo-Daro in 1925. Much later, in 1947, R.E.M. Wheeler, then Director-General of the ASI, tried to correlate this archaeological evidence with that of the Rigveda, the earliest known text in the subcontinent.

He wrote: The Rigveda mentions pur, meaning rampart, fort, or stronghold. Indra, the Aryan war god is called Puram Dara, the fort-destroyer. Where are - or were - these citadels? It has in the past been supposed that they were mythical. The recent excavation of Harappa may be thought to have changed the picture. Here we have a highly evolved civilization of essentially non-Aryan type, now known to have employed massive fortifications. What destroyed this firmly settled civilization? Climatic, economic, or political deterioration may have weakened it, but its ultimate extinction is more likely to have been completed by deliberate and large-scale destruction. It may be no mere chance that at a late period of Mohenjodaro men, women, and children, appear to have been massacred there. On circumstantial evidence, Indra stands accused.

FROM R.E.M. WHEELER, “Harappa 1946”, Ancient India, 1947.

In the 1960s, the evidence of a massacre in Mohenjodaro was questioned by an archaeologist named George Dales. He demonstrated that the skeletons found at the site did not belong to the same period: Whereas a couple of them definitely seem to indicate a slaughter,....the bulk of the bones were found in contexts suggesting burials of the sloppiest and most irreverent nature. There is no destruction level covering the latest period of the city, no sign of extensive burning, and no bodies of warriors clad in armour and surrounded by the weapons of war. The citadel, the only fortified part of the city, yielded no evidence of a final defence.

FROM G.F. DALES, “The Mythical Massacre at Mohenjo-Daro”, Expedition, 1964.

As you can see, a careful re-examination of the data can sometimes lead to a reversal of earlier interpretations.

Q1. Name the archeologist who presented this source.

Ans- John Marshal

Q2. Which argument of the destruction of Harappa civilization, this excerpt indicates?

Ans. This exert indicates that the Harappa civilization was destroyed by foreign invasion.

Q3. Who co-relate this evidence with Rigveda? Why ?

Ans. R.E.M. Wheeler. Because, the Rigveda mentions pur, meaning rampart, fort or stronghold. Indra, the Aryan war-God is called Puram Dara, the fort-destroyer.

Q4. Who and how propounded the theory opposite to this ?

What the king’s officials did?

Here is an excerpt from the account of Megasthenes: Of the great officers of state, some ... superintend the rivers, measure the land, as is done in Egypt, and inspect the sluices by which water is let out from the main canals into their branches, so that everyone may have an equal supply of it. The same persons have charge also of the huntsmen, and are entrusted with the power of rewarding or punishing them according to their deserts. They collect taxes, and superintend the occupations connected with the land; as those of woodcutters, carpenters, blacksmiths, and miners.

Q.1- Explain the duties of the officers of the state.

  • Some superintended the rivers, measured lands, and inspected the sluices by which water was let out from the main canals into their branches so that everyone would have an equal supply of it.
  • They had also charge of huntsmen, entrusted with the power of rewarding or punishing them according to their deserts.
  • They collected the taxes, and superintended the occupations connected with the land; as those of woodcutters, carpenters, blacksmiths, and miners.

Q2. Explain the role of the sub-committees in coordinating military activities.

  • Megasthenes mentioned the committee with six subcommittees for coordinating military activity.
  • They looked after the navy, transport and provisions, foot soldiers, horses, chariots, and elephants.
  • The second committee had to arrange bullock carts to carry equipment procure food for soldiers and fodder for animals and recruit servants and artisans to look after the soldiers.

Q3. What did Ashoka do to hold his empire together?

  • Ashoka tried to hold his empire together by propagating dhamma.
  • Special officers called dhamma mahamattas were appointed to spread the message of dhamma.

Draupadi’s Marriage

Drupada the king of Panchal organized a competition where the challenges was to string a bow and hit a target: the winner would be chosen to marry his daughter Draupadi. Arjuna was victorious and was garlanded by Draupadi. The Pandavas returned with her to their mother Kunti, who, even before she saw them asked them to share whatever they had got .she realized her mistake when she saw Drupadi, but her command could not be violated. After much deliberation, Yudhisthira decided that Drupadi would be their common wife. When Drupda was told about this, he protested. However, the seer Vyasa arrived and told him that the Pandavas were in reality incarnations of Indra, whose wife had been reborn as Draupadi and they were thus destined for each other. Vyasa added that in another instance a young woman had prayed to shiva for a husband, and in her enthusiasm, had prayed five times instead of once. This woman was know reborn as Draupadi and Shiva had fulfilled her desire Convinced by these stories, Drupada consented to the marriage.

(Q1) What was the competition organized by the Panchala king Drupada for the marriage of his daughter?

Ans. Drupada organized a competition where the challenge was to string a bow and hit a target.

(Q2) What two explanations were given by Vyasa to convince king Drupada for

Draupadi being the common wife of the Pandvas?

Ans. Vyasa told that Pandvas were in reality incarnations of Indra. He also told that a women was blessed by Lord Shiva to have five husband was now reborn as Draupadi.

(Q3) What form of the marriage was Draupadi’s marriage to the pandvas? Give two views of historians about the form of marriage.

Why were Stupa’s built?

“This is an excerpt from the Mahaparinibbana Sutta, part of the Sutta Pitaka: As the Buddha lay dying, Ananda asked him: “What are we to do Lord, with remains of the Tathagata (another name for the Buddha)?” The Buddha replied : “Hinder not yourselves Ananda by honouring the remains of the Tathagata. Be zealous, be intent on your own good.” But when pressed further, the Buddha said: “At the four crossroads they should erect a thupa (Pali for stupa) to the Tathagata. And whosever shall there place garlands or perfume .... or make a salutation there, or become in its presence calm of heart, that shall long be to them for a profit and joy.”

Q1. What are the Stupas? Who advised the Ananda to build the Stupa? 1

Ans. The Stupa were sacred place. They preserved the relics of the Buddha such as his bodily remains or the objects used by him. All these things were buried in the stupas.

Q2. From which chapter has this excerpt been taken? It is a part of which book?1

Ans. This excerpt has been taken from the “ Mahaparinibbhana Sutta.” It was a part of the “Sutta Pitaka.”

Q3. Who was the Tathagata? What had he told about the importance of the stupa? 2

Ans. Tathagata was another name for the Buddha. He told Ananda that the honour to his worldly remains was not important. He laid stress on the importance of one’s good deeds. The stupas should be erected in holy places. If anybody placed garlands or perfume or saluted them, he will not only get peace of mind but also profit and joy.

Q4. Name any three places where the Stupas have been built. 3

THE SYSTEM OF VARNAS

This is Al-Biruni’s account of the system of varnas: The highest caste is the Brahmana, of whom the books of the Hindus tell us that they were created from the head of Brahman. And as the Brahman is only another name for the force called nature, and the head is the highest part of the ......body, the Brahmana is the choice part of the whole genus. Therefore, the Hindus consider them the very best of mankind. The next caste is the Kshatriya who were created, as they say, from the shoulders and hands of Brahman. Their degree is not much below that of the Brahmana. After them, follow the Vaishya, who were created from the thigh of Brahman. The Sudras were created from his feet. Between the latter two classes, there is no very great distance. Much, however, as these classes differ from each other, they live together in the same towns and villages, mixed together in the same houses and lodgings.

Q1. Explain Al-Biruni’s account of the system of varnas.

Ans. According to Al-Biruni, the higher caste is the Brahmana who was created from the head of Brahma. Hindus consider them the very best of mankind. The second caste is the Kshatriya who were created from the shoulders and hands of Brahman. They are followed by the vaishya, who are created from the thigh of Brahman. The last caste was the Shudra who was created from his feet.

Q2. Do you consider this type of division justified? Explain with reasons.

Ans No, such type of division is not justified because no one is high or low by birth. Men became high or low by their own karma.

Q3. How was the system not quite rigid in the real life? Explain.

Ans It is right that this system was not quite rigid in real life because these castes live together in the same towns and villages, mixed together in the same house and lodgings.

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

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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.

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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

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Case Study Question for Class 12 Physics Chapter 1 Electric Charges and Fields

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Case Study Question for Class 12 Physics Chapter 1 Electric Charges and Fields

There is Case Study Questions in class 12 Physics in session 2020-21. The first two questions in the board exam question paper will be based on Case Study and Assertion & Reason. Case Study Questions will have 5 MCQs out of which students will have to attempt any 4 questions. Here are the questions based on case study.

Case Study Question 1:

Electric field strength is proportional to the density of lines of force i.e., electric field strength at a point is proportional to the number of lines of force cutting a unit area element placed normal to the field at that point. As illustrated in given figure, the electric field at P is stronger than at Q.

what is case study class 12

(i) Electric lines of force about a positive point charge are (a) radially outwards (b) circular clockwise (c) radially inwards (d) parallel straight lines

(ii) Which of the following is false for electric lines of force? (a) They always start from positive charge and terminate on negative charges. (b) They are always perpendicular to the surface of a charged conductor. (c) They always form closed loops. (d) They are parallel and equally spaced in a region of uniform electric field.

(iii) Which one of the following patterns of electric line of force is not possible in field due to stationary charges?

what is case study class 12

(iv) Electric field lines are curved (a) in the field of a single positive or negative charge (b) in the field of two equal and opposite charges. (c) in the field of two like charges. (d) both (b) and (c)

(v) The figure below shows the electric field lines due to two positive charges. The magnitudes E A , E B and E C of the electric fields at point A, B and C respectively are related as

what is case study class 12

(a) E A >E B >E C (b) E B >E A >E C (c) E A =E B >E C (d) E A >E B =E C

Case Study Question 2:

Smallest charge that can exist in nature is the charge of an electron. During friction it is only the transfer of electron which makes the body charged. Hence net charge on any body is an integral multiple of charge of an electron (1.6 x 10 -19 C) i.e., q=±ne where r= 1, 2, 3, 4 …. Hence no body can have a charge represented as 1.8e, 2.7e, 2e/5, etc. Recently, it has been discovered that elementary particles such as protons or neutrons are elemental units called quarks.

(i) Which of the following properties is not satisfied by an electric charge? (a) Total charge conservation. (b) Quantization of charge. (c) Two types of charge. (d) Circular line of force.

(ii) Which one of the following charges is possible? (a) 5.8 x 10 -18 C (b) 3.2 x 10 -18 C (c) 4.5 x 10 -19 C (d) 8.6 x 10 -19 C

(iii) If a charge on a body is 1 nC, then how many electrons are present on the body? (a) 6.25 x 10 27 (b) 1.6 x 10 19 (c) 6.25 X 10 28 (d) 6.25 X 10 9

(iv) If a body gives out 10 9 electrons every second, how much time is required to get a total charge of 1 from it? (a) 190.19 years (b) 150.12 years (c) 198.19 years (d) 188.21 years

(v) A polythene piece rubbed with wool is found to have a negative charge of 3.2 x 10 -7 C. Calculate the number of electrons transferred. (a) 2 x 10 12 (b) 3 x 10 12 (c) 2 x 10 14 (d) 3 x 10 14

Case Study Question 3:

When electric dipole is placed in uniform electric field, its two charges experience equal and opposite forces, which cancel each other and hence net force on electric dipole in uniform electric field is zero. However these forces are not collinear, so they give rise to some torque on the dipole. Since net force on electric dipole in uniform electric field is zero, so no work is done in moving the electric dipole in uniform electric field. However some work is done in rotating the dipole against the torque acting on it.

what is case study class 12

(i) The dipole moment of a dipole in a uniform external field Ē is B. Then the torque τ acting on the dipole is (a) τ=p x E (b) τ = P. Ē (c) τ = 2(p + Ē) (d) τ = (P + E)

(ii) An electric dipole consists of two opposite charges, each of magnitude 1.0 μC separated by a distance of 2.0 cm. The dipole is placed in an external field of 10 5 NC -1 . The maximum torque on the dipole is (a) 0.2 x 10 -3 Nm (b) 1x 10 -3 Nm (c) 2 x 10 -3 Nm (d) 4x 10 -3 Nm

(iii) Torque on a dipole in uniform electric field is minimum when θ is equal to (a) 0° (b) 90° (c) 180° (d) Both (a) and (c)

(iv) When an electric dipole is held at an angle in a uniform electric field, the net force F and torque τ on the dipole are (a) F= 0, τ = 0 (b) F≠0, τ≠0 (c) F=0, τ ≠ 0 (d) F≠0, τ=0

(v) An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle with the direction of the field. Assuming that potential energy of the dipole to be zero when 0 = 90°, the torque and the potential energy of the dipole will respectively be (a) pEsinθ, -pEcosθ (b) pEsinθ, -2pEcosθ (c) pEsinθ, 2pEcosθ (d) pEcosθ, – pEsinθ

Case Study Question 4:

A charge is a property associated with the matter due to which it experiences and produces an electric and magnetic field. Charges are scalar in nature and they add up like real number. Also, the total charge of an isolated system is always conserved. When the objects rub against each other charges acquired by them must be equal and opposite.

what is case study class 12

(i) The cause of a charging is: (a) the actual transfer of protons. (b) the actual transfer of electrons. (c) the actual transfer of neutrons. (d) none the above

(ii) Pick the correct statement. (a) The glass rod gives protons to silk when they are rubbed against each other. (b) The glass rod gives electrons to silk when they are rubbed against each other. (c) The glass rod gains protons from silk when they are rubbed against each other. (d) The glass rod gains electrons when they are rubbed against each other.

(iii) If two electrons are each 1.5 × 10 –10 m from a proton, the magnitude of the net electric force they will exert on the proton is (a) 1.97 × 10 –8 N (b) 2.73 × 10 –8 N (c) 3.83 × 10 –8 N (d) 4.63 × 10 –8 N

(iv) A charge is a property associated with the matter due to which it produces and experiences: (a) electric effects only (b) magnetic effects only (c) both electric and magnetic effects (d) none of these.

(v) The cause of quantization of electric charges is: (a) Transfer of an integral number of neutrons. (b) Transfer of an integral number of protons. (c) Transfer of an integral number of electrons. (d) None of the above.

Case Study Question 5:

Surface Charge Density. Surface charge density is defined as the charge per unit surface area the surface (Arial) charge symmetric distribution and follow Gauss law of electro statics mathematical term of surface charge density σ=ΔQ/ΔS

what is case study class 12

Two large thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite sign (± s). Having magnitude 8.8 × 10 –12 cm –2 as shown here. The intensity of electrified at a point is E =σ/ε 0   and flux is Φ=E.ΔS, where ΔS = 1 m 2 (unit arial plate)

(i) E in the outer region (I) of the first (A) plate is (a) 1.7 × 10 –22 N/C (b) 1.1 × 10 –12 V/m (c) Zero (d) Insufficient data

(ii) E in the outer region (III) of the second plate (B) is (a) 1 N/C (b) 0.1 V/m (c) 0.5 N/C (d) zero

(iii) E between (II) the plate is (a) 1 N/C (b) 0.1 V/m (c) 0.5 N/C (d) None of these

(iv) The ratio of E from left side of plate A at distance 1 cm and 2 m respectively is (a) 1 : 2 (b) 10 : 2 (c) 1 : 1 (d) 20 : 1

(v) In order to estimate the electric field due to a thin finite plane metal plate the Gaussian surface considered is (a) Spherical (b) Linear (c) Cylindrical (d) Cybic

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What Is a Case Study?

Weighing the pros and cons of this method of research

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

what is case study class 12

Cara Lustik is a fact-checker and copywriter.

what is case study class 12

Verywell / Colleen Tighe

  • Pros and Cons

What Types of Case Studies Are Out There?

Where do you find data for a case study, how do i write a psychology case study.

A case study is an in-depth study of one person, group, or event. In a case study, nearly every aspect of the subject's life and history is analyzed to seek patterns and causes of behavior. Case studies can be used in many different fields, including psychology, medicine, education, anthropology, political science, and social work.

The point of a case study is to learn as much as possible about an individual or group so that the information can be generalized to many others. Unfortunately, case studies tend to be highly subjective, and it is sometimes difficult to generalize results to a larger population.

While case studies focus on a single individual or group, they follow a format similar to other types of psychology writing. If you are writing a case study, we got you—here are some rules of APA format to reference.  

At a Glance

A case study, or an in-depth study of a person, group, or event, can be a useful research tool when used wisely. In many cases, case studies are best used in situations where it would be difficult or impossible for you to conduct an experiment. They are helpful for looking at unique situations and allow researchers to gather a lot of˜ information about a specific individual or group of people. However, it's important to be cautious of any bias we draw from them as they are highly subjective.

What Are the Benefits and Limitations of Case Studies?

A case study can have its strengths and weaknesses. Researchers must consider these pros and cons before deciding if this type of study is appropriate for their needs.

One of the greatest advantages of a case study is that it allows researchers to investigate things that are often difficult or impossible to replicate in a lab. Some other benefits of a case study:

  • Allows researchers to capture information on the 'how,' 'what,' and 'why,' of something that's implemented
  • Gives researchers the chance to collect information on why one strategy might be chosen over another
  • Permits researchers to develop hypotheses that can be explored in experimental research

On the other hand, a case study can have some drawbacks:

  • It cannot necessarily be generalized to the larger population
  • Cannot demonstrate cause and effect
  • It may not be scientifically rigorous
  • It can lead to bias

Researchers may choose to perform a case study if they want to explore a unique or recently discovered phenomenon. Through their insights, researchers develop additional ideas and study questions that might be explored in future studies.

It's important to remember that the insights from case studies cannot be used to determine cause-and-effect relationships between variables. However, case studies may be used to develop hypotheses that can then be addressed in experimental research.

Case Study Examples

There have been a number of notable case studies in the history of psychology. Much of  Freud's work and theories were developed through individual case studies. Some great examples of case studies in psychology include:

  • Anna O : Anna O. was a pseudonym of a woman named Bertha Pappenheim, a patient of a physician named Josef Breuer. While she was never a patient of Freud's, Freud and Breuer discussed her case extensively. The woman was experiencing symptoms of a condition that was then known as hysteria and found that talking about her problems helped relieve her symptoms. Her case played an important part in the development of talk therapy as an approach to mental health treatment.
  • Phineas Gage : Phineas Gage was a railroad employee who experienced a terrible accident in which an explosion sent a metal rod through his skull, damaging important portions of his brain. Gage recovered from his accident but was left with serious changes in both personality and behavior.
  • Genie : Genie was a young girl subjected to horrific abuse and isolation. The case study of Genie allowed researchers to study whether language learning was possible, even after missing critical periods for language development. Her case also served as an example of how scientific research may interfere with treatment and lead to further abuse of vulnerable individuals.

Such cases demonstrate how case research can be used to study things that researchers could not replicate in experimental settings. In Genie's case, her horrific abuse denied her the opportunity to learn a language at critical points in her development.

This is clearly not something researchers could ethically replicate, but conducting a case study on Genie allowed researchers to study phenomena that are otherwise impossible to reproduce.

There are a few different types of case studies that psychologists and other researchers might use:

  • Collective case studies : These involve studying a group of individuals. Researchers might study a group of people in a certain setting or look at an entire community. For example, psychologists might explore how access to resources in a community has affected the collective mental well-being of those who live there.
  • Descriptive case studies : These involve starting with a descriptive theory. The subjects are then observed, and the information gathered is compared to the pre-existing theory.
  • Explanatory case studies : These   are often used to do causal investigations. In other words, researchers are interested in looking at factors that may have caused certain things to occur.
  • Exploratory case studies : These are sometimes used as a prelude to further, more in-depth research. This allows researchers to gather more information before developing their research questions and hypotheses .
  • Instrumental case studies : These occur when the individual or group allows researchers to understand more than what is initially obvious to observers.
  • Intrinsic case studies : This type of case study is when the researcher has a personal interest in the case. Jean Piaget's observations of his own children are good examples of how an intrinsic case study can contribute to the development of a psychological theory.

The three main case study types often used are intrinsic, instrumental, and collective. Intrinsic case studies are useful for learning about unique cases. Instrumental case studies help look at an individual to learn more about a broader issue. A collective case study can be useful for looking at several cases simultaneously.

The type of case study that psychology researchers use depends on the unique characteristics of the situation and the case itself.

There are a number of different sources and methods that researchers can use to gather information about an individual or group. Six major sources that have been identified by researchers are:

  • Archival records : Census records, survey records, and name lists are examples of archival records.
  • Direct observation : This strategy involves observing the subject, often in a natural setting . While an individual observer is sometimes used, it is more common to utilize a group of observers.
  • Documents : Letters, newspaper articles, administrative records, etc., are the types of documents often used as sources.
  • Interviews : Interviews are one of the most important methods for gathering information in case studies. An interview can involve structured survey questions or more open-ended questions.
  • Participant observation : When the researcher serves as a participant in events and observes the actions and outcomes, it is called participant observation.
  • Physical artifacts : Tools, objects, instruments, and other artifacts are often observed during a direct observation of the subject.

If you have been directed to write a case study for a psychology course, be sure to check with your instructor for any specific guidelines you need to follow. If you are writing your case study for a professional publication, check with the publisher for their specific guidelines for submitting a case study.

Here is a general outline of what should be included in a case study.

Section 1: A Case History

This section will have the following structure and content:

Background information : The first section of your paper will present your client's background. Include factors such as age, gender, work, health status, family mental health history, family and social relationships, drug and alcohol history, life difficulties, goals, and coping skills and weaknesses.

Description of the presenting problem : In the next section of your case study, you will describe the problem or symptoms that the client presented with.

Describe any physical, emotional, or sensory symptoms reported by the client. Thoughts, feelings, and perceptions related to the symptoms should also be noted. Any screening or diagnostic assessments that are used should also be described in detail and all scores reported.

Your diagnosis : Provide your diagnosis and give the appropriate Diagnostic and Statistical Manual code. Explain how you reached your diagnosis, how the client's symptoms fit the diagnostic criteria for the disorder(s), or any possible difficulties in reaching a diagnosis.

Section 2: Treatment Plan

This portion of the paper will address the chosen treatment for the condition. This might also include the theoretical basis for the chosen treatment or any other evidence that might exist to support why this approach was chosen.

  • Cognitive behavioral approach : Explain how a cognitive behavioral therapist would approach treatment. Offer background information on cognitive behavioral therapy and describe the treatment sessions, client response, and outcome of this type of treatment. Make note of any difficulties or successes encountered by your client during treatment.
  • Humanistic approach : Describe a humanistic approach that could be used to treat your client, such as client-centered therapy . Provide information on the type of treatment you chose, the client's reaction to the treatment, and the end result of this approach. Explain why the treatment was successful or unsuccessful.
  • Psychoanalytic approach : Describe how a psychoanalytic therapist would view the client's problem. Provide some background on the psychoanalytic approach and cite relevant references. Explain how psychoanalytic therapy would be used to treat the client, how the client would respond to therapy, and the effectiveness of this treatment approach.
  • Pharmacological approach : If treatment primarily involves the use of medications, explain which medications were used and why. Provide background on the effectiveness of these medications and how monotherapy may compare with an approach that combines medications with therapy or other treatments.

This section of a case study should also include information about the treatment goals, process, and outcomes.

When you are writing a case study, you should also include a section where you discuss the case study itself, including the strengths and limitiations of the study. You should note how the findings of your case study might support previous research. 

In your discussion section, you should also describe some of the implications of your case study. What ideas or findings might require further exploration? How might researchers go about exploring some of these questions in additional studies?

Need More Tips?

Here are a few additional pointers to keep in mind when formatting your case study:

  • Never refer to the subject of your case study as "the client." Instead, use their name or a pseudonym.
  • Read examples of case studies to gain an idea about the style and format.
  • Remember to use APA format when citing references .

Crowe S, Cresswell K, Robertson A, Huby G, Avery A, Sheikh A. The case study approach .  BMC Med Res Methodol . 2011;11:100.

Crowe S, Cresswell K, Robertson A, Huby G, Avery A, Sheikh A. The case study approach . BMC Med Res Methodol . 2011 Jun 27;11:100. doi:10.1186/1471-2288-11-100

Gagnon, Yves-Chantal.  The Case Study as Research Method: A Practical Handbook . Canada, Chicago Review Press Incorporated DBA Independent Pub Group, 2010.

Yin, Robert K. Case Study Research and Applications: Design and Methods . United States, SAGE Publications, 2017.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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what is case study class 12

CBSE 12th Standard Maths Subject Linear Programming Case Study Questions 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

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Cbse 12th standard maths linear programming case study questions 2021.

12th Standard CBSE

Final Semester - June 2015

Case Study Questions

Linear programming is a method for finding the optimal values (maximum or minimum) of quantities subject to the constraints when relationship is expressed as linear equations or inequations. Based on the above information, answer the following questions. (i) The optimal value of the objective function is attained at the points

(ii) The graph of the inequality 3x + 4y < 12 is

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(iv) The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is

(v)  The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20,40), (60,20), (60, 0). The objective function is Z = 4x + 3y. Compare the quantity in Column A and Column B

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(ii) The corner points of the feasible region shown in above graph are

(iii) If Z = x + y be the objective function and max Z = 30. The maximum value occurs at point

(iv) If Z = 6x - 9y be the objective function, then maximum value of Z is

(v) If Z = 6x + 3y be the objective function, then what is the minimum value of Z?

Corner points of the feasible region for an LPP are (0, 3), (5, 0), (6, 8), (0, 8). Let Z = 4x - 6y be the objective function. Based on the above information, answer the following questions. (i) The minimum value of Z occurs at

(ii) Maximum value of Z occurs at

(iii) Maximum of Z - Minimumof Z =

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(v) The feasible solution of LPP belongs to

what is case study class 12

(ii) Let the constraints in the given problem is represented by the following inequalities x + y ≤ 20 360x + 240y ≤ 5760 x, y ≥ 0 Then which of the following point lie in its feasible region.

(iii) If the objective function of the given problem is maximise z = 22x + 18y, then its optimal value occur at

(iv) Suppose the following shaded region APDO, represent the feasible region corresponding to mathematical formulation. of given problem. Then which of the following represent the coordinates of one of its corner points.

what is case study class 12

Let R be the feasible region (convex polygon) for a linear programming problem and let Z = ax + by be the objective function. When Z has an optimal value (maximum or minimum), where the variables x and y are subject to, constraints described by linear inequalities, this optimal value must occur at a corner point (vertex) of the feasible region. Based on the above information, answer the following questions. (i) Objective function of a L.P.P. is

(ii) Which of the following statement is correct?

(iii) In solving the LPP : "minimize f = 6x + 10y subject to constraints x ≥  6, Y ≥ 2, 2x + y  ≥ 10,x  ≥ 0,y ≥ 0" redundant constraints are

what is case study class 12

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Cbse 12th standard maths linear programming case study questions 2021 answer keys.

what is case study class 12

(iv) (d): Value of Z = px + qy at (15, 15) = 15p + 15q and that at (0, 20) = 20 q. According to given condition, we have 15p + 15q = 20q \(\Rightarrow\) 15p = 5q \(\Rightarrow\) q = 3p (v) (b): Construct the following table of values of the objective function:

(i) (b):  Let B(x, y) be the point of intersection of the given lines 2x + 5y = 100 ....(i) and  \(\frac{x}{25}+\frac{y}{40}=1 \Rightarrow 8 x+5 y=20\) ...(ii) Solving (i) and (ii), we get \(x=\frac{50}{3}, y=\frac{40}{3}\) ஃ The point of intersection \(B(x, y)=\left(\frac{50}{3}, \frac{40}{3}\right)\) (ii) (d): The corner points of the feasible region shown in the given graph are \((0,0), A(25,0), B\left(\frac{50}{3}, \frac{40}{3}\right), C(0,20)\) (iii) (a): Here Z = x + y

Thus, max Z = 30 occurs at point  \(\left(\frac{50}{3}, \frac{40}{3}\right)\) (iv) (b): 

Construct the following table of values of objective function

(i) (d): Minimum value of Z is -48 which occurs at (0,8). (ii) (a): Maximumvalue of Z is 20, which occurs at (5,0). (iii) (b): Maximum of Z - Minimum of Z = 20 - (-48) = 20 + 48 = 68 (iv) (c): The corner points of the feasible region are O(0,0), A(3, 0), B(3, 2), C(2, 3), D(0, 3). (v) (d)

(i) (c) (ii) (b): Since (8, 12) satisfy all the inequalities therefore (8, .1.2) is the point in its feasible region. (iii) (c) : At (0, 0), z = 0 At (16, 0), z = 352 At (8, 12), z = 392 At (0, 20), z = 360 It can be observed that max z occur at (8, 12). Thus, z will attain its optimal value at (8, 12). (iv) (c) : We have, x + y = 20 ... (i) and 3x + 2y = 48.. (ii) On solving (i) and (ii), we get X = 8, y = 12. Thus, the coordinates of P are (8,12) and hence (8, 12) is one of its corner points. (v) (b): The optimal solution occurs at every point on the line joining these two points.

(i) (b): Objective function is a linear function (involve variable) whose maximum or minimum value is to be found. (ii) (c): If optimal solution is obtained at two distinct points A and B (corners of the feasible region), then optimal solution is obtained at every point of segment [AB]. (iii) (b): When x ≥ 6 and y ≥ 2, then 2x + y ≥ 2 x 6 + 2, i.e., 2x + y ≥ 14 Hence, x ≥ 0, Y ≥ 0 and 2x + y ≥ 10 are automatically satisfied by every point of the region. \(\{(x, y): x \geq 6\} \cap\{(x, y): y \geq 2\}\) (iv) (b): Construct the following table of values of the objective function:

Minimum of Z = - 32 at (0, 8) (v) (a): Construct the following table of values of the objective function F

Hence, maximum of F = 0

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Case Study Chapter 2 Electrostatic Potential and Capacitance Class 12 Physics

Please refer to below Case Study Chapter 2 Electrostatic Potential and Capacitance Class 12 Physics. These Case Study Questions Class 12 Physics will be coming in your examinations. Students should go through the Chapter 2 Electrostatic Potential and Capacitance Case Study based questions in their Class 12 Physics CBSE, NCERT, KVS book as this will help them to secure more marks in upcoming exams.

Case Study Based Questions Physics Class 12 – Chapter 2 Electrostatic Potential and Capacitance

Read the para given below and answer the  questions that follow:

Potential difference (Δv) between two points A and B separated by a distance x, in a uniform electric field E is given by Δv = –Ex, where x is measured parallel to the field lines. If a charge q 0 moves from A to B, the change in potential energy (Δv) is given as Δv = q 0 Δv. A proton is released from rest in uniform electric field of magnitude 8.0 × 10 4 Vm –1 directed along the positive X–axis. The Proton undergoes a displacement of 0.50 m in the direction of E. Mass of a Proton = 1.66 × 10 –27 Kg and charge on a proton = 1.6 × 10 –19 C.

what is case study class 12

With the help of the passage given above, choose  the most appropriate alternative for each of the  following questions:

Question. As the Proton moves from A to B, then (a) The Potential energy of Proton decreases (b) The Potential energy of Proton Increases (c) The Proton loses kinetic energy. (d) Total energy of the proton Increases.

Question. The change in electric potential of the Proton between the points A and B is (a) 4.0 × 10 4 V (b) –4.0 × 10 4 V (c) 6.4 × 10 –19 V (d) –6.4 × 10 –19 V

Question. The change in electric potential energy of the proton for displacement from A to B is (a) –6.4 × 10 19 J (b) 6.4 × 10 –19 J (c) –6.4 × 10 –15 J (d) 6.4 × 10 –15 J

Question. The velocity (VB) of the proton after it has moved 0.50 m starting from rest is (a) 1.6 × 10 8 m s–1 (b) 2.77 × 10 6 ms –1 (c) 2.77 × 10 4 ms –1 (d) 1.6 × 10 6 ms –1

Question. If in place of charged plates, two similar point charges of 1μC have kept in air at 1m distance from each other. Then, potential energy is (a) 1 J (b) 1 eV (c) 9 × 10 –3 J (d) Zero

Read the para given below and answer the questions that follow:

An arrangement of two conductors separated by an insulating medium can be used to store electric charge and electric energy. Such a system is called a capacitor. The more charge a capacitor can store, the greater is its capacitance. Usually, a capacitor consists of two capacitors having equal and opposite charge + Q and –Q. Hence, there is a potential difference V between them. By the capacitance of a capacitor, we mean the ratio of the charge Q to the potential difference V. By the charge on a capacitor we mean only the charge Q on the positive plate. Total charge of the capacitor is Zero. The capacitance of a capacitor is a constant and depends on geometric factors, such as the shapes, sizes and relative positions of the two conductors, and the nature of the medium between them. The unit of capacitance Farad (F), but the more convenient units are μF and PF. A commonly used capacitor consists of two long strips or metal foils, separated by two long strips of dielectrics, rolled up into a small cylinder. Common dielectric materials are plastics (such as polyestor and polycarbonates) and aluminum oxide. Capacitors are widely used in television, computer, and other electric circuits.

Question. A parallel plate capacitor C has charge Q. The actual charge on its plates are: (a) Q, Q (b) Q/2, Q/2 (c) Q, –Q (d) Q/2, –Q/2

Question. A parallel plate capacitor is charged. If the plate are pulled apart, (a) the capacitance increases. (b) the potential difference increases. (c) the total charge increases. (d) the charge and the potential difference remains the same.

Question. If n capacitors, each of capacitance C, are connected in series, then the equivalent capacitance of the combination will be. (a) n C (b) n 2 C (c) C/n (d) C/n 2

Question. Three capacitors 2.0, 3.0 and 6.0 microfarad are connected in series to a 10 v source. The charge on the 3.0 microfarad capacitor is: (a) 5 microcoulomb (b) 10 microcoulomb (c) 12 microcoulomb (d) 15 microcoulomb

Question. What is the potential difference across 2 microfarad capacitor in the circuit shown?

what is case study class 12

(a) 12 V (b) 4 V (c) 6 V (d) 18 V

Read the para given below and answer the questions that follow:

Potential of Two Point Charges. The potential at any observation point P of a static electric field is defined as work done by the external agent (or negative of work done by electrostatic field) in slowly bringing a unit positive point charge form infinity to the observation point. The figure given below shows the potential variation along the line of charges. Two point charges Q 1 and Q 2 lie along a line at a distance from each oth er.

what is case study class 12

Question. At which the points 1, 2 and 3 is the electric field is zero? (a) 1 (b) 2 (c) 3 (d) Both (a) and (b)

Question. The signs of charges Q 1 and Q 2 respectively are (a) positive and negative (b) negative and positive (c) positive and positive (d) negative and negative

Question. Which of the charges Q 1 and Q 2 is greater in magnitude? (a) Q 2 (b) Q 1 (c) Same (d) Cannot determined

Question. Which of the following statement is not true? (a) Electrostatic force is a conservative force. (b) Potential energy of charge q at a point is the work done per unit charge in bringing a charge form any point to infinity. (c) When two like charges lie infinite distance apart, their potential energy is zero. (d) Both (a) and (c).

Question. Positive and negative point charges of equal magnitude are kept at (0,0, a/2) and (0,0, a/2) respectively. The work done by the electric field when another positive point charge is moved from (–a, 0, 0) to (0, a, 0) is (a) positive (b) negative (c) zero (d) depends on the path connecting the initial and final positions.

Equipotential Surfaces. For the various charge systems, we represent equipotential surfaces by curves and line of force by full line curves. Between any two adjacent equipotential surfaces, we assume a constant potential difference the equipotential surfaces of a single point charge are concentric spherical shells with their centres at the point charge. As the lines of force point radially outwards, so they are perpendicular to the equipotential surfaces at all points.

what is case study class 12

Question. Identify the wrong statement. (a) Equipotential surfaces due to a single point charge is spherical. (b) Equipotential surfaces can be constructed for dipoles too. (c) The electric field is normal to the equipotential surfaces through the point. (d) The work done to move a test charge on the equipotential surface is positive.

Question. Nature of equipotential surface for a point charge is (a) Ellipsoid with charge at foci. (b) Sphere with charge at the centre of the sphere. (c) Sphere with charge on the surface of the sphere. (d) Plane with charge on the surface.

Question. A spherical equipotential surface is not possible (a) inside a uniformly charged sphere. (b) for a dipole. (c) inside a spherical condenser. (d) for a point charge.

Question. The work done in carrying a charge q once round a circle of radius a with a charge Q at its centre is

what is case study class 12

Question. The work done to move a unit charge along an equipotential surface from P to Q (a) must be defined as 

what is case study class 12

(b) is zero (c) can have a non-zero value (d) Both (a) and (b) are correct

Spherical Capacitor. The electrical capacitance of a conductor is the measure of its ability to hold electric charge. An isolated spherical conductor of radius R. The charge Q is uniformly distributed over its entire surface. It can be assumed to be concentrated at the sphere. The potential at any point on the surface of the surface of the spherical conductor will be V = 1/4π∈ 0 , Q/R  

what is case study class 12

Capacitance of the spherical conductor situated in vacuum is

what is case study class 12

Clearly, the capacitance of a spherical conductor is proportional to its radius. The radius of the spherical conductor of 1F capacitance is R = 1/ 4π∈ 0 . C and this radius is about 1500 times the radius of the earth (∼ 6 × 10 3 km).

Question. If an isolated sphere has a capacitance 50pF. Then radius is (a) 90 cm (b) 45 cm (c) 45 m (d) 90 m

Question. How much charge should be placed on a capacitance of 25 pF to raise its potential 10 5  V? (a) 1 μC (b) 1.5 μC (c) 2 μC (d) 2.5 μC

Question. Dimensions of capacitance is (a) [M –1 L –2 T 4 A 2 ] (b) [M –1 L –1 T 3 A 1 ] (c) [M L –2 T 4 A 2 ] (d) [M 0 L –2 T 4 A 1 ]

Question. Metallic sphere of radius R is charged to potential V. Then charge q is proportional to (a) V (b) R (c) Both V and R (d) none of these

Question. If 64 identical spheres of charge q and capacitance C each are combined to form sphere the charge and capacitance of the large sphere is (a) 64q, C (b) 16q, 4C (c) 64q, 4C (d) 16q, 64C

Case Study Chapter 2 Electrostatic Potential and Capacitance Class 12 Physics

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