CBSE Sample Papers for Class 12 Geography Term 2 Set 2 with Solutions

Students can access the CBSE Sample Papers for Class 12 Geography with Solutions and marking scheme Term 2 Set 2 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 12 Geography Term 2 Set 2 with Solutions

Time Allowed: 2 Hours
Maximum Marks: 35
Roll No. ___________

General Instructions:

  • Question paper is divided into 5 sections A, B, C, D & E
  • In section A, question number 1 to 3 are Very Short Answer type questions. Attempt any 3 questions.
  • In section B, question number 4 is Source based question.
  • In section C, question number 5 & 6 are Short Answer type questions.
  • In section D, question number 7 to 9 are Long Answer type questions.
  • In section E, question number 10 is a Map based question.

Section – A
Very Short Answer type Questions 

Question 1.
Differentiate between tertiary activities and quaternary activities. (2)
Or
Differentiate between trade and trading centres.
Answer:
Tertiary activities are related to the service sector. Tertiary activities include both production and exchange. The production involves the provision of services that are ‘consumed’. On the other hand, the service sector which is knowledge oriented comes under quaternary activities. These activities centre around research, development and may be seen as an advance form of services involving specialised knowledge and technical skills.
Or
Trade is essentially buying and selling of items produced elsewhere. All the services in retail and wholesale trading or commerce are specifically intended for profit. On the other hand, the towns and cities where all these works take place are known as trading centres.

Question 2.
Among the non-metallic minerals produced in India, mica is one of the most important minerals. Name the states where mica is produced. (2)
Answer:
Mica is one of the most important non-metallic minerals produced in India. In India, it is produced in Jharkhand, Andhra Pradesh, Telangana and Rajasthan followed by Tamil Nadu, West Bengal and Madhya Pradesh.

CBSE Sample Papers for Class 12 Geography Term 2 Set 2 with Solutions

Question 3.
Outline the distribution of sources of manganese in two major states in India. (3)
Answer:
The distribution of sources of manganese in two major states in India are

  • Major mines in Odisha are located in the central part of the iron ore belt of India, particularly in Bonai, Kendujhar, Sundergarh, Gangpur, Koraput, Kalahandi and Bolangir.
  • Karnataka is another major producer and here the mines are located in Dharwar, Ballari, Belagavi, North Canara, Chikkmagaluru, Shivamogga, Chitradurg and Tumakuru.

SECTION – B
Source Based Question

Question 4.
Read the source given below and answer the following questions by choosing the correct option.
Land Transport
Most of the movement of goods and services takes place over land. In early days, humans themselves were carriers. Have you ever seen a bride being carried on a palanquin (palki/doli) by four persons (Kahars in North India). Later animals were used as beasts of burden. Have you seen mules, horses and camels, carrying loads of cargo in rural areas? With the invention of the wheel, the use of carts and wagons became important. The revolution in transport came about only after the invention of the steam engine in the eighteenth century.

Perhaps the first public railway line was opened in 1825 between Stockton and thern England and then onwards, railways became the most popular and fastest form of transport in the nineteenth century. It opened up continental interiors for commercial grain farming mining and manufacturing in U.S.A. The invention of the internal combustion engine revolutionised road transport in terms of road quality and vehicles (motor cars and trucks) plying over them.

Among the newer developments in land transportation are pipelines, ropeways and cableways. Liquids like mineral oil, water, sludge and sewers are transported by pipelines. The great freight carriers are the railways, ocean vessels, barges, boats and motor trucks and pipelines. In general, the old and elementary forms like the human porter, pack animal, cart or wagon are the most expensive means of transportation and large freighters are the cheapest. They are important in supplementing modern channels and carriers which penetrate the interiors in large countries. In the densely populated districts of India and China, overland transport still takes place by human porters or carts drawn or pushed by humans.

i. Which were the earliest mode of land transportation? (1)
Answer:
Humans and animals were the earliest mode of land transportation.

ii. Which event can be considered as a revolution in transport? (1)
Answer:
Invention of steam engine can be considered as a revolution in transport.

iii. Which place in Europe witnessed the first public railway line? (1)
Answer:
England witnessed the first public railway line in Europe.

CBSE Sample Papers for Class 12 Geography Term 2 Set 2 with Solutions

Section – C
Short Answer Questions

Question 5.
How does access to labour supply and transportation and communication facilities influence industrial locations? (3)
Or
Explain the difference between household industries and small scale manufacturing.
Answer:
Access to labour supply and transportation and communication facilities influence industrial location in the following ways

  • Labour supply is an important factor in the location of industries. Some types of manufacturing require skilled labour.
  • Speedy and efficient transport facilities to carry raw materials to the factory and to move finished goods to the market are essential for the development of industries.
  • The cost of transport plays an important role in the location of industrial units. For example, Western Europe and Eastern North America have a highly-developed transport system which has always induced the concentration of industries in these areas.
  • Modern industry is inseparably tied to transportation systems. Improvements in transportation led to integrated economic development and regional specialisation of manufacturing.

Or
Household industries is the smallest manufacturing unit. The artisans use local raw materials and simple tools to produce everyday goods in their homes with the help of their family members or part time labour. Finished products may be for consumption in the same household or, for sale in local (village) markets, or, for barter.

Capital and transportation do not wield much influence as this type of manufacturing has low commercial significance and most of the tools are devised locally. Manufacturing of jewellery, artefacts and crafts made of wood or bamboo, fabrics, mats tools etc are examples of household industries.

Small scale manufacturing is distinguished from household industries by its production techniques and place of manufacture. This type of manufacturing uses local raw material, simple power-driven machines and semi-skilled labour. It provides employment and raises local purchasing power. Examples of small scale industry can include the manufacturing of spices, biscuits, soaps and oils etc.

CBSE Sample Papers for Class 12 Geography Term 2 Set 2 with Solutions

Question 6.
What is the role of the National Highways Authority of India? Highlight some major projects undertaken by the National Highways Authority of India. (3)
Answer:
The National Highways Authority of India (NHAI) was operationalised in 1995. It is an autonomous body under the Ministry of Surface Transport. It is entrusted with the responsibility of development, maintenance and operation of National Highways. This is also the apex body to improve the quality of the roads designated as National Highways.

NHAI has taken up some major projects in the country under different phases which are

i. Golden Quadrilateral It comprises construction of 5,846-km long 4/6 lane, high density traffic corridor, to connect India’s four big metro cities of Delhi-Mumbai- Chennai-Kolkata. With the construction of Golden Quadrilateral, the time, distance and cost of movement among the mega cities of India will be considerably minimised.

ii. North-South and East-West Corridors North-South Corridor aims at connecting Srinagar in Jammu and Kashmir with Kanniyakumari in Tamil Nadu (including Kochchi-Salem Spur) with 4,076-km long road. The East-West Corridor has been planned to connect Silchar in Assam with the port town of Porbandar in Gujarat with 3,640-km of road length.

Section – D
Long Answer Questions 

Question 7.
What are secondary economic activities and the role of manufacturing in secondary activity? (5)
Or
The locations of industries are dependent on several factors including access to raw material, transport and energy. Discuss these dependent factors for industry locations.
Answer:
Secondary economic activities are the activities which add value to natural resources by transforming raw materials into valuable products. It refers to those activities which produce a finished and usable product. For instance, cotton in the boll has limited use but after it is transformed into yarn, becomes more valuable and can be used for making clothes. Iron ore, cannot be used; directly from the mines, but after being converted into steel it gets its value and can be used for making many valuable machines, tools, etc. The same is true of most of the materials from the farm, forest, mine and the sea.

Secondary activities, therefore, are concerned with manufacturing processing and construction (infrastructure) industries. Manufacturing which is an essential first step in a secondary activity can involve a full array of production from handicrafts to moulding iron and steel and stamping out plastic toys to assembling delicate computer components or space vehicles. The role of manufacturing in secondary activities may entail the following common characteristics (i) The application of power. (ii) The mass production of identical products. (iii) Specialised labour in factory settings for the production of standardised commodities.
Or
The location of industries are dependent on the following factors

→ Access to Market The existence of a market for manufactured goods is the most important factor in the location of industries.

→ Access to Raw Material Raw material used by industries should be cheap and easy to transport. Industries based on cheap, bulky and weight-losing material (ores) are located close to the sources of raw material such as steel, sugar, and cement industries.

→ Access to Labour Supply Labour supply is an important factor in the location of industries. Increasing mechanisation, automation and flexibility of industrial processes have reduced the dependence of industry upon the labours.

→ Access to Sources of Energy Industries which use more power are located close to the source of the energy supply such as the aluminium industry.

→ Access to Transportation and Communication Facilities Speedy and efficient transport facilities to carry raw materials to the factory and to move finished goods to the market are essential for the development of industries. Access to Agglomeration Economies Links between Industries Many industries benefit from nearness to a leader industry and other industries. These benefits are termed as agglomeration economies. Savings are derived from the linkages which exist between different industries.

Question 8.
What is a mineral? State its characteristics and types with relevant example. (5)
Answer:
A mineral is a natural substance of organic or inorganic origin with definite chemical and physical properties, e.g. gold, silver, iron ore, bauxite, etc. Minerals have certain characteristics such as

→ They are unevenly distributed over space. In India, bulk of the valuable minerals are associated with metamorphic and igneous rocks of the peninsular India. The vast alluvial plain tract of North India is devoid of minerals of economic use.

→ There is an inverse relationship in quality and quantity of minerals i.e. good quality minerals are less in quantity as compared to low quality minerals.

→ All minerals are exhaustible over time. These take long to develop geologically and they cannot be replenished immediately at the time of need. Thus, they have to be conserved and not misused as they do not have the second crop. Minerals may be grouped under two main categories of metallic and non-metallics based on chemical and physical properties

(i) Metallic minerals are the sources of metals. Iron ore, copper, gold produce metal and are included in this category. Metallic minerals are further divided into ferrous and non-ferrous metallic minerals. Ferrous refers to iron. All those minerals which have iron content are ferrous such as iron ore itself and those which do not have iron content are non-ferrous such as copper, bauxite, etc.

(ii) Non-metallic minerals are either organic in origin such as fossil fuels also known as mineral fuels which are derived from the buried animal and plant life such as coal and petroleum. Other type of non-metallic minerals are inorganic in origin such as mica, limestone and graphite, etc..

CBSE Sample Papers for Class 12 Geography Term 2 Set 2 with Solutions

Question 9.
Non-conventional sources of energy are considered to be an environmental friendly and sustainable alternative to conventional fossil fuels. Discuss non-conventional sources of energy available in India along with their current status and examples. (5)
Answer:
Non-conventional sources of energy such as solar and wind energy, are renewable sources. They are equitably distributed and environment friendly as there are no carbon or pollution emissions upon their use. They are not exhaustible as they do not have fixed deposits or reserves.

These sources can provide sustained, cheap and environment friendly energy and hence they are considered as a sustainable alternative to fossil fuels. Some of the commonly used nonconventional sources of energy in India are

→ Solar Energy Sun rays tapped in photovoltaic cells can be converted into energy, known as solar energy. The two effective processes considered to be very effective to tap solar energy are photovoltaics and solar thermal technology, The Western part of India has greater potential for the development of solar energy in Gujarat and Rajasthan.

→ Wind Energy This form of energy is absolutely pollution free, inexhaustible source of energy. The kinetic energy of wind, through turbines is converted into electrical energy. The permanent wind systems such the trade winds, westerlies and seasonal wind like monsoon have been used as source of energy. Besides these, local winds, land and sea breezes can also be used to produce electricity. In Rajasthan, Gujarat, Maharashtra and Karnataka, favourable conditions for wind energy exist.

→ Tidal and Wave Energy Ocean currents are the store house of infinite energy. Large tidal waves are known to occur along the West Coast of India. Hence, India has great potential for the development of tidal energy along the coasts but so far these have not yet been utilised.

→ Geothermal Energy When the magma from the interior of earth, comes out on the surface, tremendous heat is released. This heat energy can successfully be tapped and converted to electrical energy. Apart from this, the hot water that gushes out through the geyser wells is also used in the generation of thermal energy. It is popularly known as geothermal energy. In India, a geothermal energy plant has been commissioned at Manikaran in Himachal Pradesh.

Section – E
Map Based Question

Question 10.
On a political map of India, mark and indicate the following features. (Attempt any 5) (1 × 5 = 5)
(i) Khetri copper mine
(ii) Ratnagiri iron ore mine
(iii) Mathura oil refinery
(iv) Important node of North connidor
(v) Katni bauxite mine
(vi) Jharia coal mine
Answer:
CBSE Sample Papers for Class 12 Geography Term 2 Set 2 with Solutions 1

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 5 with Solutions

Students can access the CBSE Sample Papers for Class 12 Business Studies with Solutions and marking scheme Term 2 Set 5 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 5 with Solutions

Time allowed: 2 Hours
Maximum Marks: 40

General Instructions:

  • This is a Subjective Question Paper containing 12 questions.
  • This paper contains 4 questions of 2 marks each, 4 questions of 3 marks each and 4 questions of 5 marks each.
  • 2 marks questions are Short Answer Type Questions and are to be answered in 30-50 words.
  • 3 marks questions are Short Answer Type Questions and are to be answered in 50-80 words.
  • 5 marks questions are Long Answer Type Questions and are to be answered in 80-120 words.
  • This question paper contains Case/Source Based Questions.

Question 1.
State the steps in selection procedure, after the employment interview but before the medical examination. (2)
Answer:
The steps in selection procedure, involved after the employment interview but before the medical examination are as follows:

(1) Reference and Background Checks: Many employers request names, addresses, and telephone numbers of references for the purpose of verifying information and, gaining additional information on an applicant. Previous employers, known persons, teachers and university professors can act as references.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 5 with Solutions

(2) Selection Decision: The final decision has to be made from among the candidates who pass the tests, interviews and reference checks. The views of the concerned manager will be generally considered in the final selection because it is he/she who is responsible for the performance of the new employee.

Question 2.
Training is considered as an important part of the staffing process. Explain. (2)
Answer:
Training is an attempt to improve the current or future employee performance by increasing an employee’s ability to perform through learning, usually by changing the employee’s attitude or increasing his or her skills and knowledge.

Question 3.
You are a management guru. You have been asked by a business firm to make its managers understand the importance of controlling. Give any two arguments. (2)
Answer:
Controlling is an indispensable function of management. Without control, the best of plans may go awry. The importance of controlling is as follows. (any two)

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 5 with Solutions

(1) Accomplishing organisational goals: The controlling function measures progress towards the organisational goals and brings to light the deviations, if any, and indicates corrective action. It, thus, guides the organisation and keeps it on the right track so that organisational goals might be achieved.

(2) Judging accuracy of standards: A good control system enables management to verify whether the standards set are accurate and objective. A good control system keeps a careful check on the changes taking place in the organisation and in the environment and helps to review and revise the standards in light of such changes.

(3) Making efficient use of resources: By exercising control, a manager seeks to reduce wastage and spoilage of resources.

(4) Improving employee motivation: A good control system ensures that employees
know well in advance what they are expected to do and what are the standards of performance on the basis of which they will be appraised. It, thus, motivates them and helps them to give better performance.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 5 with Solutions

Question 4.
Mr. Rohit is into transport business. His buses are hired by schools for transportation of students. He is willing to expand and diversify his business to inter-state transportation purposes. State any two factors that will affect his fixed capital requirements. (2)
Answer:
The factors affecting fixed capital requirements are: (any two)

  • Scale of operations
  • Financing alternatives
  • Growth prospects
  • Nature of Business
  • Diversification
  • Level of Collaboration
  • Technology Upgradation
  • Financing Alternatives

Question 5.
What is the meaning of Directing? State any two points of importance of Directing as a function of management.
OR
The workers of‘Glory Ltd.’ are unable to work on new computerised machines imported by the company to fulfill the increased demand. Therefore, the workers are seeking extra guidance from the supervisor and the supervisor is overburdened with the frequent calls of workers.
Suggest how the supervisor, by increasing the skills and knowledge of workers, can make them handle their work independently. Also state any two benefits that the workers will derive by the decision of the supervisor. (3)
Answer:
The process of acquiring human resources and physical assets and placing them under suitable roles and responsibilities should be directed towards achieving organisational goals. Directing or direction is the essence of all operations in an organisation that involves leading human and physical resources together through motivation, collaboration, coordination and delegation.

The points of importance of directing as a function of management are: (any two)
(1) Initiates action: Direction initiates action based on the preconditions set under planning, organising and staffing. This implies that managers stimulate actions by supervising, motivating and leading their subordinates in the right way. Direction activates employees to work for achieving organisational goals.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 5 with Solutions

(2) Integrates employees’ efforts: The work and activities of employees across all levels are interrelated and direction attempts to integrate all individual efforts. Individual efforts are integrated through coordination between plans, resources and human efforts and through guidance, supervision and counselling.

(3) Means of motivation: Organisational goals can be achieved by motivated employees who work willingly and perform to their best of their abilities. Directing helps in motivating employees to contribute their maximum efforts towards achieving organisational goals.

(4) Facilitates changes: Direction enables an organisation to adapt to changing conditions through better leadership and communication.
OR
The supervisor can provide ‘technical training’ to the workers regarding the use of machines. With increased and improved knowledge, the workers will be able to work independently.
The benefits that the workers will derive by the decision of the supervisor are as follows:

  • Career growth: Training helps employees to improve their skills and knowledge.
  • Increased earnings: Training helps to improve the performance and productivity of workers and with improved performance workers can earn higher wages and incentives.

Question 6.
How are the terms “motive”, “motivation” or “motivator” related to each other. (3)
Answer:
The term ‘motive’ means a need or desire that causes a person to work, while motivation is the condition of being motivated by a motivator and ‘motivator’ gives a person the reasons to work. In other words we can say that “motivation is the process by which a motivator gives a motive to other person to work hard.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 5 with Solutions

Question 7.
“The overall objective of SEBI is to protect the interest of investors and to promote the development of, and regulate the securities market.” In light of the given statement, state any three objectives of SEBI. (3)
Answer:
The objectives of SEBI are: (any three)

  • To regulate stock exchanges and the securities industry to promote their orderly functioning.
  • To protect the rights and interests of investors, particularly individual investors and to guide and educate them.
  • To prevent trading malpractices and achieve a balance between self-regulation by the securities industry and its statutory regulation.
  • To regulate and develop a code of conduct and fair practices by intermediaries like brokers, merchant bankers etc., with a view to making them competitive and professional

Question 8.
“Comparing the actual performance with laid standard, finding out deviations and taking corrective action is an important process of a function of management.” Name and explain the process. (3)
Answer:
The name of this function of management is “controlling”. The steps involved in the controlling process are as following:

(1) Step 1: Setting performance standards: The first step in the controlling process is setting up performance standards. Standards serve as benchmark towards which an organisation strives to work.

(2) Step 2: Measurement of actual performance: Once performance standards are set, the next step is measurement of actual performance. Performance should be measured in an objective and reliable manner.

(3) Step 3: Comparing actual performance with standards: This step involves comparison of actual performance with the standards. Such comparison wilL reveal the deviation between actual and desired results.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 5 with Solutions

(4) Step 4: Analysing deviations: Some deviation in performance can be expected in all activities. It is, therefore, important to determine the acceptable range of deviations.

(5) Step 5: Taking corrective action: The final step in controlling process is taking corrective action. No corrective action is required when the deviation are within acceptable limits.

Question 9.
‘In an interview with a leading news channel, Mr. Rakesh Kwatra, CEO of ‘Get My Job’ has suggested that the companies which want more and more people to apply for jobs in their organisation should make the process for applying for jobs easier and candidate friendly.’
Name and explain the next two steps which follow the step, in the process of the function of management being discussed above. (5)
OR
Horizon Shoes Ltd. has received on order for manufacturing and supply of 5,000 pairs of shoes. The supply was to be completed within 90 days. The production manager made all the production schedules accordingly. After 60 days, he assessed that the production was not running according to schedule and the completion of the order may be delayed by a substantial period. He decided to reassess the situation and completed the order within the schedule time. Identify the function of management discussed here and discuss two steps taken by the production manager. (5)
Answer:
Selection is the step in the process of staff ing discussed here. Selection is the process of choosing from among the pool of the prospective job condidates developed at the stage of recruitment. Even in case of highly specialised jobs where the choice space is very narrow, the regour of the selection process serves two important purposes:

(1) It ensures that the organisation gets the best among the available;

(2) It enhances the self-esteem and prestige of those selected and conveys to them the seriousness with which the things are done in the organisation. The rigour involves a host of tests and interviews. Those who are able to successfully negotiate the test and the inverviews are offered an employment contract, a written document containing the offer of employment, the terms and conditions and the date of joining.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 5 with Solutions

The next two steps following the step of selection in the process of staffing are as follows:
(i) Orientation: Joining a job marks the beginning of socialisation of the employee at the work place. Orientation is introducing the selected employee to other employees and familiarising him with the rules and policies of the organisation.

Placement: Placement refers to the employee occupying the position or post for which the person has been selected.
OR
The function of management which enable the management to assess whether the set standards are followed is called controlling. Controlling means ensuring that activities in an organisation are performed as per the plans. Thus, it is a goal oriented function.
The two steps of controlling process taken by production manager in this case are:

(i) Analysing deviations: It is important for a manager to determine the acceptable range of deviations. If the deviations are significant, critical point control and management by exception should be used by the manager. In this case, the delay in completion of order by substantial period is a matter of concern.

(ii) Taking corrective action: The final step in controlling process is taking corrective action. No corrective action is required when the deviations are within acceptable limits. In this case, the delay is expected to be substantial period. The production manager take corrective action which might involve additional workers and equipment to the project and overtime work.

Question 10.
Name and define the activity which essentially involves preparation of financial blue print of an enterprise’s future operations. Also state any two reasons why this activity is important?
Answer:
Financial planning is the blue print of an enterprise’s future operations. It can be defined as the process and function of estimating capital requirements of a business, determining the forms and proportion of sources or capital for use and formulating policies for administration of funds. Financial planning is important because of following reasons:

  • Adequate funds: Financial planning aims to plan adequate and sufficient funds to carry out daily business operations that cater to short-term, medium-term and long-term goals.
  • Minimum cost of capital: Financial planning involves determining an appropriate mix of equity and debt, which makes capital available at minimum cost.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 5 with Solutions

Question 11.
The issue of equity shares involves huge floatation cost To meet the expenses of floatation companies may decide to tap the money market
(A) Name and explain the money-market instrument the companies can use for the above purpose.
(B) What is the duration for which the companies can get funds through this instrument?
(C) State any other purpose for which this instrument can be used. (5)
Answer:
(A) Commercial Papers can be used for Bridge financing by the company as they are issued by large and credit worthy companies. Bridge financing is the funds raised to meet the floatation costs. The instrument is in the form of an unsecured promissory note and is freely transferable by endorsement It is sold at discount and redeemed at par.
(B) Its maturity period may range from a fortnight to a year.
(C) It is also used to meet the short-term seasonal and working capital requirements of a business enterprise.

Question 12.
State any 5 responsibilities that a consumer should discharge while purchasing, using and consuming goods and services.
OR
How does cost of debt and cost of equity affect the capital structure of an organisation? (5)
Answer:
A consumer should keep in mind the following responsibilities while purchasing, using and consuming goods and services.

(1) Be aware about various goods and services available in the market so that an intelligent and wise choice can be made.

(2) Buy only standardised goods as they provide quality assurance. Thus, look for ISI mark on electrical goods, FPO mark on food products, Hallmark on jewelry etc.

(3) Learn about the risks associated with products and services, follow manufacturer’s instructions and use the products safely.

(4) Read labels carefully so as to have information about prices, net weight, manufacturing and expiry dates, etc.

(5) Assert yourself to ensure that you get a fair deal

(6) Be honest in your dealings. Choose only from legal goods and services and discourage unscrupulous practices like black-marketing, hoarding etc.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 5 with Solutions

(7) Ask for a cash memo on purchase of goods or services. This would serve as a proof of the purchase made.

(8) File a complaint in an appropriate consumer forum in case of a shortcoming in the quality of goods purchased or services availed. Do not fail to take an action even when the amount involved is small

(9) Form consumer societies which would play an active part in educating consumers and safeguarding their interests.

(10) Respect the environment. Avoid waste, littering and contributing to pollution, (any five)
OR
Cost of debt: A firm’s ability to borrow at a lower rate increases its capacity to employ higher debt. Thus, more debt can be used if debt can be raised at a lower rate.

Cost of Equity: Stock owners expect a rate of return from the equity which is commensurate with the risk they are assuming. When a company increases debt, the financial risk faced by the equity holders, increases. Consequently, their desired rate of return may increase. It is for this reason that a company cannot use debt beyond a point.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 5 with Solutions

If debt is used beyond that point cost of equity may go up sharply and share price may decrease inspite of increased EPS. Consequently, for maximisation of shareholders’ wealth, debt can be used only upto a level.

CBSE Sample Papers for Class 12 Economics Term 2 Set 1 with Solutions

Students can access the CBSE Sample Papers for Class 12 Economics with Solutions and marking scheme Term 2 Set 1 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 12 Economics Term 2 Set 1 with Solutions

Time allowed: 2 Hours
Maximum Marks: 40

General Instructions:

  • This is a Subjective Question Paper containing 13 questions.
  • This paper contains 5 questions of 2 marks each, 5 questions of 3 marks each and 3 questions of 5 marks each.
  • 2 marks questions are Short Answer Type Questions and are to be answered in 30-50 words.
  • 3 marks questions are Short Answer Type Questions and are to be answered in 50-80 words.
  • 5 marks questions are Long Answer Type Questions and are to be answered in 80-120 words.
  • This question paper contains Case/Source Based Questions.

CBSE Sample Papers for Class 12 Economics Term 2 Set 1 with Solutions

Question 1.
Distinguish between Rnal Goods and Intermediate Goods.
OR
Distinguish between positive externalities and negative externalities. (2)
Answer:
Final goods refer to those goods which are used either for final consumption or for investment purposes. Whereas Intermediate goods refer to those goods which are used either for resale or for further production purposes.

Explanation:

Final Goods Intermediate Goods
Goods which are used for either consumption or investment is known as final goods. Goods which are used for further production as raw material or purchased for resale is known as intermediate goods.
Final goods included in estimation national income. Intermediate goods the are not included in of the estimation of national income.

OR
Positive externalities refer to benefits caused by one entity to another, without being paid for it. Whereas Negative externalities refer to the harms caused by one entity to another without being penalized for it.

Explanation:

Positive Externalities Negative Externalities
Positive externalities refer to the benefits of an economy activity to the others without involving any price paid for that. Negative externalities refer to the negative impact of an economy activity on the others without involving any penalty.
Employment generated due to establishment of a factory is an example of positive externality. Smoke omitted by factories causes air pollution is an example of negative externality.

CBSE Sample Papers for Class 12 Economics Term 2 Set 1 with Solutions

Question 2.
Calculate equilibrium level of income for a hypothetical economy, for which it is given that:
(1) Autonomous Investments = ₹500 crores, and
(2) Consumption function, C = 100 + 0.80 Y
OR
Calculate Change in Income (ΔY) for a hypothetical economy. Given that
(1) Marginal Prospensity to Consume (MPC) = 0.8, and
(2) Change in Investment (Δl) = ₹1,000 crores (2)
Answer:
Given Consumption function is,
C = 100 + 0.8 Y
Autonomous investments = ₹500 crores We know, at equilibrium level
Y = C + l
Y = 100 + 0.8 Y + 500
Y – 0.8Y = 600 0.2 Y = 600
Y = ₹3,000 crores

Explanation:
Given,
Consumption function (C) = 100 + 0.8Y
Autonomous investments (I) = 500 crores
Y = C + l
Y = 100 + 0.8Y + 500
Y – 0.8Y = 600
0.2Y = 600
Y = ₹ 3,000 crores
OR
P Given ΔI = ₹1,000 crores
MPC = 0.8
As we know,
Multiplier (K) = \(\frac{1}{1-M P C}=\frac{1}{1-0.8}=\frac{1}{0.2}\)
= 5 times
We know K = \(\frac{\Delta Y}{\Delta l}\)
5 = \(\frac{\Delta Y}{1000}\)
ΔY = ₹ 5,000 crores

Explanation: Given,
Change in Investment
(Δl) = ₹ 1,000 crores
Marginal Propensity to Consume (MPC) = 0.8
Multiplier (K) = 1/1 – MPC
= 1/1 – 0.8
= 1/0.2 = 5
Multiplier (K) = Change in Income (ΔY)/
Change in Investment (Δl) =
5 = ΔY/1,000 ΔY = ₹ 5,000 crores

CBSE Sample Papers for Class 12 Economics Term 2 Set 1 with Solutions

Question 3.
‘As the income increases, people tend to save more’. Justify the given statement. (2)
Answer:
At a lower level of income, a consumer spends a larger proportion of his/her income on consumption expenditure (basic survival requirements). As the income increases, owing to the psychological behavior of a consumer (rational), people tend to consume less and save more for future uncertainty.

Explanation:
It is true that as the income increases, people tend to save more. At a lower Level of income, a person spends most of his income on the basic survival requirements. People on very low income cannot afford the Luxury of saving. But as the income increases, households tend to have a higher marginal propensity to save as they save more for future uncertainty.

Question 4.
State and discuss any two indicators that help in measuring the health status of a country.
OR
Compare and analyze the ‘Women Worker Population Ratio’ in Rural and Urban areas based on following information: Worker-Population Ratio in India, 2017-2018. (2)

Sex Worker-Population Ratio
Total Rural Urban
Men 52.1 51.7 53.0
Women 16.5 17.5 14.2
Total 34.7 35.0 33.9

Answer:
Two indicators that help to measure the health status of a country are:

  1. Infant Mortality Rate – Infant Mortality Rate (or IMR) indicates the number of children that survive first year of their life.
  2. Literacy Rate – Literacy rate measures the proportion of literate population in the age group of seven years or above.

Explanation:
Two indicators that help to measure the health status of a country are:

  1. Life expectancy: It refers to the number of years a person is expected to live based on the statistical average.
  2. Infant Mortality Rate: The infant mortality rate is the number of infant deaths for every 1,000 live births.

OR

The data in the given table reveals that:
(1) Women constitute 16.5% of the total worker population in the economy.

(2) The number of women workers in rural areas (17.5%) are relatively higher than the women workers in urban areas (14.2%). Due to the abject poverty in rural areas, rural women are compelled to work more than their urban counterparts.

Explanation:
Women constitute 16.5% of the total worker population in the economy. The difference in participation rates is large as in urban areas, for every 100 urban females, only about 14 are engaged in some economic activities. In rural areas, for every 100 rural women about 18 participate in the employment market. As poverty in the rural areas is more widespread than in the urban areas, so, the rural women engage themselves in low productive jobs just to support the livelihood of their families.

CBSE Sample Papers for Class 12 Economics Term 2 Set 1 with Solutions

Question 5.
‘Investment in infrastructure contributes to the economic development of a country’. Justify the given statement with a valid argument. (2)
Answer:
The given statement is true; infrastructural development in an economy increases productivity, induces higher investment, facilitates employment, and generates more income. With the rise in income the quality of life of the people improves. Thus, conclusively we may say that infrastructure contributes to the economic development of a country.

Explanation:
Infrastructure contributes to economic development of a country both by increasing the productivity of the factors of production and improving the quality of life of its people.

Question 6.
Giving valid reasons explain which of the following will not be included in estimation of National Income of India?
(A) Purchase of shares of X. Ltd. by an investor in the National Stock Exchange.
(B) Salaries paid by the French Embassy, New Delhi to the local workers of the housekeeping department.
(C) Compensation paid by the Government of India to the victims of floods.

OR
Estimate the value of Nominal Gross Domestic Product for a hypothetical economy, the value of Real Gross Domestic Product and Price Index are given as ₹500 crores and 125 respectively. (2)
Answer:
Following will not be included in estimation of National Income of India:
(A) As such transactions are mere paper claims and do not lead to any value addition.
(B) Compensation paid by the Government of India is mere transfer payment and does not lead to any flow of goods and services in an economy.

CBSE Sample Papers for Class 12 Economics Term 2 Set 1 with Solutions

Explanation:
(A) Purchase of shares of X. Ltd. by an investor in the National Stock Exchange will not be included in the estimation of national income because it is just a financial transaction, leading to change of ownership of financial asset. There is no flow of goods or services in the economy.
(B) This will be included in estimation of the National Income of India.
(C) Compensation paid by the Government of India to the victims of floods will not be included in the estimation of national income because it is a transfer payment. There is no flow of goods or services in the economy.
OR
CBSE Sample Papers for Class 12 Economics Term 2 Set 1 With Solutions 1

Question 7.
Study the following information and compare the Economies of India and Singapore on the grounds of investment in Infrastructure as a percentage of GDP’. (2)

Some Infrastructure in India and Other Countries, 2018
CBSE Sample Papers for Class 12 Economics Term 2 Set 1 With Solutions 2
Sources: World Development Indicators 2019, World Bank website: www.worldbank.org.:
BP Statistical Review of World Energy 2019, 69th Edition Note: (*) refers to Gross Capital Formation.
Answer:
“Investment in infrastructure as a percentage of GDP’ is that proportion of Gross Domestic Product which is invested for the development of infrastructural facilities in a country. According to the given data it is evident that India is contributing 30% of its total GDP on infrastructural progress, which is just a notch above the corresponding figure of 28% for Singapore.

Considering the vast geography of India this is a relatively lower proportion in this direction. If India wants to grow at a faster rate, she must concentrate on higher judicious investment on development of infrastructure.

CBSE Sample Papers for Class 12 Economics Term 2 Set 1 with Solutions

Explanation:
The data given in the table reveals that India is contributing 30% of its GDP on infrastructure, whereas Singapore is contributing 28% of its GDP. So it can be concluded that India is investing in infrastructural facilities more than Singapore but this gap is not that large. Some economists have projected that India will become the third biggest economy in the world a few decades from now. Considering this fact, this is a relatively lower proportion in this direction. For that to happen, India will have to boost its infrastructure investment.

Read the following text carefully and answer questions number 8 and 9 given below:

SINO-PAK FRIENDSHIP CORRIDOR
The China-Pakistan Economic Corridor (CPEC) relationship between the two nations. But it has also sparked criticism for burdening Pakistan with mountains of debt and allowing China to use its debt strategic assets of Pakistan.

The foundations of CPEC, part of China’s Belt and Road Initiative, were laid in May 2013. At the time, Pakistan was reeling under weak economic growth. China committed to play an integral role in supporting Pakistan’s economy.

Pakistan and China have a strategic relationship that goes back decades. Pakistan turned to China at a time when it needed a rapid increase in external financing to meet critical investments in hard infrastructure, particularly power plants and highways. CPEC’s early harvest projects met this need, leading to a dramatic increase in Pakistan’s power generation capacity, bringing an end to supply-side constraints that had made rolling blackouts a regular occurrence across the country.

Pakistan leaned into CPEC, leveraging Chinese financing and technical assistance in an attempt to end power shortages that had paralyzed its country’s economy. Years later, China’s influence in Pakistan has increased at an unimaginable pace.

China As Pakistan’s Largest Bilateral Creditor: China’s ability to exert influence on Pakistan’s economy has grown substantially in recent years, mainly due to the fact that Beijing is now Islamabad’s largest creditor. According to documents released by Pakistan’s finance ministry, Pakistan’s total public and publicly guaranteed external debt stood at $44.35 billion in June 2013, just 9.3 percent of which was owed to China. By April 2021, this external debt had ballooned to $90.12 billion, with Pakistan owning 27.4 percent -$24.7 billion – of its total external debt to China, according to the International Monetary Fund (IMF). Additionally, China provided financial and technical expertise to help Pakistan build its road infrastructure, expanding north-south connectivity to improve the efficiency of moving goods from Karachi all the way to Gilgit-Baltistan (POK). These investments were critical in better integrating the country’s ports, especially Karachi, with urban centers in Punjab and Khyber- Pakhtunkhwa provinces.

CBSE Sample Papers for Class 12 Economics Term 2 Set 1 with Solutions

Despite power asymmetries between China and Pakistan, the latter still has tremendous agency in determining its own policies, even if such policies come at the expense of the longterm socioeconomic welfare of Pakistani citizens.

(https://www.usip.org/publications /2021/ 05/ pakistans-growing-problem-its-china-economic-corridor – Modified)

Question 8.
Outline and discuss any two economic advantages of China Pakistan Economic Corridor (CPEC) accruing to the economy of Pakistan. (3)
Answer:
Economic advantages of China Pakistan Economic Corridor (CPEC) to the economy of Pakistan are:

  • China provided financial and technical expertise to help Pakistan build its road infrastructure, supporting employment and income in the economy
  • CPCE has led to a massive increase in power generation capacity of Pakistan. It has brought an end to supply-side constraints in the nation, which had made blackouts a regular phenomenon across the country.

Explanation: Economic advantages of China Pakistan Economic Corridor (CPEC) accruing to the economy of Pakistan:

  1. CPEC’s early harvest projects met investment needs of Pakistan in power plants, leading to a dramatic increase in Pakistan’s power generation capacity, bringing an end to supply-side constraints that had made rolling blackouts a regular occurrence across the country.
  2. China provided financial and technical expertise to help Pakistan build its road infrastructure, expanding north-south connectivity to improve the efficiency of moving goods.

Question 9.
Analyse the implication of bilateral ‘debt-trap’ situation of Pakistan vis-a-vis the Chinese Economy. (3)
Answer:
China has become famous for its ‘Debt Trap Diplomacy’ in recent times. Under this China provides financial and technical expertise/ assistance to help various nations to bring them under its direct or indirect influence.

The first and the foremost implication of the diplomacy is that Beijing has now become Islamabad’s largest creditor. According to documents released by Pakistan’s finance
ministry, its total public external debt stood at $44.35 billion in June 2013, just 9.3 percent of which was owed to China. By April 2021, this external debt had ballooned to $90.12 billion, with Pakistan owing 27.4 percent -$24.7 billion – of its total external debt to China, according to the IMF.

CBSE Sample Papers for Class 12 Economics Term 2 Set 1 with Solutions

Explanation:
China’s ability to exert influence on Pakistan’s economy has grown substantially in recent years, mainly due to the fact that Beijing is now Islamabad’s largest creditor. It is the first and foremost implication of this ‘Debt=trap’ diplomacy. According to documents released by Pakistan’s finance ministry, Pakistan’s total public and publicly guaranteed external debt stood at $44.35 billion in June 2013, just 9.3 percent of which was owed to China. By April 2021, this external debt had ballooned to $90.12 billion, with Pakistan owing 27.4 percent -$24.7 billion – of its total external debt to China, according to the International Monetary Fund (IMF).

Question 10.
Explain how ‘Non-Monetary Exchanges’ impact the use of Gross Domestic Product as an index of economic welfare. (3)
Answer:
Non-monetary exchange transactions are not included in the estimation of Gross Domestic Product on account of practical difficulties like non-availability of reliable data. Although these activities enhance public welfare which may lead to underestimation of GDP.

For example: kitchen gardening, services of homemaker etc.

Explanation:
Such exchanges which don’t involve the use of money as a medium of exchange are known as non-monetary exchanges. In non-monetary exchanges, goods are exchanged for goods.

As these transactions are outside the monetary system of exchange, thus, are not included in gross domestic product of the economy. Due to this, GDP remains underestimated. Thus, non-monetary exchanges make GDP an inappropriate index of welfare.

Question 11.
‘Monetary measures offer a valid solution to the problem of Inflationary gap in an economy’. State and discuss any two monetary measures to justify the given statement. (5)
Answer:
Two measures which may be used to solve the problem of inflation are:
(i) An increase in Cash Reserve Ratio (CRR) may reduce the credit creation capacity of the commercial banks in the economy. This may lead to a fall in the borrowings from
banks causing a fall in Aggregate Demand in the economy, and helps to correct the inflationary gap in the economy.

(ii) Sale of Government Securities in the open market by the Central Bank will adversely affect the ability of the Commercial Banks to create credit in the economy. As a result Aggregate Demand in the economy may fall and correct the inflationary gap in the economy.

CBSE Sample Papers for Class 12 Economics Term 2 Set 1 with Solutions

Explanation:
Two measures which may be used to solve the problem of inflation are:
(i) Repo Rate: The rate at which central bank lends money to the commercial banks is known as repo rate. To correct the situation of inflationary gap, repo rate should be increased. A rise in repo rate is expected to cause a rise in market rate of interest, leading to a fall in demand for funds in the money market. Implying a fall in expenditure or AD, correcting inflationary gap.

(ii) Open Market Operations: In the situation of inflationary gap, cash balances need to be reduced. In this situation, Central bank starts selling securities. It reduces purchasing power from the money market. Consequently, aggregate demand is decreased and inflationary gap is corrected.

Question 12.
(A) From the following data calculate the value of Domestic Income:

Items Amount (in crores)
Compensation Employees of 2,000
Rent and Interest 800
Indirect Taxes 120
Corporate Tax 460
Consumption Fixed Capital of 100
Subsidies 20
Dividend 940
Undistributed Profits 300
Net Factor Income from Abroad 150
Mixed-Income of Self Employed 200

(B) Distinguish between ‘Value of Output’ and ‘Value Added’.
OR
(A) Given the following data, find Net Value Added at Factor Cost by Sambhav (a farmer) producing Wheat:

Items Amount (in crores)
Sale of wheat by the farmer in the local market 6,800
Purchase of Tractor 5,000
Procurement of wheat by the Government from the farmer 200
Consumption of wheat by the farming family during the Year 50
Expenditure on the maintenance of existing capital stock 100
Subsidies 20

(B) State any two components of‘Net Factor Income from Abroad’. (5)
Answer:
(A) Domestic Income (NDP@fc)
= (i) + (ii) + (iv) + (vii) + (viii) + (x)
= ₹ 2000 + ₹ 800 + ₹ 460 + ₹ 940 + ₹ 300 + ₹ 200
= ₹4,700 crore

CBSE Sample Papers for Class 12 Economics Term 2 Set 1 with Solutions

Explanation:
Domestic Income (NDPFC) = Compensation of Employees + Rent and Interest + Corporate Tax + Dividend + Undistributed Profits + Mixed Income of Self Employed
= ₹ 2000 + ₹ 800 + ₹ 460 + ₹ 940 + ₹ 300 + ₹ 200
= ₹ 4,700 crores

(B) Value of output is the estimated money value of all the goods and services, inclusive of change in stock and production for self-consumption. Whereas, Value added is the excess of value of output over the value of intermediate consumption.

Explanation:
Monetary value of all the goods and services produced in a given period of time is known as value of output, whereas, value-added is the excess of value of output over the value of intermediate consumption.
OR
(A) Net Value Added at Factor Cost (NVA @ FC)
= (i) + (iii) + (iv) + (vi) – (v)
= ₹ 6800 + ₹200 + ₹ 50 + ₹20 – ₹100
= R6,970crore

Explanation:
Net Value Added at Factor Cost (NVAFC) = Sale of wheat by the farmer in the local market+ Procurement of wheat by the Government from the farmer+ Consumption of wheat by the farming family during the Year + Subsidy – Expenditure on the maintenance of existing capital stock
= ₹ 6800 + ₹ 200 + ₹ 50 + ₹ 20 – ₹ 100
= ₹ 6,970 crores

(B) Component of net factor income from abroad are:

  • Net compensation of employees
  • Net income from property and entrepreneurship
  • Net retained earnings of resident companies abroad (any two)

Explanation:
Components of Net Factor Income from Abroad are:

  • Net compensation of employees
  • Net income from property and entrepreneurship
  • Net retained earnings of resident companies abroad.

CBSE Sample Papers for Class 12 Economics Term 2 Set 1 with Solutions

Question 13.
(A) ‘Pesticides are chemical compounds designed to kill pests. Many pesticides can also pose health risks to people even if exposed to nominal quantities. ‘

In the light of the above statement, suggest any two traditional methods for replacement of the chemical pesticides.

(B) ‘In recent times the Indian Economy has experienced the problem of Casualisation of the workforce. This problem has only been aggravated by the outbreak of COVID-19.’

Do you agree with the given statement? Discuss any two disadvantages of casualisation of the workforce in the light of the above statement. (5)
Answer:
(A) The traditional practices can help in controlling contamination without the use of chemical fertilizers, as follows:

  1. Neem trees and its by products are a natural pest-controller, which has been used since ages in India. Recently, the government promoted the sale Neem coated urea as a measure of natural pest control.
  2. Large variety of birds should be allowed to dwell around the agricultural areas, they can clear large varieties of pests including insects

Explanation: Traditional methods for replacement of the chemical pesticides are:
(i) Neem: Neem is a naturally occurring pesticide that comes from the seeds of the neem tree. Neem seeds and leaves contain many compounds which are useful for pest control. Neem repels or reduces the feeding of many species of pest insects as well as some nematodes.

(ii) Animals and Birds: Animals and birds are also one of the traditional methods of pest control. For example, snakes are one of the prime group of animals which prey upon rats, mice and various other pests. Similarly, large varieties of birds, for example, owls and peacocks, prey upon vermin and pests. If these are allowed to dwell around the agricultural areas, they can clear large varieties of pests including insects. Lizards are also important in this regard.

(B) The given statement is quite appropriate with reference to the ‘casualisation of labour’ in India.

(i) For casual workers, the rights of the labour are not properly protected by labour laws. Particularly, during pandemic times, as demand for goods and services fell the casual workers were left jobless, without any compensation or support.

(ii) During the COVID-19 lockdown millions of casual workers lost their jobs, raising the question of their survival. Also, additional health expenditure added to their troubles. Had such workers been working under the formal sector, it would have given them some respite in their difficult times.

CBSE Sample Papers for Class 12 Economics Term 2 Set 1 with Solutions

Explanation:
It is true that in recent times the Indian Economy has experienced the problem of Casualisation of the workforce. This problem has only been aggravated by the outbreak of COVID-19. India lacks of opportunities in the organised sector, thus people start working as casual workers. The coronavirus pandemic comes as huge shock to the labour market in India.

Disadvantages to casual workers during Covid-19:

  • The Indian labor market is largely informal, lacks a social security net, which increases labor vulnerability and distress during lockdowns.
  • Thousands of casual workers and self-employed in cities like Mumbai and Pune have left for their native places in the last few months after the Covid-19 outbreak.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 4 with Solutions

Students can access the CBSE Sample Papers for Class 12 Business Studies with Solutions and marking scheme Term 2 Set 4 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 4 with Solutions

Time allowed: 2 Hours
Maximum Marks: 40

General Instructions:

  • This is a Subjective Question Paper containing 12 questions.
  • This paper contains 4 questions of 2 marks each, 4 questions of 3 marks each and 4 questions of 5 marks each.
  • 2 marks questions are Short Answer Type Questions and are to be answered in 30-50 words.
  • 3 marks questions are Short Answer Type Questions and are to be answered in 50-80 words.
  • 5 marks questions are Long Answer Type Questions and are to be answered in 80-120 words.
  • This question paper contains Case/Source Based Questions.

Question 1.
Why employees become lethargic when the organisation uses internal source of recruitment? Also state one other limitation of internal source of recruitment. (2)
Answer:
The employees may become lethargic if they are sure of timebound promotions.
The limitations of using internal sources of recruitment are as follows: (any one)

  • When vacancies are filled through internal promotions, the scope for induction of fresh talent is reduced. Hence, complete reliance on internal recruitment involves danger of ‘inbreeding’ by stopping the infusion of new blood’ into the organisation.
  • A new enterprise cannot use internal sources of recruitment No organisation can fill all its vacancies from internal sources.
  • The spirit of competition among the employees may be hampered; and
  • Frequent transfers of employees may often reduce the productivity of the organisation.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 4 with Solutions

Question 2.
External sources of recruitment are better than internal sources of recruitment. Give any two reasons in support of this answer. (2)
Answer:
The reasons of external sources of recruitment being better than internal sources of recruitment are: (any two)

(1) Qualified Personnel: By using external sources of recruitment, the management can attract qualified and trained people to apply for vacant jobs in the organisation.

(2) Wider Choice: When vacancies are advertised widely, a large number of applicants from outside the organisation apply. The management has a wider choice while selecting the people for employment

(3) Competitive Spirit: If a company taps external sources, the extisting staff will have to compete with the outsiders. They will work harder to show better performance.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 4 with Solutions

Question 3.
“If anything goes wrong with the performance of key activities, the entire organisation suffers. Therefore, the organisation should focus on them.” Explain the statement. (2)
Answer:
The given statement refers to the importance of ‘Critical point control’ in order to ensure effective performance of key activities.

It may not be either easy nor economical to monitor each and every activity in the organisation. Therefore, every organisation identifies and states its specific Key Result Areas (KRAs) or critical points which require tight control and are likely to have a significant effect on the working of the business.

Any deviations on these points are attended to urgently by the management. For example, if in an organisation, the expenditure on stationery goes up by 10%, it can be ignored but if the production cost goes up by 5%, it may call for managerial action.

Question 4.
‘Cost of equity’ affect the choice of capital structure of a company. Explain. (2)
Answer:
Stock owners expect a rate of return from the equity which is commensurate with the risk they are assuming. When a company increases debt, the financial risk faced by the equity holders, increases. Consequently, their desired rate of return may increase.

It is for this reason that a company can not use debt beyond a point. If debt is used beyond that point, cost of equity may go up sharply and share price may decrease inspite of increased EPS. Consequently, for maximisation of shareholders’ wealth, debt can be used only upto a level

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 4 with Solutions

Question 5.
“Leadership indicates the ability of an individual to motivate its followers to contribute for achieving organisational objectives.” Discuss. (3)
Answer:
Leadership is the process of influencing the behaviour of people by making them strive voluntarily towards achievement of organisational goals. The important features of leadership are as follows:

  • Leadership indicates ability of an individual to influence others;
  • Leadership tries to bring change in the behaviour of others;
  • Leadership indicates interpersonal relations between leaders and followers;
  • Leadership is exercised to achieve common goals of the organisation;

Question 6.
“Motivation means incitement or inducement to act or move”. Explain the features of motivation. (3)
Answer:
Motivation is the act or process of giving someone a reason to act towards a desired goal. It is a psychological factor that stimulates people to act in a desired manner. The features of motivation are as follows:

(1) Internal feeling: Motivation is an inner psychological force which compels employees to behave in a particular manner originating from personal needs, recognition, power, sense of recognition, etc.

(2) Goal directed behaviour: Motivation is a process of stimulating and channelising individuals’ energies towards achieving certain goals.

(3) Positive or negative motivation: Motivation, however, can be positive or negative wherein positive includes incentives rewards or bonuses and negative includes punishment, fear, use of force, etc.

(4) Complex process: The process of motivation requires analysing and understanding of human behaviour that can determine factors which lead to desirable working behaviour which can be complex and challenging.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 4 with Solutions

Question 7.
“It is generally believed that measurement of performance should be done after the task is completed.” Identify and explain the step in the process of the function of management being discussed above and the step followed by the same in the process. (3)
Answer:
The step discussed here is the process of controlling function of managment. Measurement of Actual performance: Performance should be measured in an objective and reliable manner. There are several techniques for measurement of performance. Wherever possible measurement of work should be done during the performance.

The step followed in the process is:
Comparing actual performance with standards: This step involves comparison of actual performance with the standard. Such comparison will reveal the deviation between actual and desired results. Standards become easier when standards are set in quantitative terms.

Question 8.
“Financial markets play an important role in the allocation of scarce resources in an economy by performing important functions.” In light of the given statement, state any three functions performed by Financial Market.
OR
Apex Ltd. a reputed automobile manufacturer needs ? ten crores as additional capital to expand its business. Atul Sharma, the CEO of the company wanted to raise funds through equity. On the other hand the Finance Manager, Nimi Sahdev said that the public issue may be expensive on account of various mandatory and non-mandatory expenses. Therefore, it was decided to allot the securities to institutional investors.
Name the method through which the company decided to raise additional capital (3)
Answer:
The functions of Financial Market are: (any three)

  • Financial markets mobilise savings of households and channelize them into the most productive uses.
  • It facilitates price discovery of a financial asset through interaction between supply and demand of funds.
  • Financial markets provide liquidity to financial assets, so that they can be easily converted into cash whenever required.
  • Financial markets provide valuable information about securities being traded in the market and thereby, help to reduce cost of transaction in terms of time, effort and money.

OR
Private placement is method through which the company decided to raise additional capital. Private placement is the allotment of securities by a company to institutional investors and some selected individuals. It helps to raise capital more quickly than a public issue.

Access to the primary market can be expensive on account of various mandatory and nonmandatory expenses. Some companies, therefore, cannot afford a public issue and choose to use private placement.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 4 with Solutions

Question 9.
“Internal sources of recruitment are more economical for an organisation but it has some drawbacks too”. Discuss.
OR
How does recruitment take place through employment exchange and labour contractor. (5)
Answer:
Staffing is putting people to jobs. Staffing is that part of the process of management which is concerned with obtaining, utilising and maintaining a satisfactory and satisfied workforce. Proper staffing ensures the following benefits to the organisation:

  • It helps in discovering and obtaining competent personnel for various jobs.
  • It makes for higher performance, by putting right person on the right job.
  • It ensures the continuous survival and growth of the enterprise through the succession planning for managers.
  • It improves job satisfaction and morale of employers through objective assessment and fair rewarding for their contribution.

OR
Employment Exchange: Employment exchanges run by the Government are regarded as a good source of recruitment for unskilled and skilled operative jobs. In some cases, compulsory notification of vacancies to employment exchange is required by law.

Thus, employment exchanges help to match personnel demand and supply by serving as link between job-seekers and employers. Unfortunately, the records of employment exchange are often not up to date and many of the candidates referred by them may not be found suitable.

Labour Contractors: Labour contractors maintain close contacts with labourers and they can provide the required number of unskilled workers at short notice. Workers are recruited through labour contractors who are themselves employees of the organisation.

The disadvantages of this system are that if the contractor himself decides to leave the organisation, all the workers employed through him will follow him.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 4 with Solutions

Question 10.
“Financial planning is an important part of overall planning of any business enterprise.” Explain. (5)
Answer:
Financial planning aims at enabling the company to tackle the uncertainty in respect of the availability and timing of the funds and helps in smooth functioning of an organisation. The importance of financial planning can be explained as follows: (any four)

  • It tries to forecast what may happen in future under different business situations. By doing so, it helps the firms to face the eventual situation in a better way. In other words, it makes the firm better prepared to face the future.
  • It helps in avoiding business shocks and surprises and helps the company in preparing for the future.
  • It helps in coordinating various business functions e.g. sales and production functions, by providing clear policies and procedures.
  • Detailed plans of action prepared under financial planning reduce waste, duplication of efforts, and gaps in planning.
  • It tries to link the present with the future.
  • It provides a link between investment and financing decisions on a continuous process.
  • By spelling out detailed objectives for various segments, it makes the evaluation of actual performance easier.

Question 11.
State the differences between Primary market and Secondary Market. (5)
Answer:

Basis Primary market Secondary market
(1) Meaning It means the market where corporate 1 sector, government and public bodies issue securities to raise funds from the public. It means the market where listed shares, debentures and other secu­rities are traded for investment and speculative purposes.
(2) Also Known as New issues market. Stock Exchange
(3) Capital Formation It promotes capital fomation directly l as funds flow directly from savers to  investors. It promotes capital formation indi­rectly.
(4) Pricing Prices are determined and decided by the management of the company. Prices are determined by demand and supply for the security.
(5) Nature of securities dealt in New securities are traded. Already existing securities in market are traded.

Question 12.
State any five responsibilities that a consumer must keep in mind while purchasing gold jewellery.
OR
Elite private Limited deals in the automobiles. It has a share capital of ₹10,00,000 divided into shares of ₹100 each. The company wants to expand its business. For this purpose, it requires additional funds of ₹5,00,000 . The management is considering the following alternatives for raising funds :
Alternative 1: Issue of 5000 Equity shares of ₹ 100 each
Alternative 2: Issue of 10% Debentures of ₹ 5,00,000
The company’s present Earnings Before Interest and Tax ( EBIT) is ₹4,00,000 p.a. Assuming that the rate of Return of Investment remains the same after expansion, which alternative should be used by the company in order to maximise the returns to the equity shareholders. The Tax rate is 50%. Show the working. (5)
Answer:
The responsibilities that a consumer must keep in mind while purchasing gold jewellery are: (any three)
(1) Be aware about various goods(types of jewellery) available in the market so that an intelligent and wise choice can be made.
(2) Buy only standardized jewellery as they provide quality assurance. Thus, look for Hallmark on jewellery.
(3) Learn about risks associated with the product, follow the manufacturer’s instructions.
(4) Read labels carefully so as to have information about prices, net weight, etc.
(5) Assert yourself to ensure a fair deal.
(6) Be honest in your dealings.
OR
Rate of Return of Investment is
4,00,000/10,00,000 x 100 = 40%
EBIT after expansion = 40% x 15,00,000 = 6,00,000

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 4 with Solutions

Working:
Alternative I
EBIT — 6,00,000
(-) intrest ——–
= EBT 6.00.000
(-) Tax 3,00,000 (@50%)
= EAT 3,00,000
No. of shares 15000
EPS = EAT/no. of shares
= 3,00,000/15000
= 20

Alternative II
EBIT 6,00,000
(-) interest 50,000
= EBT 550,000
(-) Tax 2,75,000 (@50%)
=EAT 275,000
No.of shares 10000
EPS = EAT/no. of shares
= 2 75,000/10000
= 27.5
In atternative PI, Compnay’s EPS is higher than
Alternative I
Hence, company shouLd use Plan 2 in order to increase the return to the equity shareholders.

CBSE Sample Papers for Class 12 Physics Term 2 Set 8 with Solutions

Students can access the CBSE Sample Papers for Class 12 Physics with Solutions and marking scheme Term 2 Set 8 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 12 Physics Standard Term 2 Set 8 with Solutions

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions:

  • There are 12 questions in all. All questions are compulsory.
  • This question paper has three sections: Section A, Section B and Section C.
  • Section A contains three questions of two marks each, Section B contains eight questions of three marks each, Section C contains one case study-based question of five marks.
  • There is no overall choice. However, an internal choice has been provided in one question of two marks and two questions of three marks. You have to attempt only one of the chokes in such questions.
  • You may use log tables if necessary but use of calculator is not allowed.

SECTION – A
(Section A contains 3 questions of 2 marks each.)

Question 1.
What is ‘greenhouse effect’? State its importance for us.
OR
Explain the dual nature of radiation. (2)
Answer:
The sun’s rays warms the surface of earth. A part of the radiation which falls on the earth is reflected back into the space and only a part of it is absorbed. This trapped radiation further warms the earth. The trapping of radiation by the earth’s atmosphere is known as Greenhouse effect. Life would not have been possible without this process. Carbon dioxide is one of the gases responsible for this effect. Some other gases like methane, nitrous oxide and water vapours also contribute towards this process.
OR
Dual nature of radiation is:
(A) The phenomenon of radiation such as photoelectric effect, Compton effect, Stark effect, Raman effect etc can only be explained on the basis of particle nature of radiation.
(B) The phenomenon of radiation such as interference, diffraction, polarization, reflection, refraction etc. can be explained on the basis of wave nature of radiation. Therefore, radiation has dual character wave and particle wave.

Question 2.
Considering the V-l characteristics of a p-n diode answer the following questions.
(A) Why under reverse bias almost independent of the applied potential up to a critical voltage?

(B) Why does the reverse current show a sudden increase in the critical voltage? 2
Answer:
(A) In reverse biasing, the current of order micro ampere is due to the drifting of minority charge carriers from one region to another through the junction. A small applied voltage is sufficient t o s weep t he minority charge carriers through thejunction. Therefore, reverse current is almost independent of critical voltage.

(B) At critical voltage which is also known as breakdown voltage, a large number of covalent bonds break, resulting in the increase of large number of charge carriers. Hence current increases at voltage.

Related Theory
After the cut-in voltage, the diode current increases exponentially even for a very small increase in diode bias voltage. Here, the majority charge carriers feet negligible resistance at the junction.

CBSE Sample Papers for Class 12 Physics Term 2 Set 8 with Solutions

Question 3.
Two convex lenses of same focal length but of aperture A1 and A2 (A2 > A1), are used as the objective lenses in two astronomical telescopes having identical eyepieces. What is the ratio of their resolving power? Which telescope will you prefer and why? Give reason. (2)
Answer:
Resolving power of a telescope is proportional to its aperture, and is given by a relation, Therefore, the telescope with objective of aperture A1 should be preferred for viewing as this would:
(A) give a better resolution.
(B) has a higher light gathering power of telescope.

SECTION – B
(Section B consists of 8 questions of 3 marks each.)

Question 4.
Why is the mass of a nucleus always less than the sum of masses of constituents? If the total number of protons and neutrons in a nuclear reaction is conserved, then how is the energy absorbed or evolved in reaction? (3)
Answer:
When nucleons combine to form nucleus, some mass is converted into binding energy in accordance with mass-energy equivalence relation. Hence, the mass of the nucleus is less than that of nucleons. The number of protons and number of neutrons are the same before a nuclear reaction and different after a nuclear reaction. This difference is called the mass defect.. It is denoted by ΔM.
ΔM =[ Zmp+( A – Z)mn ] – M
Einstein’s mass energy relation can be express this mass difference in terms of
ΔEb = ΔMc2
This shows that if a certain number of neutrons and protons are brought together to form a nucleus of a certain charge and mass, an energy will be released in the process. That energy is termed as binding energy. If we separate a nucleus into its nucleons we would have to transfer a total energy to AEb, to the particles.

Question 5.
(A) When violet light is incident of a lens instead of red light, how does the focal length changes?
(B) Why does bluish colour predominate in a clear sky?
(C) Why does sun appear red at sunrise and sunset? (3)
Answer:
(A) Refractive index of a material is inversely proportional to the wavelength of the incident light. So, the focal length will decrease with decrease in wavelength according to the Lens maker formula,
\(\frac{1}{f}\) = (μ – 1)(\(\frac{1}{R_{1}}-\frac{1}{R_{2}}\))
Therefore, when violet light replaces the red light, then due to increase in wavelength, the focal length of the lens decreases.

(B) While light from the sun reaches the atmosphere that is comprised of the tiny particles of the atmosphere. These act as a prism and cause the different components to scatter. As blue light travels in shorter and smaller waves in comparison to the other colours of the spectrum, it is scattered the most, causing the sky to appear bluish.

(C) Sun appears red at sunrise and sunset due to the Least scattering of red light as it has the longest wavelength.

Related Theory
w Scattering of light is the phenomenon in which light is deflected from its path due to its interaction with the particles of the medium through which it passes.

CBSE Sample Papers for Class 12 Physics Term 2 Set 8 with Solutions

Question 6.
What do you mean by Q-value of nuclear reaction?
OR
Explain the colours in thin film and state the uses of interference. (3)
Answer:
Q vo[ue of reaction is calculated from Einsteins mass energy equivalence relation. E = mc2, It may be positive or negative. A nuclear reaction in which Q vaLue is positive, energy is released. Such a reaction is caL[ed exoergic. A nuclear reaction in which Q vaLue is negative, energy has to be supplied beftwe the reaction occurs. Such a reaction is called endoergic.
CBSE Sample Papers for Class 12 Physics Term 2 Set 8 with Solutions 1
When white light is incident on a thin film (like oil film on the surface of water or a soap bubble) then interference takes place between the waves reflected from its two surfaces and waves refracted through it. The intensity becomes maximum and minimum as a result of interference and colours are seen. The source of light must be an extended source. The colours obtained in reflected and transmitted light are mutually complementary. The colours obtained in thin films are due to interference whereas those obtained in prims are due to dispersion.

The thin layer of oil on water and soap bubbles shows different colours due to interference of waves reflected from two surfaces of their films. Here we get two coherent beams by division of amplitude making use of partial reflection and partial refraction.

The interference effect can be used to determine the wavelength of Light precisely. It can be used to determine refractive index or thickness of transparent sheet. It is also used in holography to produce three-dimensional images.

Question 7.
(A) How does one understand the temperature dependence of resistivity of semiconductor?
(B) Calculate the resistance of the diode at (A) I = 15 mA and at (B) V = -10 V with the help of V-l characteristic of a silicon diode given below.
CBSE Sample Papers for Class 12 Physics Term 2 Set 8 with Solutions 2
Answer:
(A) When temperature increases, covalent bonds of neighbouring atom breaks and charge carriers become free to cause conduction, so resistivity of semiconductor decreases with the rise of temperature.

(B) (i) From the given curve, voltage,
V = 0.7 V for current
I = 15 mA for voltage
Resistance= \(\frac{V}{I}\) = \(\frac{0.7}{15 \times 10^{-3}}\)
= 46.66 Ω

(ii) For V =-10V,
we have I = -1 μA
= -1 × 10-6A
R = \(\frac{10}{1 \times 10^{-6}}\)
= 1.0 × 107Ω

Caution
If the junction does not permit the flow of current, the diode is known to be at zero bias conditions and voltage is zero.

CBSE Sample Papers for Class 12 Physics Term 2 Set 8 with Solutions

Question 8.
The intensity of central maxima (0) in YDSE is lo. If the distance OP equals to \(\frac{1}{3}\) rd of fringe width, then show that the intensity at a point p would be \(\frac{I_{0}}{4}\)
CBSE Sample Papers for Class 12 Physics Term 2 Set 8 with Solutions 3
Answer:
Given that
OP = Yn
OP is equal to \(\frac{1}{3}\) rd of fringe width at the pattern.
Yn = \(\frac{1}{3}\left(\frac{D \lambda}{d}\right)\)
\(\frac{d Y_{n}}{D}=\frac{\lambda}{3}\)
Phase difference,
ΔΦ = \(\frac{2 \pi}{\lambda} \times \frac{\lambda}{3}\)
= \(\frac{2 \pi}{3}\)

If the intensity at central fringe is Io, then intensity at a point P, where phase difference is ΔΦ is given by,
I = Io cos2ΔΦ
I = Io (-cos\(\frac{\pi}{3}\))2
I = Io(-\(\frac{1}{2}\))2
= \(\frac{\mathrm{I}_{0}}{4}\)
The intensity at point P would be \(\frac{\mathrm{I}_{0}}{4}\) .

Question 9.
A triangular prism of refracting angle 60° is made of a transparent material of refractive
index 2√3 A ray of light is incident normally on the face KL as shown in the figure. Trace the path of the ray as it passes through the prism and calculate the angle of emergence and angle of deviation.

A convex lens of focal length 30 cm is placed coaxially in contact with a concave lens of focal length 40 cm. Determine the power of the combination. Will the system be converging or diverging in nature? (3)
Answer:
From diagram it is clear that incidence angle at face KM is 60°.
CBSE Sample Papers for Class 12 Physics Term 2 Set 8 with Solutions 5
sin C \(\frac{1}{\mu}\) = \(\frac{\sqrt{3}}{2}\)
Hence, critical angle is also 60°.
Therefore, incident light ray will not emerge from KM face due to total internal reflection at this face. Hence, it will move along face KM Angle of emergence = 90°.
Hence angle of deviation = 30° (from fig.)
OR
focal length of convex lens,
f1 = + 30 cm
= 0.30 m
Focal length of concave lens
f2 = – 40 cm
= – 0.40 m
Equivalent focal length
\(\frac{1}{\mathrm{~F}}=\frac{1}{f_{1}}+\frac{1}{f_{2}}\)
= \(\frac{1}{30}+\frac{1}{(-40)}\)
= \(\frac{40-30}{1200}=\frac{1}{120}\)
∴ F = 120 m
= 1.2 m
∴ Power of the combination,
p = \(\) = 0.83D
The focal length of combination = 1.2 m = 120 cm. As the focal length is positive the system will be converging in nature.

CBSE Sample Papers for Class 12 Physics Term 2 Set 8 with Solutions

Question 10.
(A) How does one explain the emission of electrons from a photosensitive surface with the help of Einstein’s photoelectric equation?
(B) The work function of the following metals is given: Na = 2.75 eV, K = 23 eV, Mo = 4.17 eV and Ni = 5.15 eV. Which of these metals will not cause photoelectric emission for radiation of wavelength 3300 A from a laser source placed 1 m away from these metals ? What happens if the laser source is brought nearer and placed 50 cm away? (3)
Answer:
(A) According to Einstein’s photoelectric equation,
hv = hv0 + Emax
Emax = hv- hv0
Emax = h(v – V0)
If v < v0 then Emax will be negative so, no emission takes place.

If v > v0 then Emax will be positive and directly proportional to □ so, emission takes place.

(B) E = \(\frac{h c}{\lambda}\)
E = \(\frac{6.63 \times 10^{-34} \times 3 \times 10^{8}}{3300 \times 10^{-10} \times 1.6 \times 10^{-19}}\)
E = 3.76 eV

The work function of Na and K is less than the energy of incident radiation. Therefore, Na and K will cause photoelectric emission while M0 and Ni will not cause photoelectric emission. There will be no effect on photoelectric emission if the source is brought nearer.

Question 11.
(A) Using Bohr’s second postulate of quantization of orbital angular momentum show that the circumference of the electron in the nth orbital state in hydrogen atom is n times the de Broglie wavelength associated with it.

(B) The electron in hydrogen atom is initially in the third excited state. What is the maximum number of spectral lines which can be emitted when it finally moves to the ground state? 3
Answer:
(A) According to Bohr’s second postulate of quantization, the electron can revolve around the nucleus only in those circular orbits in which the angular momentum of the electron is integral multiple of \(\frac{h}{2 \pi}\) where h is Planck’s constant (= 6.62 × 10-34 Js).
So, if m is the mass of electron and v is the velocity of electron in permitted quantized orbit with radius r then
mvr = n \(\frac{h}{2 \pi}\) ……….(i)
Where n is the principal quantum number and can take integral values like
n = 1, 2, 3,…
This is the Bohr’s quantization condition. Now, de-Broglie wavelength is given as,
λ = \(\frac{h}{m v}\)
Where λ = Wavelength of wave associated with electron
m = Mass of the electron
h = Planck’s constant
mv = \(\frac{h}{\lambda}\)
or mvr = \(\frac{h r}{\lambda}\) ……………. (ii)
From equation (i) and (ii)
∴ \(\frac{h}{\lambda} r=\frac{2 h}{2 \pi}\)
\(\frac{r}{\lambda}=\frac{n}{2 \pi}\)
2πr = nλ
Now, circumference of the electron in the nth orbital state of Hydrogen atom with radius r is nλ.

(B) If n is quantum number of the highest energy level involved in the transitions, then the total number of possible lines emitted is
N = \(\frac{n(n-1)}{2}\)
Third excited state means fourth energy level i.e., n = 1. So, highest number is n = 4.
Thus, possible spectral lines
N = \(\frac{4(4-1)}{2}\)
= \(\frac{4 \times 3}{2}\) = 6
The maximum possible number of spectral lines is 6.

CBSE Sample Papers for Class 12 Physics Term 2 Set 8 with Solutions

SECTION – C
(Section C consists one case study-based question of 5 marks.)

Question 12.
Due to movement of holes and electrons along the electric field sets up current. There are few basic features of forward biasing. Within the junction diode the current is due to both types of majority charge carriers but in external circuit it is due to electrons only. The current is due to diffusion of majority charge carriers through the junction and is of the order of milliamperes. In the same way the current is set up diode is reverse biased. There are two basic features of reverse biasing. Within junction diode the current is due to both types of minority charge carriers but in external circuit it is due to electrons only. The current is due to minority charge carriers through the junction and is very small of the order of microampere.
CBSE Sample Papers for Class 12 Physics Term 2 Set 8 with Solutions 6
CBSE Sample Papers for Class 12 Physics Term 2 Set 8 with Solutions 7
(A) When the forward bias voltage of a diode is changed from 0.6 V to 0.7 V, the current changes from 5 mA to 15 mA. Then its forward bias resistance is:
(i) 0.01
(ii) 0.1
(iii) 10.0
(iv) 100.00

(B) In the circuit, if the forward voltage drop for the diode is 0.5 V, the current will be:
0.5 V
CBSE Sample Papers for Class 12 Physics Term 2 Set 8 with Solutions 8
(i) 3.4 mA
(ii) 2 mA
(iii) 2.5 mA
(iv) 3 mA

(C) In a reverse biased diode when the applied voltage changes by 1 V, the current is found to change by 0.5 The reverse bias resistance of the diode is:
(i) 2 × 105 Ω
(ii) 2 × 106 Ω
(iii) 200 Ω
(iv) 2Ω

(D) In the given figure, which of the diodes are forward biased?
CBSE Sample Papers for Class 12 Physics Term 2 Set 8 with Solutions 9
(i) 1, 2, 3
(ii) 2,4, 5
(iii) 1, 3, 4
(iv) 2, 3, 4

CBSE Sample Papers for Class 12 Physics Term 2 Set 8 with Solutions

(E) In a diode, when there is a saturation current, the plate resistance will be:
(i) Data insufficient
(ii) Zero
(iii) Some finite quantity
(iv) Infinite quantity (5)

(A) (c) 10
Explanation: Forward biased resistance
\(\frac{\Delta V}{\Delta I}\) = \(\frac{0.7-0.6}{(15-5) \times 10^{-3}}\)
= \(\frac{0.1}{10 \times 10^{-3}}\) = 10Ω

Caution
The resistance in reverse bias is different from forward bias. Forward bias resistance is low whereas reverse bias resistance is high.

(B) (a) 3.4 mA
Explanation: When diode is forward biased, then there is a small voltage drop across it
i = \(\frac{V-V^{\prime}}{R}\)
Given, V = 8 volt,
V’ = 0.5 volt,
R = 2.2 kΩ
= 2.2 × 103Ω
∴ i = \(\frac{8-0.5}{2.2 \times 10^{5}}=\frac{7.5 \times 10^{-5}}{2.2}\)
= 3.4 × 10-3 A
= 3.4 mA

Related Theory
For forward bias, the voltage of an anode is greater than cathode and for reverse bias, the voltage for cathode is greater than an anode.

(C) (b) 2 x 106Ω
Explanation: Reverse resistance
= \(\frac{\Delta V}{\Delta l}\) = \(\frac{1}{0.5 \times 10^{-6}}\)
= 2 x 106 Ω

(D) (b) 2, 4, 5
Explanation: In figure 2, 4 and 5 P-crystals are more positive as compared to N- crystals.

(E) (d) Infinite quantity
Explanation: We know that plate resistance is given by:
∴ rp = \(\frac{\Delta V}{\Delta l}\)
where ΔV is change in voltage and Δl is change in current.
Also, at saturation change in current is zero.
∴ rp = \(\frac{\Delta V}{0}\) = ∞

Hence, plate resistance will be infinite.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 2 with Solutions

Students can access the CBSE Sample Papers for Class 12 Business Studies with Solutions and marking scheme Term 2 Set 2 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 2 with Solutions

Time allowed: 2 Hours
Maximum Marks: 40

General Instructions:

  • This is a Subjective Question Paper containing 12 questions.
  • This paper contains 4 questions of 2 marks each, 4 questions of 3 marks each and 4 questions of 5 marks each.
  • 2 marks questions are Short Answer Type Questions and are to be answered in 30-50 words.
  • 3 marks questions are Short Answer Type Questions and are to be answered in 50-80 words.
  • 5 marks questions are Long Answer Type Questions and are to be answered in 80-120 words.
  • This question paper contains Case/Source Based Questions.

Question 1.
Name and explain the method of training in which trainees learn on the equipments they will be using. (2)
Answer:
Vestibule training: Employees learn their jobs on the equipment they will be using, but the training is conducted away from the actual work floor. Actual work environments are created in a classroom and employees use the same material, files and equipment. This is usually done when employees are required to handle sophisticated machinery and equipment. Vestibule training can be classified as off-the-job method of training.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 2 with Solutions

Question 2.
“Our assets walk out of the door each evening. We have to make sure that they come back the next morning”. Name and explain any two advantages of the function of management. (2)
Answer:
This statement relates to staffing function of management. Staffing is the process of determining the man’s power needed to meet the company’s objective and recruiting, selecting, training and developing the new and existing staff.
The advantages of staffing are: (Any two)

  • Growth of enterprise: By appointing efficient staff, staffing ensures continuous survival and growth of the enterprise.
  • Placing right person at the right job: It ensures higher performance by placing right person on the right job by proper recruitment and selection.
  • Optimum utilisation of human resources: Through manpower planning and job analysis we can find out the number of employees and type of employees required in the organisation.

Question 3.
Why is it said that controlling is looking back? (2)
Answer:
Controlling is looking back as it is like a post-mortem of past activities to find out deviations from the standards established. Controlling is done with an aim to check the factors responsible for poor performance or deviation in the actual performance, so that such mistakes are not repeated in future and the organisation can achieve its predetermined objectives.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 2 with Solutions

Question 4.
“Money market is essentially a market for short term funds” State any two money market instruments. (2)
Answer:
The money market instruments are: (Any two)
(1) Treasury Bill: Treasury Bill is basically an instrument of short-term borrowing by the Government of India maturing in less than one year.

(2) Commercial Paper: Commercial paper is a short-term unsecured promissory note, negotiable and transferable by endorsement and delivery with a fixed maturity period.

(3) Call money: Call money is short term finance repayable on demand, with a maturity period of one day to fifteen days used for inter bank transactions.

(4) Certificate of Deposit: Certificate of deposit are unsecured, negotiable, short term instruments in bearer form, issued by commercial banks and development financial institutions.

(5) Commercial Bill: Commercial bill is a bill of exchange used to finance the working capital requirements of business firms.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 2 with Solutions

Question 5.
How does directing facilitate introduction of needed changes in the organisation? (3)
Answer:
Directing facilitates introduction of needed changes in the organisation. Generally, people have a tendency to resist changes in the organisation. Effective directing through motivation, communication and leadership helps to reduce such resistance and develop required cooperation in introducing changes in the organisation.

For example, if a manager wants to introduce new system of accounting, there may be initial resistance from accounting staff But, if manager explains the purpose, provides training and motivates with additional rewards, the employees may accept change and cooperate with manager.

Question 6.
“Directing techniques must help every individual in the organisation to contribute to his maximum potential for achievement of organisational objectives.” Explain.
OR
“Training is used to indicate the process by which attitudes, skills and abilities of employees to perform specific jobs are increased.” Explain the benefits of training to employees. (3)
Answer:
This principle emphasises that directing techniques must help every individual in the organisation to contribute to his maximum potential for achievement of organisational objectives. It should bring out untapped energies of employees for the efficiency of organisation.

For example, a good motivation plan with suitable monetary and non-monetary rewards can motivate an employee to contribute his maximum efforts for the organisation as he or she may feel that their efforts will bring them suitable rewards.
OR
The benefits of training activity to the employees are as follows:
(1) Improved skills and knowledge due to training lead to better career of the individual.
(2) Increased performance by the individual help him to earn more.
(3) Training makes the employee more efficient to handle machines. Thus, less prone to accidents.
(4) Training increases the satisfaction and morale of employees.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 2 with Solutions

Question 7.
Why is it said that controlling is a continuous activity? (3)
Answer:
Controlling is a continuous activity. It is a function that brings back the management cycle back to the planning function. The controlling function finds out how far actual performance deviates from standards, analyses the causes of such deviations and attempts to take corrective actions based on the same.

This process helps in formulation of future plans in the light of the problems that were identified and, thus, helps in better planning in the future periods. Thus, controlling only completes one cycle of management process and improves planning in the next cycle.

Question 8.
Dheeraj wants to start a business of selling N-95 masks after the outbreak of the global pandemic of COVID-19. Due to the uncertain market conditions he wants to make a low investment in fixed capital. Suggest how the decisions related to the choice of technique and financing alternatives can help Dheeraj in ensuring a low investment in fixed capital requirements. (3)
Answer:
Choice of Technique: As Dheeraj wishes to stick to a low investment model, we may suggest him to go with the labour-intensive approach to manufacture N-95 masks. Since better technology would cost him much and his risk appetite is not conducive for capital intensive techniques of production.

Financial Alternatives: As Dheeraj wishes to stick to a low investment model, we may suggest him to go with the lease option for fixed assets like building, heavy machinery etc. as this may reduce his investments requirement in the business.

Explanation:
Choice of Technique: Some organisations are capital intensive whereas others are labour intensive. A capital intensive organisation requires higher investment in plant and machinery as it relies less on manual labour. Labour intensive organisations, on the other hand, require less investment in fixed assets. Here, in this case, Deeraj can choose labour intensive option as it will require low investment.

Financing Alternatives: A developed financial market may offer leasing facilities as an alternative to outright purchase. As Dheeraj wants to make low investment in fixed capital he can take fixed asset i.e. land and building and plant and machinery on lease. When an asset is taken on lease, the firm pays lease rentals and uses it. By doing so, it avoids huge sums required to purchase it

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 2 with Solutions

Question 9.
Zenith Ltd. is a highly reputed company and many people wanted to join this company. The employees of this organisation are very happy and they discuss how they came in contact with this organisation.

Aman said that he was introduced by the present Sales Manager, Mr. John. Benu said that he had applied through the newspaper and was appointed as the H.R. Manager. Vaibhav said that he was neither related to any employee of the organisation nor was there any advertisement in the newspaper, even then, he was directly called from IIM Ahmedabad from where he was about to complete his MBA.

(A) The above discussion is indicating an important function of management. Name the function of management.
(B) The management function identified in part (A) follows a particular process. Explain the step of this process which is being discussed in the above paragraph.
OR
Prateekis working in a multinational company in Noida. He was running a temperature for the last many days. When his blood was tested, he was found to be positive for malaria. He was admitted in a hospital and a blood transfusion was advised by the doctors as his condition was very serious.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 2 with Solutions

One of his colleagues sent a text message to his superior, Mr. B. Chatterjee. Mr. B. Chatterjee immediately sent a text message to the employees of the organisation requesting them to donate blood for Prateek. When the General Manager came to know about it, he ordered for fumigation in the company premises and cleaning the surroundings. From the above paragraph, quote lines that indicate formal and informal communication. State different types of informal communication. (5)
Answer:
(A) The function of management discussed above is staffing. Staffing is ‘putting people to jobs’. It begins with workforce planning and includes different other function like recruitment, selection, training, development, promotion, compensation and performance appraisal of work force. In other words, staffing is that part of the process of management which is concerned with obtaining, utilising and maintaining a satisfactory and satisfied work force.

(B) The step of this process which is being discussed in the above paragraph is recruitment. Recruitment refers to the process of finding possible candidates for a job or a function. It has been defined as ‘the process of searching for prospective employees and stimulating them to apply for jobs in an organisation.’ Advertising is commonly part of the recruitment process, and can occur through several means, through newspapers, using newspaper dedicated to job advertisement, through professional publication, using advertisements placed in windows, through a job center, through campus interviews, etc.
OR
Formal communication: Formal communication flows through official channels designed in the organisation chart. This communication may take place between a superior and subordinate, a subordinate and superior or among same cadre employees or managers
“When the general manger came to know about it, he ordered for fumigation in the company premises and cleaning surroundings.”

Informal communication: Communication that takes place without following the formal lines of communication is said to be informal communication. “One of his colleagues sent a text message to his superior, Mr. B. Chatterjee. Mr. B. Chatterjee immediately sent a text message to the employees of the organisation requesting them to donate blood for Prateek.”

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 2 with Solutions 1

Types of informal communication:

Grapevine Network: Grapevine communication may follow different types of network. In single strand network, each person communicates to the other in sequence. In gossip network, each person communicates with all on non-selective basis.

In probability network, the individual communicates randomly with other individual. In cluster, the individual communicates with only those people whom he trusts. Of these four types of networks, cluster is the most popular in organisations.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 2 with Solutions

Question 10.
Shyam wanted to start a business of selling handicrafts by getting in touch with the craftsmen in the rural areas of Bengal. He wants to make a low investment in fixed Capital. Advise him in taking suitable decisions regarding the Nature of Business, Scale of operations and Financing Alternatives in a developed financial market) that he needs to take for the purpose. (5)
Answer:
(A) The function of management discussed above is staffing. Staffing is ‘putting people to jobs’. It begins with workforce planning and includes different other function like recruitment, selection, training, development, promotion, compensation and performance appraisal of work force. In other words, staffing is that part of the process of management which is concerned with obtaining, utilising and maintaining a satisfactory and satisfied work force.

(B) The step of this process which is being discussed in the above paragraph is recruitment. Recruitment refers to the process of finding possible candidates for a job or a function. It has been defined as ‘the process of searching for prospective employees and stimulating them to apply for jobs in an organisation.’

Advertising is commonly part of the recruitment process, and can occur through several means, through newspapers, using newspaper dedicated to job advertisement, through professional publication, using advertisements placed in windows, through a job center, through campus interviews, etc.

Question 11.
Stock exchange acts as a regulator of the securities market, it creates a continuous market where the securities are bought and sold. It gives investors the chance to disinvest and reinvest. Through this process of disinvestment and reinvestment, savings get channelised into their most productive investment avenues. To ensure that the investing public gets a safe and fair deal in the market, the membership of the stock exchange is well regulated and its dealings are well defined according to the existing legal framework.
It also ensures wider share ownership by regulating new issues, better trading practices and taking effective steps in educating the public about investments, various functions performed by the Stock. Exchange are discussed in the above para. By quoting the lines from the above para, state any four functions of stock exchange. (5)
Answer:
The various functions performed by the Stock Exchange are:
(1) Providing liquidity and marketability to existing securities as the stock exchange creates a continuous market where the securities are bought and sold. It gives investors the chance to disinvest and reinvest

(2) Contributes to economic growth as through process of disinvestment and reinvestment, savings get channelised into their most productive investment avenues.

(3) Safety of transactions as the membership of the stock exchange is well regulated and its dealings are well defined according to the existing legal framework. This ensures that the investing public gets a safe and fair deal on the market.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 2 with Solutions

(4) Spreading of equity cult as the stock exchange ensures wider share ownership by regulating new issues, better trading practices and taking effective steps in educating the public about investments.

Question 12.
‘RO Youth Club’ 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 RO Youth Club members decided to clean the premises. During their cleanliness drive, they realised that the Old Age Home also required pest control. (5)

But some of the inmates of the Old Age Home were reluctant for it because they believed that the pest control may create health problems for them. RO Youth Club, therefore, decided to provide ethical, safe and odourless pest control. They showed to the inmates of the 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. The effect of the pest control started wearing off after a fortnight.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 2 with Solutions

RO Youth Club contracted the pest control company which kept on postponing their visit. After waiting fbr a month, RO Youth Club filed a case in the consumer court. The consumer court was satisfied about the genuineness of the complaint and issued necessary directions to the pest control company. State any eight directions that might have been issued by the court.
OR
Aman, a degree holder in Entrepreneurship came to know about Piplantri Village located in Rajasthan, where in 2006 an initiative was started, in which 111 trees are planted every time a girl child is born. To keep termites away from the trees the villagers have planted 2.5 million. Aloe Vera plants around the trees. This has turned the village into an oasis, as the planting of trees led to higher water levels.
OR
Aman decided to visit the village to start a business unit, for the processing and marketing of Aloe Vera into juices, gels and other products. However, on visiting village Aman found that the villagers were suffering exploitation at the hands of local merchants who were engaged in unscruplous, exploitative trade practices like hoarding and black marketing of food product sand also selling unsafe, adulterated products to the villagers. After looking at their plight instead of a business organisation he decided to set up an organisation for the protection and promotion of the consumer interest of the villagers. State the functions that the organisation established by Aman will be performing (Any five points). (5)
Answer:
The directions that might have been issued by the court:
(1) To remove the deficiency in service.
(2) To refund the price paid for the service provided.
(3) To pay a reasonable amount of compensation for any loss suffered by the inmates of old age home.
(4) To pay punitive damages.
(5) To discontinue the unfair/ restrictive trade practice and not to repeat the same in future.
(6) To pay any amount (not less than 5% of the value of the service provided) to be credited to the Consumer Welfare Fund or any other organisation/person, to be utilised in the prescribed manner.
(7) To issue corrective advertisement to neutralize the effect of misleading pamphlet.
(8) To pay adequate costs to RO Youth Club.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 2 with Solutions
OR
The organisation established by Aman will be performing the following functions.(any five)
(1) Educating the general public about consumer rights by organising training programmes, seminars and workshops.
(2) Publishing periodicals and other publications to impart knowledge about consumer problems, legal reporting, reliefs available and other matters of interest.
(3) Encouraging consumers to strongly protest and take an action against unscrupulous, exploitative and unfair trade practices of sellers.
(4) Carrying out comparative testing of consumer products in accredited laboratories to test relative qualities of competing brands and publishing the test results for the benefit of consumers.
(5) Providing legal assistance to consumers by way of providing aid, legal advice etc. in seeking legal remedy.
(6) Filing complaints in appropriate consumer courts on behalf of the consumers.
(7) Taking an initiative in filing cases in consumer courts in the interest of the general public, not for any individual.

CBSE Sample Papers for Class 12 Physics Term 2 Set 9 with Solutions

Students can access the CBSE Sample Papers for Class 12 Physics with Solutions and marking scheme Term 2 Set 9 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 12 Physics Standard Term 2 Set 9 with Solutions

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions:

  • There are 12 questions in all. All questions are compulsory.
  • This question paper has three sections: Section A, Section B and Section C.
  • Section A contains three questions of two marks each, Section B contains eight questions of three marks each, Section C contains one case study-based question of five marks.
  • There is no overall choice. However, an internal choice has been provided in one question of two marks and two questions of three marks. You have to attempt only one of the chokes in such questions.
  • You may use log tables if necessary but use of calculator is not allowed.

SECTION – A
(Section A contains 3 questions of 2 marks each.)

Question 1.
Number of protons and number of neutrons are same on either side of a nuclear reaction. Then how is it said that energy released in a nuclear reaction is due to conversion of mass.
OR
What is a p-n junction diode and define the term dynamic resistance for the junction diode? (2)
Answer:
Total binding energy of nuclei on one side of the nuclear reaction may not be equal to that on the other side of the reactions. This fact tells that only rest mass of neutrons and protons is same on each side of the reaction difference in total binding energy on both sides can be referred to as difference in total mass in a nuclear reaction.
OR
A p-n junction diode is a single crystal of Germanium or Silicon doped in such a manner that one half portion of it acts as a p-type semiconductor and other half acts as a n-type semiconductor. As soon as a p-n junction is formed, holes from p-region and electrons from n-region diffuse which results in development of potential barrier across the junction and opposes the further diffusion of holes and electrons through the junction.
The dynamic or alternating current resistance of diode is the ratio of small applied voltage to the corresponding change in current.
rd = \(\frac{\Delta V}{\Delta l}\)
Above the threshold voltage, the diode characteristic is linear. In linear region, dynamic resistance is almost independent of voltage and Ohm’s law is obeyed.

CBSE Sample Papers for Class 12 Physics Term 2 Set 9 with Solutions

Question 2.
Find the maximum intensity in case of interference of n identical waves each of intensity l0 if the sources are:
(A) Coherent
(B) Incoherent (2)
Answer:
(A) Coherent sources
Let the amplitude be A for each wave then,
AR = (A + A + …)n times ,
= nA
lR ∝\(\) = n2l0

(B) Incoherent Sources
l = l0 + l0…. )n times
= nl0

Question 3.
State principle of reversibility of light. Define lateral shift. (2)
Answer:
Principle of reversibility of light states that if the final path of ray of light after it has suffered several reflections and refractions is reversed, it retraces its path exactly.

Lateral shift is the perpendicular distance between the incident and emergent rays when light is incident obliquely on a refracting slab with parallel faces.

SECTION – B
(Section B consists of 8 questions of 3 marks each.)

Question 4.
Answer the following questions:
(A) In a double slit experiment using light of wavelength 600 nm, the angular width of the fringe formed on a distant screen is 0.1°. Find the spacing between the two slits.
(B) Light of wavelength 5000 A propagating in air gets partly reflected from the surface of water. How will the wavelengths and frequencies of the reflected and refracted light be affected?
OR
(A) Describe any two characteristic features which distinguish between interference and diffraction phenomena. Derive the expression for the intensity at a point of the interference pattern in Young’s double slit experiment. (3)
Answer:
(A) Angular width (θ) of fringe in double-slit experiment is given by
θ = \(\frac{\lambda}{d}\)
Where d = Spacing between the slits.
Given: Wavelength of light,
λ = 600 nm
Angular width of fringe,
θ = 0.1°
= 0.1 × \(\frac{\lambda}{180}\) rad
= 0.0018 rad
∴ d = \(\frac{\lambda}{\theta}\)
d = \(\frac{600 \times 10^{-9}}{18 \times 10^{-4}}\) = 33.33 × 10-5
⇒ d = 0.33 × 10-3 m

(B) The frequency and wavelength of reflected wave will not change.
The refracted wave wiLl have same frequency, only wavelength will change.
The velocity of light v in water is given by
v = λf
where, v = Velocity of light
f = Frequency of light
λ = Wavelength of light As light ray in travelling from rarer (air) medium to denser medium, its speed will decrease. Hence wavelength (λ) will also decrease.

ReLated Theory
When a light ray traveLs from rarer medium to denser medium, then its speed and wavelength both will decrease.
(A)

Interference Diffraction
1. It is the result of interaction of light coming from two different wave fronts originating from two coherent sources. 1. It is the result of interaction of light come from different parts of same wavefronts.
2. All the bright fringes are of same intensity. 2. The bright fringes are of varying intensity (Intensity of bright fringes decreases from central bright fringe on either sides.)

A sources of monochromatic light illuminates two narrow slits S1 and S2. The two illuminated slits act as the two coherent sources. The two slits is very close to each other and at equal distance from source. The wave front S1 and S2 spread in all direction and superpose and produces dark and bright fringe on screen. Let the displacement of waves from Si and S2 at point P on screen at time t is:
CBSE Sample Papers for Class 12 Physics Term 2 Set 9 with Solutions 1
y1 = a1sin ωt
y2 = a2 sin (ωt + Φ)
The resultant displacement at point P is given by
y = y1 + y2
= a1 sin ωt + a2 sin (ωt + Φ)
= a1 sin ωt + a2 sin ωt cos Φ
+ a2 cos ωt sin Φ
= (a1 + a2 cos Φ) sin ωt + a2 sin Φ cos ωt …………. (i)
Let, a1 + a2 cos Φ
= A cos Φ …………. (ii)
a2 sin Φ = A sin Φ …………. (iii)

Therefore, equation (i) becomes
y = A cos θ sin ωt + A sin θ cos ωt
= A sin (ωt + θ)
This is the resultant displacement.
Now, squaring and adding equations (ii) and (iii)
A2 cos2 θ + A2 sin2θ
= (a1 + a2 cos Φ)2 + a22 sin2 Φ
A2 = a12 + a22 + 2a1 a2 cos Φ

The is intensity of light is directly proportional to the square of the amplitude
i.e., I = a12 + a22 + 2a1 a2 cos Φ

This is the expression for intensity at a point of interference pattern.
or I = I1+ I2 + \(2 \sqrt{I_{1} I_{2}}\) cos Φ

CBSE Sample Papers for Class 12 Physics Term 2 Set 9 with Solutions

Question 5.
(A) On what factor does the velocity of EM waves depends on?
(B) The magnetic field in a travelling
electromagnetic wave has a peak value of 20 nT. Find the peak value of electric field strength? (3)
Answer:
(A) The velocity of electromagnetic wave
depends on electric and magnetic properties of the medium.

(B) Here,
B0 = 20nT
= 20 x 10-9T,
c = 3 x 108 m/s
E0 = cB0
= 3 x 108 x 20 x 10-9
= 6 V/m

Question 6.
(A) Draw graphs showing variation of photoelectric current with applied voltage for two incident radiations of equal frequency and different intensities. Mark the graph for the radiation of higher intensity.
(B) An α-particle and a proton are accelerated through the same potential difference. Find the ratio of their de Broglie wavelengths. (3)
Answer:
(A) Graph for photoelectric current (I) versus applied potential for radiations of same frequency and varying intensity.
CBSE Sample Papers for Class 12 Physics Term 2 Set 9 with Solutions 2

(B)
CBSE Sample Papers for Class 12 Physics Term 2 Set 9 with Solutions 3
CBSE Sample Papers for Class 12 Physics Term 2 Set 9 with Solutions 4
Caution
Students are often confused in solving this problem. Here, de-Broglie wavelength is inversely proportional to the square root of mass and charge.

Question 7.
What are the important considerations required while fabricating a p-n junction diode to be used as a light emitting diode? (3)
Answer:
(A) There is a very little resistance to limit the current in LED. Therefore, a resistor must be used in series with the LED to avoid any damage to it.

(B) The reverse breakdown voltage of LEDs is very low, typically around 5 V. Therefore, care should be taken while fabricating a p-n junction diode so that the p-side should only attached positive side of the battery as LED easily get damaged by small reverse voltage.

(C) The semiconductors used for fabrication of visible LEDs must have at least band gap of 1.8 eV.

CBSE Sample Papers for Class 12 Physics Term 2 Set 9 with Solutions

Question 8.
(A) What is the position of an object
relative to the objective of compound microscope? Where is its image formed?
(B) The magnifying power of objective of compound microscope is 5. If the magnifying power of microscope is 30, then what is the magnifying power of eyepiece? (3)
Answer:
(A) When object is placed slightly larger than f0 then the final image is formed at infinity.

(B) M = M0 x Me
Here, M = 30
and M0 = 5
Me = \(\frac{\mathrm{M}}{\mathrm{M}_{o}}\)
= \(\frac{30}{5}\) = 6

Question 9.
(A) How does the de-Broglie wavelength of a charged particle change when accelerating potential increases?
(B) A proton and an a-particle have the same de-Broglie wavelength. Determine the ratio of:
(A) their accelerating potentials.
(B) their speeds. – (3)
Answer:
(A) λ ∝ \(\frac{1}{\sqrt{V}}\), WhenV increases, λ decreases.

(B) (i) The de-Broglie wavelength of a particle is given by
λ = \(\frac{h}{\sqrt{2 m q V}}\)
where, V is the accelerating potential of the particle.
It is given that
λproton = λalpha
⇒ \(\frac{h}{2 m_{p} q_{p} V_{p}}\) = \(\frac{h}{2 m_{\alpha} q_{\alpha} V_{\alpha}}\)
\(\sqrt{2 m_{\alpha} q_{\alpha} V_{\alpha}}\) = \(\sqrt{2 m_{p} q_{p} V_{p}}\)
On squaring both sides, we get
2mαqαVα = 2mpqpVp
⇒ \(\frac{V_{p}}{V_{\alpha}}\) = \(\frac{m_{\alpha} q_{\alpha}}{m_{p} q_{p}}\)
= \(\frac{4 m_{p} \times 2 q_{p}}{m_{p} q_{p}}\)
[∵ma = 4mp and qα = 2qp]
= \(\frac{8}{1}\)

(B) We can also write de-Broglie wavelength as:
λ = \(\frac{1}{2 \pi f C}\)

where h is Planck’s constant, m is mass of the particle and v is the speed of the particle.
It is given that
λproton = λalpha
We know
malpha = 4mproton
∴ λalpha = \(\frac{h}{4 m_{\text {proton }} V_{\text {alpha }}}\)
⇒ Now L
\(\frac{h}{m_{\text {proton }} v_{\text {proton }}}\) = \(\)
\(\frac{h}{4 m_{\text {proton }} v_{\text {alpha }}}\) = 4

CBSE Sample Papers for Class 12 Physics Term 2 Set 9 with Solutions

Question 10.
Distinguish between intrinsic semiconductors
and extrinsic semiconductors. 3
Answer:

Intrinsic Semiconductors Extrinsic Semiconductors
These ore pure semiconducting tetravaLent crystals. These are conducting tetravalent crystals doped with impurity atoms of group III or V.
Their electrical conductivity is Low Their electrical. conductivity is high.
There is no permitted energy state between valence and conduction bands. There is permitted energy state of the impurity atom between vaLence and conduction bands.
The number of free electrons in the conduction band is equal to the number of hoLes in valence band. The electrons are majority charge carriers in n-type semiconductors while hoLes are majority charge carriers in p-type semiconductors.
Their electrical conductivity depends on temperature. Their electrical, conductivitçj depends on the temperature as well os on the dopant concentration.

Question 11.
(A) What is the maximum number of spectral lines emitted by a hydrogen atom when it is in the third excited state? (B) The velocity of electron in the first Bohr’s orbit of radius 0.5 A.U. is 2.25 x 106 m/s. Calculate the period of revolution of the electron in the same orbit
OR
What is a nuclear chain reaction? (3)
Answer:
(A) n = 4, number of maximum transition
= \(\frac{n}{2}\) (n – 1)
= 6

(B) Here, r = 0.5A.U.
= 0.5 × 1.5 × 1011 m
[1 A.U. = 1.5 × 1011 m]
v = 2.25 × 106m/s
velocity of.electron in nth orbit
\(\frac{1}{137}\) , \(\frac{c}{n}\)
Period of revolution
= \(\frac{2 \pi}{v}\)
= \(\frac{2 \pi r \times 137 \times n}{v}\)
= \(\frac{2 \times 3.14 \times 0.5 \times 1.5 \times 10^{11} \times 137 \times 1}{2.25 \times 10^{6}}\)
= 2.86 × 108s
OR
The equation of fission of
CBSE Sample Papers for Class 12 Physics Term 2 Set 9 with Solutions 5
These three secondary neutrons produced in the reaction may cause of fission of
three more (\({ }_{92}^{235} U\)) and give 9 neutrons, which in turn, may cause of nine more fission of (\({ }_{92}^{235} U\)) ar|d so on. Thus, a continuous ‘Nuclear Chain reaction would start. If there is no control on chain reaction then in a short time (~ 10-6 sec.) a huge amount of energy will be released. (This is the principle of ‘Atom bomb’). If chain reaction is controlled then produced energy can be used for peaceful purposes. For examplenuclear reactor (Based on fission) generates electricity.

CBSE Sample Papers for Class 12 Physics Term 2 Set 9 with Solutions

SECTION – C
(Section C consists one case study-based question of 5 marks.)

Question 12.
As the focal length of the lens varies from colour to colour, the magnification m = \(\)
produced by the lens also varies from colour to colour. Therefore, for little finite sized objects, the image due to different colours formed by the lens are of different sizes. The formation of images of different colours in different sizes is called lateral chromatic aberration.
Axial chromatic aberration
CBSE Sample Papers for Class 12 Physics Term 2 Set 9 with Solutions 6
(A) An object is placed on the axis of a convex lens. Its image is formed 80 cm from the object. The magnification is 3. The focal length of the lens is:
(i) 15 cm
(ii) 20 cm
(iii) 40 cm
(iv) 45 cm

(B) The sun’s diameter is 1.4 x 109 m and its distance from the earth is 1011 m.
Determine the diameter of its image, formed by a convex lens of focal length 2 m.
(i) 0.7 cm
(ii) 1.4 cm
(iii) 2.8 cm
(iv) zero (i.e., point image)

(C) The combination of two lenses of focal lengths 20 cm and -20 cm in contact has the focal length of:
(i) 50 cm
(ii) Infinite
(iii) 10 cm
(iv) 60 cm

(D) Spherical aberration in thin lenses can be reduced by:
(i) Using monochromatic light
(ii) Increasing the size of the lens
(iii) Using a doublet combination
(iv) Using a circular annular mask over the lens.
(E) Two plano-convex lenses of equal focal lengths are arranged as shown. The ratio of combined focal length will be:
CBSE Sample Papers for Class 12 Physics Term 2 Set 9 with Solutions 7
(i) 1:2:3
(ii) 1:1:1
(iii) 1:2:1
(iv) 2:1:2
Answer:
(A) (i)
Explanation:
m = \(\frac{v}{u}\)
v = 3u
u + v = 80 cm
> 4u = 80
u = 20 cm
v = 3 x 20 cm
= 60 cm
using \(\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\)
\(\frac{1}{f}\) = \(\frac{1}{60}-\frac{1}{(-20)}\)
f = 15 cm

Caution
Students are often confused about the sign convention. Remember that u is always negative.
(B) (Hi) 2.8 cm
Explanation: Magnification
m = \(\frac{h^{\prime}}{h}\)
= \(\frac{-v}{u}\)
or h’ \(\frac{-v}{u}\) x h
= \(\frac{-2 \times\left(1.4 \times 10^{9}\right)}{10^{11}}\)
= -2.8 cm

CBSE Sample Papers for Class 12 Physics Term 2 Set 9 with Solutions

(C) (ii) Infinite
Explanation: Power = P1
= \(\)
and p2 = \(\)
= 5 D and -5D
Net power = 0
Therefore,
Focal length = \(\) = ∞

(D) (iv) Using a circular annular mask over the lens Explanation: In a thin lens, spherical aberration can be reduced by using a circular annular mask over the lens. It cuts off the marginal rays and focuses the par axial rays to a single point.

(E) (ii) 1:1:1
Explanation: The power of lens remains the same irrespective to the positioning of the lenses. So, the power and hence, their focal length in all three cases will remain the same.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

Students can access the CBSE Sample Papers for Class 12 Business Studies with Solutions and marking scheme Term 2 Set 1 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

Time allowed: 2 Hours
Maximum Marks: 40

General Instructions:

  • This is a Subjective Question Paper containing 12 questions.
  • This paper contains 4 questions of 2 marks each, 4 questions of 3 marks each and 4 questions of 5 marks each.
  • 2 marks questions are Short Answer Type Questions and are to be answered in 30-50 words.
  • 3 marks questions are Short Answer Type Questions and are to be answered in 50-80 words.
  • 5 marks questions are Long Answer Type Questions and are to be answered in 80-120 words.
  • This question paper contains Case/Source Based Questions.

Question 1.
Identify and explain the two sources of the source of recruitment which cannot be used when the existing staff is either insufficient or does not fulfill the eligibility criteria of the jobs to be filled. (2)
Answer:
Two sources of internal recruitment
(i) Promotion refers to shifting of an employee to a higher position, carrying higher responsibilities, facilities, status and pay. Transfer involves shifting of an employee from one job to another, one department to another, without substantive change in the responsibilities and status of the employee.

Explanation: The two sources of recruitment which cannot be used when the existing staff is either insufficient or does not fulfill the eligibility criteria of the jobs to be filled are promotion and transfer.

  • Promotion: Shifting of an employee to a higher position is termed as promotion. It involves carrying higher responsibilities, facilities, status and pay.
  • Transfer: The horizontal movement of an employees from one job to another, one department to another or from one shift to another, without a substantive change in the responsibilities and status is called transfer.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

Question 2.
‘MYKAA Limited ‘is dealing in all types of cosmetic products. It is enjoying increased demand for its product during the last few years. For the purpose of expansion the company needs  100 crores as additional capital. The company decides to raise funds through equity shares.
Chirag Kapoor, the finance manager of the company recommended that the shares may be sold through issuing houses or brokers. Identify and explain the method recommended by Mr. Kapoor through which the company can raise additional funds for expansion purposes. (2)
Answer:
Offer for Sale: Under this method securities are not issued directly to the public but are offered for sale through intermediaries like issuing houses or stock brokers. In this case, a company sells securities embolic at an agreed price to brokers who, in turn, resell them to the investing public.

Explanation: The method recommended by Mr. Kapoor is Offer for Sale. Intermediaries play essential role in this type of issue of securities. Companies approach intermediaries like issuing houses or stock brokers for issue of securities.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

Question 3.
Explain the two concepts which are part of the exercise which would reveal whether a company is understaffed, overstaffed or optimally staffed. (2)
Answer:

  • Workload analysis: This would enable an assessment of the number and types of human resources necessary for the performance of various jobs and accomplishment of organisational objectives.
  • Workforce analysis: This would reveal the number and type available.

Explanation: The two concepts which are part of the exercise which would reveal whether a company is understaffed, overstaffed or optimally staffed is workload analysis and workforce analysis.

The assessment of number and type of human resource available for performing a task in an organisation is called workforce analysis and the assessment of number and type of human resource required for performing a task in an organisation is called workload analysis.

Question 4.
“Measurement of a company’s progress may involve calculation of certain ratios like gross profit ratio, net profit ratio, and return on investment etc. at periodic intervals”. Identify the function of management involved in the above context. Also briefly explain the step in the process of the identified function discussed above. (2)
Answer:
(A) Controlling
(B) Measurement of actual performance Once performance standards are set, the next step is measurement of actual performance. Performance should be measured in an objective and reliable manner. There are several techniques for measurement of performance. These include personal observation, sample checking, performance reports, etc.

Explanation: The above context is related to controlling function of management and the step of controlling function discussed above is measurement of actual performance. Measurement of actual performance is done when performance standard are set. This step become easier when performance standards are set in quantitative term.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

Question 5.
Mr. Pawan Kumar, the CEO of an E-Commerce startup, which was facing the problem of huge employee turnover, decided to hold a meeting with the managers to discuss the issue. While addressing the managers in the meeting, he advised them to take certain measures which focus on psychological, social and emotional factors, in order to motivate employees.

Explain any two such measures discussed by him, when he suggested that job should be made interesting so that the job itself becomes a source of motivation, employees should be congratulated for good performance, also, stability regarding future income and work should be provided to employees, in order to develop a positive attitude among the subordinates(3)
Answer:
Non monetary incentives: (Any two)
(i) Job enrichment: It is concerned with designing jobs that include greater variety of work content, require higher level of knowledge and skill, etc,.

(ii) Employee recognition programmes: Recognition means acknowledgment with a show of appreciation.

(iii) Job security: Employees want their job to be secure. They want certain stability about income and work so that they do not feel worried about these aspects and work with greater zeal.

Explanation: Non monetary incentives:

  • Job enrichment: “Employees should be congratulated for good performance”.
  • Motivation: When jobs are enriched and made interesting, the job itself becomes a source of motivation to the individual.
  • Job security: “Stability regarding future income”. Every employee wants security and stability regarding his/her job. When they are assured of their job it works as a motivation for them.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

Question 6.
State any three points of importance of Directing.
Answer:
Importance of Directing: (Any three)
(i) Directing helps to initiate action by people in the organisation towards attainment of desired objectives.

(ii) Directing integrates employees’ efforts in the organisation in such a way that every individual effort contributes to the organisational performance.

(iii) Directing guides employees to fully realise their potential and capabilities by motivating and providing effective leadership.

(iv) Directing facilitates introduction of needed changes in the organisation.

(v) Effective directing helps to bring stability and balance in the organisation since it fosters cooperation and commitment among the people and helps to achieve balance among various groups, activities and the departments.

Explanation: Importance of directing can be seen by the following points:

  • Directing integrates employeesefforts in the organisation in such a way that every individual effort contributes to the organisational performance.
  • Directing facilitates introduction of needed changes in the organisation.
  • Directing helps to initiate action by people in the organisation towards attainment of desired objectives.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

OR

Define leadership as an element of Directing. Enumerate any two styles of Leadership. (3)
Answer:
Leadership indicates the ability of an individual to maintain good interpersonal relations with followers and motivate them to contribute for achieving organisational objectives, (or any other correct definition)

Styles of leadership (Any two):

  • Autocratic or Authoritarian leader gives orders and expects his subordinates to obey those orders.
  • Democratic or Participative leaders will develop action plans and make decisions in consultation with their subordinates.
  • Laissez faire or Free-rein leader does not believe in the use of power unless it is absolutely essential.

OR

Leadership is the art or process of influencing people so that they will strive willingly and enthusiastically towards the achievement of group goals.

The two styles of leadership are:
(i) Autocratic: In this style of leadership subordinates are suppose to obey the orders from their superiors. In autocratic leadership communication is only one-way with the subordinate only acting according to the command given by the manager.

Democratic In this style of leadership leader make plan with the consultation of his followers. He will encourage them to participate in decision making. Democratic In this style of leadership leader make plan with the consultation of his followers. He will encourage them to participate in decision making.

Question 7.
List any three factors affecting the Working Capital requirement of a company. (3)
Answer:
Factors affecting working capital requirement of the company (Any three):
(i) Nature of Business influences working capital requirements in a trading organisation which usually needs a smaller amount of working capital compared to a manufacturing organisation, while service industries which usually do not have to maintain inventory require less working capital.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

(ii) Scale of operations influences working capital requirements in large organisations which require a large amount of working capital as compared to the organisations which operate on a lower scale.

(iii) Business cycle affects the requirement of working capital by a firm, as in case of a boom a larger amount of working capital is required as compared to the period of depression.

(iv) Seasonal Factors affect the working capital requirement, as in peak season large amounts of working capital is required and lower amount is required in the lean season.

(v) Production cycle affects the working capital requirement, as it is higher in firms with longer processing cycles and lower in firms with shorter processing cycles.

(vi) Credit allowed in a firm with liberal credit policy results in a higher amount of debtors, increasing the requirement of working capital

(vii)Credit availed by a firm, to the extent to which the firm avails the credit on purchases the working capital requirement is reduced.

(viii) Operating efficiency may reduce the level of raw materials, finished goods and debtors resulting in lower requirement of working capital

(ix) Availability of raw material influences the working capital requirement as larger the lead time, larger the quantity of material to be stored and larger shall be the amount of working capital required.

(x) If the growth potential of a concern is perceived to be higher, it will require a larger amount of working capital.

(xi) Higher level of competitiveness may necessitate larger stocks and increases working capital requirement.

(xii) The working capital requirement of a business becomes higher with higher rate of marks inflation.

Explanation: The factors affecting working capital requirement are: (any three)

(i) Nature of Business: The basic nature of a business influences the amount of working capital required. A trading organisation usually needs a smaller amount of working capital compared to a manufacturing organisation.

This is because there is usually no processing. Therefore, there is no distinction between raw materials and finished goods. Sales can be effected immediately upon the receipt of materials, sometimes even before that.

In a manufacturing business, however, raw material needs to be converted into finished goods before any sales become possible. Other factors remaining the same, a trading business requires less working capital.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

(ii) Scale of Operations: For organisations which operate on a higher scale of operation, the quantum of inventory and debtors required is generally high. Such organisations, therefore, require large amount of working capital as compared to the organisations which operate on a lower scale.

(iii) Business Cycle: Different phases of business cycles affect the requirement of working capital by a firm. In case of a boom, the sales as well as production are likely to be larger and, therefore, larger amount of working capital is required. As against this, the requirement for working capital will be lower during the period of depression as the sales as well as production will be small.

(iv) Seasonal Factors: Most business have some seasonality in their operations. In peak season, because of higher level of activity, larger amount of working capital is required. As against this, the level of activity as well as the requirement for working capital will be lower during the lean season.

(v) Production Cycle: Production cycle is the time span between the receipt of raw material and their conversion into finished goods. Some businesses have a longer production cycle while some have a shorter one.

Duration and the length of production cycle, affects the amount of funds required for raw materials and expenses. Consequently, working capital requirement is higher in firms with longer processing cycle and lower in firms with shorter processing cycle.

(vi) Credit Allowed: Different firms allow different credit terms to their customers. These depend upon the level of competition that a firm faces as well as the credit worthiness of their clientele. A liberal credit policy results in higher amount of debtors, increasing the requirement of working capital.

(vii) Credit Availed: Just as a firm allows credit to its customers it also may get credit from its suppliers. To the extent it avails the credit on purchases, the working capital requirement is reduced.

(viii) Operating efficiency may reduce the level of raw materials, finished goods and debtors resulting in tower requirement of working capital

(ix) Availability of Raw Material: If the raw materials and other required materials are available freely and continuously, lower stock levels may suffice. If, however, raw materials do not have a record of un-interrupted availability, higher stock levels may be required.

In addition, the time lag between the placement of order and the actual receipt of the materials (also called lead time) is also relevant. Larger the lead time, larger the quantity of material to be stored and larger shall be the amount of working capital required.

(x) Growth Prospects: If the growth potential of a concern is perceived to be higher, it will require Larger amount of working capital so that it is able to meet higher production and sales target whenever required.

(xi) Level of Competition: Higher level of competitiveness may necessitate larger stocks of finished goods to meet urgent orders from customers. This increases the working capital requirement. Competition may also force the firm to extend liberal credit terms discussed earlier.

(xii) Inflation: With rising prices, larger amounts are required even to maintain a constant volume of production and sales. The working capital requirement of a business thus, become higher with higher rate of inflation.

It must, however, be noted that an inflation rate of 5%, does not mean that every component of working capital will change by the same percentage. The actual requirement shall depend upon the rates of price change of different components (e.g., raw material, finished goods, labour cost,) Finished goods as well as their proportion in the total requirement.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

Question 8.
Priya is a regional manager of XYZ. Ltd. She is a hardworking employee and is trying to reduce wastage of resources in her company. She has set standards for performance of different activities and is ensuring that targets are met according to these standards with minimal wastage of resources. She has set up CCTV cameras which helps her to keep a close check on the activities of the subordinates and know how the employees are performing.

She also rewards the employees with a bonus when these standards are met. She is trying her best to ensure a good performance of her team this year through the application of an important function of management. Explain any two benefits of the function of management highlighted above. (3)
Answer:
Importance of controlling (Any two):
(i) Accomplishing organisational goals: The controlling function measures progress towards the organisational goals and brings to light the deviations, if any, and indicates corrective action.

(ii) Ensuring Order and discipline: Controlling creates an atmosphere of order and discipline in the organisation. It helps to minimise dishonest behaviour by keeping a close check on their activities.

(iii) Making efficient use of resources: Each activity is performed in accordance with predetermined standards and norms. This ensures that resources are used in the most effective and effcient manner.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

(vi) Improving employee motivation: A good control system ensures that employees know welt in advance what they are expected to do and what are the standards of performance on the basis of which they will be appraised. It, thus, motivates them and helps them to give better performance.

Explanation: The function of management highlighted here is Controlling.

The importance of controlling is as follows: (any two)

(i) Accomplishing organisational goals: The controlling function measures progress towards the organisational goals and brings to light the deviations, if any, and indicates corrective action. It, thus, guides the organisation and keeps it on the right track so that organisational goals might be achieved.

(ii) Judging accuracy of standards: A good control system enables management to verify whether the standards set are accurate and objective. An efficient control system keeps a careful check on the changes taking place in the organisation and in the environment and helps to review and revise the standards in light of such changes.

(iii) Making efficient use of resources. By exercising control, a manager seeks to reduce wastage and spoilage of resources. Each activity is performed in accordance with predetermined standards and norms. This ensures that resources are used in the most effective and efficient manner.

(iv) Improving employee motivation: A good control system ensures that employees know well in advance what they are expected to do and what are the standards of performance on the basis of which they will be appraised. It, thus, motivates them and helps them to give better performance.

(v) Ensuring order and discipline: Controlling creates an atmosphere of order and discipline in the organisation. It helps to minimise dishonest behaviour on the part of the employees by keeping a close check on their activities. The box explains how an importexport company was able to track dishonest employees by using computer monitoring as a part of their control system.

(vi) Facilitating coordination in action: Controlling provides direction to all activities and efforts for achieving organisational goals. Each department and employee is governed by predetermined standards which are well coordinated with one another. This ensures that overall organisational objectives are accomplished.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

Question 9.
Enumerate any five rights of a consumer under the Consumer Protection Act, 2019.
Answer:
Rights of a Consumer under the Consumer Protection Act, 2019 (Any five):
(i) Right to safety: The consumer has a right to be protected against goods and services which are hazardous to life, health and property.

(ii) Right to be informed: The consumer has a right to have complete information about the product he intends to buy including its ingredients, date of manufacture, price, quantity, directions for use, etc.

(iii) Right to be assured: The consumer has the freedom to assess a variety of products at competitive prices.

(iv) Right to be heard: The consumer has a right to file a complaint and to be heard in case of dissatisfaction with a good or a service.

(v) Right to seek redressal: The consumer has a right to get relief against unfair trade practice of restrictive trade practices or unscrupulous exploitation in case the product or a service falls short of his expectation.

(vi) Right to consumer education: The consumer has a right to acquire knowledge and to be a well informed consumer throughout life.

Explanation: The Rights of a Consumer under the Consumer Protection Act, 2019: (any five)

(i) Right to Safety: The consumer has a right to be protected against goods and services which are hazardous to life, health and property. For example, electrical appliances which are manufactured with substandard products or do not conform to the safety norms might cause serious injury. Thus, consumers are educated that they should use electrical appliances which are ISI marked as this would be an assurance of such products meeting quality specifications.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

(ii) Right to be informed: The consumer has a right to have complete information about the product he intends to buy including its ingredients, date of manufacture, price, quantity, directions for use, etc. It is because of this reason that the legal framework in India requires the manufactures to provide such information on the package and Label of the product.

(iii) Right to be assured: The consumer has the freedom to access variety of products at competitive prices. This implies that the marketers should offer a wide variety of products in terms of quality, brand, prices, size, etc. and allow the consumer to make a choice from amongst these.

(iv) Right to be heard: The consumer has a right to file a complaint and to be heard in case of dissatisfaction with a good or a service. It is because of this reason that many enlightened business firms have set up their own consumer service and grievance cells. Many consumer organisations are also working towards this direction and helping consumers in redressal of their grievances.

(v) Right to seek redressal: The consumer has a right to get relief against unfair trade practice of restrictive trade practices or unscrupulous exploitation in case the product or a service falls short of his expectations. The Consumer Protection Act 2019 provides for redressal to the consumers including replacement of the product, removal of defect in the product, compensation paid for any loss or injury suffered by the consumer, etc.

(vi) Right to Consumer Education: The consumer has a right to acquire knowledge and to be a well informed consumer throughout life. He should be aware about his rights and the reliefs available to him in case of a product or service falling short of his expectations. Many consumer organisations and some enlightened businesses are taking an active part in educating consumers in this respect.
OR
Enumerate any five responsibilities of a Consumer Protection Act, 2019. (5)
Answer:
Responsibilities of a Consumer under the Consumer Protection Act, 2019 (Any five):
(i) Be aware of various goods and services available in the market so that an intelligent and wise choice can be made.

(ii) Buy only standardised goods as they provide quality assurance.

(iii) Learn about the risks associated with products and services, follow manufacturer’s instructions and use the products safely.

(iv) Read labels carefully so as to have information about prices, net weight, manufacturing and expiry dates, etc.

(v) Assert yourself to ensure that you get a fair deal.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

(vi) Be honest in your dealings. Choose only from legal goods and services and discourage unscrupulous practices.

(vii) Ask for a cash memo on purchase of goods or services.

(viii) File a complaint in an appropriate consumer forum in case of a shortcoming in the quality of goods purchased or services availed.

(ix) Form consumer societies which would play an active part in educating consumers and safeguarding their interests.

Explanation: The responsibilities of a Consumer under the Consumer Protection Act, 2019 are: (Any five)

(i) Be aware about various goods and services available in the market so that an intelligent and wise choice can be made.

(ii) Buy only standardised goods as they provide quality assurance. Thus, look for ISI mark on electrical goods, FPO mark on food products, Hallmark on jewelry, etc.

(iii) Learn about the risks associated with products and services, follow manufacturer’s instructions and use the products safely.

(iv) Read labels carefully so as to have information about prices, net weight, manufacturing and expiry dates, etc.

(v) Assert yourself to ensure that you get a fair deal.

(vi) Be honest in your dealings. Choose only from legal goods and services and discourage unscrupulous practices like black-marketing, hoarding, etc.

(vii) Ask for a cash memo on purchase of goods or services. This would serve as a proof of the purchase made.

(viii) File a complaint in an appropriate consumer forum in case of a shortcoming in the quality of goods purchased or services availed. Do not fail to take an action even when the amount involved is small.

(ix) Form consumer societies which would play an active part in educating consumers and safeguarding their interests.

(x) Respect the environment. Avoid waste, littering and contributing to pollution.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

Question 10.
State any five regulatory functions of the Securities and Exchange Board of India. (5)
Answer:
Regulatory Functions of Securities and Exchange Board of India (Any five)

  • Registration of brokers and sub-brokers and other players in the market.
  • Registration of collective investment schemes and Mutual Funds.
  • Regulation of stock brokers, portfolio exchanges, underwriters and merchant bankers and the business in stock exchanges and any other securities market.
  • Regulation of takeover bids by companies.
  • Calling for information by under-taking inspection, conducting enquiries and audits of stock exchanges and intermediaries.
  • Levying fee or other charges for carrying out the purposes of the Act.
  • Performing and exercising such power under Securities Contracts (Regulation) Act 1956, as may be delegated by the Government of India.

Explanation: Regulatory Functions of Securities and Exchange Board of India are: (any five)

  • Registration of brokers and subbrokers and other players in the market.
  • Registration of collective investment schemes and Mutual Funds.
  • Regulation of stock brokers, portfolio exchanges, underwriters and merchant bankers and the business in stock exchanges and any other securities market.
  • Regulation of takeover bids by companies.
  • Calling for information by undertaking inspection, conducting enquiries and audits of stock exchanges and intermediaries.
  • Levying fee or other charges for carrying out the purposes of the Act.
  • Performing and exercising such power under Securities Contracts (Regulation) Act 1956, as may be delegated by the Government of India.

Question 11.
In an interview with a leading news channel, Mr. Rakesh Kwatra, CEO of‘Get My Job” has suggested that the Companies which want more and more people to apply for jobs in their organisation should make the process of applying for jobs easier and candidate friendly.

It is for this reason, he said, that most progressive companies today have a short application process. He also said that the application form filled by the candidate is very important as it is the information supplied in the application forms, which helps the manager in eliminating unqualified or unfit job seekers.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

The company can create a mechanism that attempts to measure certain characteristics of individuals like aptitude, manual dexterity, and intelligence to personality. The candidate may then be called for an in-depth conversation to evaluate their suitability for the job.

(A) Name the process and steps in the process of identifying and choosing the best person out of a number of prospective candidates for a job discussed above.
(B) Also explain the next three steps in the process which can be subsequently performed by the company. (5)
Answer:
(A) Selection: Steps in the process of selection discussed:

  • Preliminary Screening.
  • Selection Tests.
  • Employment interview

(B) Next two steps:

(i) Reference and background checks:
Many employers request names, addresses and telephone numbers of references for the purpose of verifying information and gaining additional information on an applicant. Previous employers, known persons, teachers and university professors can act as references.

(ii) Selection Decision: The final decision has to be made from among the candidates who passed the tests, interviews and reference checks. The views of the concerned manager will be generally considered in the final selection.

(iii) Medical Examination: After the selection decision and before the job offer is made, the candidate is required to undergo a medical fitness test. The job offer is given to the candidate being declared fit after the medical examination.

Explanation:

(A) The process discussed here is Selection. The steps in the process of selection discussed are:

  • Preliminary Screening.
  • Selection Tests.
  • Employment interview

(B) The next three steps in the process are:

(i) Reference and Background Checks:
Many employers request names, addresses, and telephone numbers of references for the purpose of verifying information and, gaining additional information on an applicant. Previous employers, known persons, teachers and university professors can act as references.

(ii) Selection Decision: The final decision has to be made from among the candidates who pass the tests, interviews and reference checks. The views of the concerned manager will be generally considered in the final selection because it is he/she who is responsible for the performance of the new employee.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

(iii) Medical Examination: After the selection decision and before the job offer is made, the candidate is required to undergo a medical fitness test. The job offer is given to the candidate being declared fit after the medical examination.

Question 12.
Vansh Limited is a large and reputed company which manufactures ventilators. After the outbreak of ‘COVID-19’ in 2020 the company witnessed an increase in revenue by 40%. It has plans to further increase its production capacity and also start production of PPE kits, sanitisers and masks in 2022.

The Finance manager of the Company Mr. Rajiv feels confident about the future of the company and its liquidity position. Discuss the meaning of Dividend Decision and in the light of the above statement explain any two factors which should be considered by ‘Vansh Limited’ while formulating the dividend policy of the company.
Answer:
Dividend decision: The decision involved here is how much of the profit earned by the company (after paying tax) is to be distributed to the shareholders and how much of it should be retained in the business.

Factors affecting Dividend decision: (Any two)

(i) Amount of Earnings: Dividends are paid out of current and past earnings. Therefore, earnings are a major determinant of the decision about dividend.

(ii) Growth Opportunities: Companies having good growth opportunities retain more money out of their earnings so as to finance the required investment. The dividend in growth companies is, therefore, smaller, than that in the non-growth companies.

(iii) Cash Flow Position: The payment of dividend involves an outflow of cash. A company may be earning profit but may be short on cash. Availability of enough cash in the company is necessary for declaration of dividend.

(iv) Access to Capital Market: Large and reputed companies generally have easy access to the capital market and, therefore, may depend less on retained earnings to finance their growth. These companies tend to pay higher dividends than the smaller companies which have relatively low access to the market

Explanation: Dividend decision: Dividend is that portion of profit which is distributed to shareholders. The decision involved here is how much of the profit earned by company (after paying tax) is to be distributed to the shareholders and how much of it should be retained in the business. While the dividend constitutes the current income re-investment as retained earning increases the firm’s future earning capacity.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

The extent of retained earnings also influences the financing decision of the firm. Since the firm does not require funds to the extent of re-invested retained earnings, the decision regarding dividend should be taken keeping in view the overall objective of maximising shareholder’s wealth.

The factors affecting Dividend decision are:

(i) Amount of Earnings: Dividends are paid out of current and past earning. Therefore, earnings is a major determinant of the decision about dividend.

(ii) Stability Earnings: Other things remaining the same, a company having stable earning is in a better position to declare higher dividends. As against this, a company having unstable earnings is likely to pay smaller dividend.

(iii) Stability of Dividends: Companies generally follow a policy of stabilising dividend per share. The increase in dividends is generally made when there is confidence that their earning potential has gone up and not just the earnings of the current year. In other words, dividend per share is not altered if the change in earnings is small or seen to be temporary in nature.

(iv) Growth Opportunities: Companies having good growth opportunities retain more money out of their earnings so as to finance the required investment. The dividend in growth companies is, therefore, smaller, than that in the non-growth companies.

(v) Cash Flow Position: The payment of dividend involves an outflow of cash. A company may be earning profit but may be short on cash. Availability of enough cash in the company is necessary for declaration of dividend.

(vi) Shareholders’ Preference: While declaring dividends, managements must keep in mind the preferences of the shareholders in this regard. If the shareholders in general desire that at least a certain amount is paid as dividend, the companies are likely to declare the same. There are always some shareholders who depend upon a regular income from their investments.

(vii) Taxation Policy: The choice between the payment of dividend and retaining the earnings is, to some extent, affected by the difference in the tax treatment of dividends and capital gains. If tax on dividend is higher, it is better to pay less by way of dividends.

As compared to this, higher dividends may be declared if tax rates are relatively lower. Though the dividends are free of tax in the hands of shareholders a dividend distribution tax is levied on companies. Thus, under the present tax policy, shareholders are likely to prefer higher dividends.

(viii) Stock Market Reaction: Investors, in general, view an increase in dividend as a good news and stock prices react positively to it. Similarly, a decrease in dividend may have a negative impact on the share prices in the stock market. Thus, the possible impact of dividend policy on the equity share price is one of the important factors considered by the management while taking a decision about it.

(ix) Access to Capital Market: Large and reputed companies generally have easy access to the capital market and, therefore, may depend less on retained earning to finance their growth. These companies tend to pay higher dividends than the smaller companies which have relatively low access to the market.

(x) Legal Constraints: Certain provisions of the Companies Act place restrictions on payouts as dividend. Such provisions must be adhered to while declaring the dividend, (k) Contractual Constraints: While granting loans to a company, sometimes the lender may impose certain restrictions on the payment of dividends in future. The companies are required to ensure that the dividend does not violate the terms of the loan agreement in this regard

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

OR

Vedansh Limited has a share capital of ₹ 10,00,000 divided into shares of ₹100 each. For expansion purpose ,the company requires additional funds of ₹ 5,00,000. The management is considering the following alternatives for raising funds :
Alternative 1: Issue of 5000 Equity shares of ₹ 100 each
Alternative 2: Issue of 10% Debentures of ₹5,00,000 The company’s present Earnings Before Interest and Tax (EBIT) is ₹4,00,000 p.a. Assuming that the rate of Return of investment remains the same after expansion, which alternative should be used by the company in order to maximise the returns to the equity shareholders. The Tax rate is 50%. Show the working. (5)
Answer:
Rate of Return of Investment is 4,00,000/10,00,000 x 100 = 40%
EBIT after expansion = 40% x 15,00,000 = 6,00,000
Calculation of EPS

Plan I Plan II
EBIT 600000 600000
(-) Interest —— 50000
EBT 600000 550000
(-) Tax @50% 300000 275000
  EAT 300000 275000
No. of shares 15000 10,000
EPS 20 27.5

The company should use Plan 2 in order to increase the return to the equity shareholders.

CBSE Sample Papers for Class 12 Business Studies Term 2 Set 1 with Solutions

Explanation: Rate of Return of Investment is 4,00,000/10,00,000 x 100 = 40%EBIT after expansion = 40% x 15,00,000 = 6,00,000
Calculation of EPS

Calculation of EPS
Plan I Plan II
EBIT 600000 600000
(-) Interest —– 50000
EBT 600000 550000
(-) Tax @50% 300000 275000
EAT 300000 275000
No. of shares 15000 10,000
EPS 20 27.5

The company should use Plan 2 in order to increase the return to the equity

CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions

Students can access the CBSE Sample Papers for Class 12 Maths with Solutions and marking scheme Term 2 Set 8 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions:

  • This question paper contains three sections-A. B and C. Each part is compulsory.
  • Section-A has 6 short answer type (SA1) questions of 2 marks each.
  • Section-B has 4 short answer type (SA2) questions of 3 marks each.
  • Section-C has 4 long answer type questions (LA) of 4 marks each.
  • There is an Internal choice in some of the questions.
  • Q14 is a case-based problem having 2 sub parts of 2 marks each.

Section – A
(Section – A has 6 short answer type (SA-1) questions of 2 marks each.)

Question 1.
Evaluate
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 1
Answer:
Let
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 2
= [0 – (-1 – 1)] + [(1 + 1) – 0]
= 2 + 2
= 4

Question 2.
Identify the functions P(x) and Q(x) from the linear differential equation (tan-1 x – y) dx = (1 + x2) dy.
Or
Solve the differential equation \(\frac{d y}{d x}\) + 1 = ex+y
Answer:
We have
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 3
Given, differential equation is
\(\frac{d y}{d x}\) + 1 = ex+y ….(i)
Let x + y = t
On differentiating w.rt x, we get
1 + \(\frac{d y}{d x}=\frac{d t}{d x}\) ….(ii)

∴ From equation (i) and (ii),
\(\frac{d y}{d x}\) = ex
⇒ e-tdt = dx
On integrating both sides, we get
⇒ \(\frac{-e^{-t}}{e^{x+y}}\) = x + c
⇒ -1 = (x + c)ex+y
⇒ (x + c)ex+y = 0

Caution:
Do the necessary substitution. wherever needed.

CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions

Question 3.
Urn I contains 5 white and 4 blue balls. Urn II contains 4 white and 5 blue balls. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is blue, what is the probability that it is drawn from Urn II? (2)
Answer:
Let E1 and E2 be the events of selecting Urn I
and Urn II respectively,
Also, let B be the event of drawing a blue ball
∴ P(E1) = \(\frac{1}{2}\) and P(E2) = \(\frac{1}{2}\)
Also, P = \(\left(\frac{B}{E_{1}}\right) \frac{4}{9}\) and P = \(\left(\frac{\mathrm{B}}{\mathrm{E}_{2}}\right) \frac{5}{9}\)

Using Bayes Theorem,
Required Probability
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 4

Question 4.
Find the intercepts made on the coordinate axes by the plane x + 2y – 2z = 9. Also, find the direction cosines of the normal to the plane. (2)
Answer:
Given Equationsof plane is:
x +2y – 2z = 9
Or
\(\frac{x}{9}+\frac{2 y}{9}-\frac{2 z}{9}\) = 1
Or
\(\frac{x}{9}+\frac{y}{\frac{9}{2}}+\frac{z}{\frac{-9}{2}}\) = 1

Thus, the intercepts made by the plane on the coordinate axes are 9, \(\frac{9}{2},-\frac{9}{2}\) respectively.
Now, direction ratios of the normal to the plane are (1, 2, -2).
Therefore, direction cosines of the normal to the plane
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 5

Question 5.
Two cards are drawn successively with replacement from a well-shuffled pack of 52 playing cards. Find the probability distribution of the number of queens. (2)
Answer:
Let X denotes the discrete random variable “the number of queens”. When two cards are drawn with replacement.
Then, X takes values 0,1, 2.
P(X = 0) = P(both cards are not queen)
= \(\frac{48}{52} \times \frac{48}{52}=\frac{144}{169}\)
P(X = 1) = P(one card is queen)
= \(\frac{4}{52} \times \frac{48}{52}+\frac{48}{52} \times \frac{4}{52}=\frac{24}{169}\)
P(X = 2) = P(both are queen cards)
= \(\frac{4}{52} \times \frac{4}{52}=\frac{1}{169}\)

So, the required probability distribution of X is
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 6

Question 6.
The dot products of a vector with the vectors î + ĵ – 3k̂, î + 3ĵ – 2k̂ and 2î + ĵ + 4k̂ are 0, 5 and 8 respectively. Find the vector. (2)
Answer:
Let the required vector be
\(\vec{a}\) = αî + βĵ + γk̂

Then, according to the question,
(αî + βĵ + γk̂). (î + 3ĵ – 2k̂) =0
⇒ α + 3β – 2γ = 5 …(ii)
and, (αî + βĵ + γk̂) ,(2î + ĵ + 4k̂) = 8
⇒ 2α + β + 4γ = 8 …(iii)
Solving equation (i), (ii) and (iii) we get
Thus, the required vector is î + 2ĵ + k̂

Section – B
(Section – B has 4 short answer type (SA-2) questions of 3 marks each.)

Question 7.
Evaluate ∫\(\frac{\sin 4 x}{\sin x}\)dx.
or
Evaluate ∫09 f(x) dx. (3)
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 7
Answer:
Let I = ∫\(\frac{\sin 4 x}{\sin x}\)dx.
= ∫\(\frac{2 \sin 2 x \cos 2 x}{\sin x}\) dx
[∵ sin 2θ = 2 sin θ cos θ]
= ∫\(\frac{2(2 \sin x \cos x) \cos 2 x}{\sin x}\) dx
= 4∫cos x cos 2x dx
= 4∫cos x(1 – 2 sin2x)dx
[∵ cos 2x = 1 – 2 sin2x]

Put sin x = t
⇒ cos x dx = dt
∴ I = 4∫(1 – 2t2) dt
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 8

CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions

Question 8.
A(-4, 7, 2),B(2, -5, 8) and C(-5, -1, 5) are three points. Find the equation of the line AB. If D is the foot of the perpendicular drawn from the point C to the Line AB, find the coordinates of D. (3)
Answer:
Equation of Line AB is
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 9
∴ Any point on this line is (λ – 4, – 2λ + 7, λ + 2).

Let it be the point D and is the foot of the perpendicular from C (-5, – 1, 5) on the line AB.
Now, direction ratios of CD = (λ, – 4 + 5, – 2λ + 7 + 1, λ + 2 – 5)
= {λ + 1, – 2λ + 8, λ – 3}

Since, CD is perpendicular to AB.
∴ (λ + 1) × 1 + (- 2λ + 8) × (- 2) + (λ – 3) × 1 = 0
⇒ 6λ – 18 = 0
⇒ λ = 3
Thus, the coordinates ofthe point Dare (3 – 4, -2 × 3 + 7, 3 + 2), i.e., (- 1, 1, 5).

Related Theory
Two lines with directions ratios a1, b1, c1 and a2, b2, c2 are perpendicular, if a1a2 + b1b2 + c1c2 = 0

Question 9.
Find the area of the region bounded by the curve y = |x – 5| and the Lines x = 0 and x = 1.
Or
Draw a rough sketch of the curve y = 1 + |x + 1|, x = -3, x = 3, y = 0 and find the area of the region bounded by them, using integration. (3)
Answer:
We have, y = |x – 5|
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 10
∴ Required area = ar(region OABC)
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 11
Given curves are y = 1 + |x + 1|, x = -3, x = 3 and y = 0
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 12

CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions

Question 10.
Using vectors show that the median of an isosceles triangle is perpendicular to the base. (3)
Answer:
Let ABC be an isosceles triangle with AB = AC.
Let the position vectors of B and C taking A as origin be \(\vec{b}\) and \(\vec{c}\).

We have,
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 13
Since, AD is median of ∆ABC
∴ D bisect the base BC
∴ Using mid-point formula,
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 14
So, angle between \(\overrightarrow{A D}\) and \(\overrightarrow{B C}\) is \(\frac{π}{2}\)
Thus, AD is perpendicular to BC.
Hence proved.

Section – C
(Section – C has 4 long answer type questions (LA) of 4 marks each.)

Question 11.
If y(x) is a solution of \(\left(\frac{2+\sin x}{1+y}\right)\) = -cos x and y(0) = 1, then find the value of y \(\frac{π}{2}\).
Answer:
Given \(\left(\frac{2+\sin x}{1+y}\right)\) = -cos x
⇒ \(\frac{d y}{1+y}=-\left(\frac{\cos x}{2+\sin x}\right)\)dx

On integrating both sides, we get cosx
∫\(\frac{1}{1+y}\)dy = -∫\(\frac{\cos x}{2+\sin x}\)dx
⇒ log(1 + y) = -log(2 + sin x) + log c
⇒ log(1 + y)(2 + sin x) = log c
⇒ (1 + y)(2 + sin x) = c
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 15

Question 12.
Two dice are thrown together and the total score is noted. The events E, F and G are “a total of 4”, “a total of 9 or more” and “a total which is divisible by 5” respectively. Calculate P(E), P(F) and P(G) and decide which pairs of events, if any, are independent.
Or
A bag contains 2 red and 3 black balls. Find the probability distribution of the number of red balls, if 4 balls are drawn out (i) with replacement from the bag. (ii) without replacement from the bag. (4)
Answer:
We have,
F = (3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)
G = (1, 4), (2, 3), (3, 2), (4,1), (4, 6), (5, 5), (6, 4)

∴ P(E) = \(\frac{3}{36}=\frac{1}{12}\)
P(F) = \(\frac{10}{36}=\frac{5}{18}\)
P(G) = \(\frac{7}{36}\)

Further, E ∩ F = Φ, E ∩ G = Φ and F ∩ G = {(4, 6), (5, 5), (6, 4)}
P(E ∩ F) = 0, P(F ∩ G) = \(\frac{3}{36}=\frac{1}{12}\)

Now, P(E) × P(F) = \(\frac{1}{12} \times \frac{5}{18}\)
= \(\frac{5}{216}\) ≠ P(E ∩ F)
⇒ E and F are not independent.

P(E) × P(G) = \(\frac{1}{12} \times \frac{7}{36}\)
= \(\frac{7}{432}\) ≠ P(E ∩ G)
⇒ E and G are not independent.

P(F) × P(G) = \(\frac{5}{18} \times \frac{7}{36}\)
= \(\frac{35}{648}\) ≠ P(F ∩ G)
⇒ E and G are not independent.
Thus, event E, F and G are not pair-wise independent.

Or

(i) Let X be the discrete random variable defined as the number of red balls, when four ball are drawn with replacement.
Then, X can take values 0,1, 2, 3, 4.
Now, ‘
P(X = 0) = P(allfour balls are black)
\(\frac{3}{5} \times \frac{3}{5} \times \frac{3}{5} \times \frac{3}{5}=\frac{81}{625}\)
P(X = 1) = P(1 red ball and 3 black balls)
= P(first ball is red and next three balls are black) + P(second ball is red and rest are black balls) + P(third ball is red and rest are black balls) + P(fourth ball is red and rest are black balls)
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 16

P(X = 2) = P(2 red balls and 2 black balls)
= P(first two are red balls, next two balls are black) + P(First, third ball are red) + P(second, fourth ball are red) + P(last two balls are red) + P(First, fourth balls are red) + P(second, third balls are red)
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 17

P(X = 3) = P(3 red balls and 1 black ball)
= P(first three balls are red) + P(second ball is black) + P(first ball is black) + P(third ball is black)
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 18
P(X = 4) = P(All four balls are red)
= \(\frac{2}{5} \times \frac{2}{5} \times \frac{2}{5} \times \frac{2}{5}=\frac{16}{625}\)

Thus, the probability distribution of X is:
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 19
(ii) Let X be the discrete random variable defined as the number of red balls, when four balls are drawn without replacement.
Then, X can take values 1, 2
P(X = 1) = P(1 red ball and 3 black balls)
= \(\frac{{ }^{2} C_{1} \times{ }^{3} C_{3}}{{ }^{5} C_{4}}=\frac{2 \times 1}{5}=\frac{2}{5}\)

P(X = 2) = P(2 red balls and 2 black balls)
= \(\frac{{ }^{2} C_{2} \times{ }^{3} C_{2}}{{ }^{5} C_{4}}=\frac{1 \times 3}{5}=\frac{3}{5}\)

Thus, the probability distribution of X is
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 20

Caution:
In part (ii). X cannot take O i.v1ue os there ore total of 3 block 1 and 2 red balls So on drawing four baILš. without replacement one of them wilt definitely be red.

CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions

Question 13.
Evaluate ∫x(logx)2dx. (4)
Answer:
Let I = ∫x(logx)2dx
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 21

Case-Based/Data-Based

Question 14.
Ranjana’s house is situated at Roop Nagar at point O. For going to Nita’s house, she first travels 10 km by bus in the East. Here at point A, a hospital is situated. From hospital, Ranjana takes an auto and goes 8 km in the North. Here at point B, a school is situated. From school, she travels by bus to reach Nita’s house at point C, which is at 30° East 12 km from point B.
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 22
Based on the above information, answer the following two questions:
(A) What is the vector distance between Ranjana’s house and school? (2)
(B) What is the vector distance from school to Nita’s house? (2)
Answer:
(A) Required distance, \(\overrightarrow{\mathrm{OB}}=\overrightarrow{\mathrm{OA}}+\overrightarrow{\mathrm{AB}}\)
[Using triangle law of vector addition]
= 10î + 8ĵ

(B) Required distance = \(\overrightarrow{\mathrm{BC}}\)
CBSE Sample Papers for Class 12 Maths Term 2 Set 8 with Solutions 23
12 cos 30° î + 12 sin 30°ĵ = 12 × \(\frac{\sqrt{3}}{2}\)î + 12 × \(\frac{1}{2}\)ĵ
= 6√3 î + 6ĵ

CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions

Students can access the CBSE Sample Papers for Class 12 Maths with Solutions and marking scheme Term 2 Set 7 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions:

  • This question paper contains three sections-A. B and C. Each part is compulsory.
  • Section-A has 6 short answer type (SA1) questions of 2 marks each.
  • Section-B has 4 short answer type (SA2) questions of 3 marks each.
  • Section-C has 4 long answer type questions (LA) of 4 marks each.
  • There is an Internal choice in some of the questions.
  • Q14 is a case-based problem having 2 sub parts of 2 marks each.

Section – A
(Section – A has 6 short answer type (SA-1) questions of 2 marks each.)

Question 1.
The direction cosines of a line segment AB are \(\frac{-2}{\sqrt{17}}, \frac{3}{\sqrt{17}}, \frac{-2}{\sqrt{17}}\) If AB = \(\sqrt{17}\) and the coordinates of A are (3, -6, 10), then find coordinates of B. (2)
Answer:
Since, direction cosines of AB are \(\frac{-2}{\sqrt{17}}, \frac{3}{\sqrt{17}}, \frac{-2}{\sqrt{17}}\)
So, direction ratios of the Line AB are < -2, 3, -2>.
DR of the line AB = Coordinates of B – coordinates A
Let the coordinates of B be (x, y, z).
So, direction ratios of AB = <x – 3, y + 6, z – 10>
⇒ <-2, 3, -2> = <x – 3, y + 6, z – 10>
⇒ x – 3 = -2; y + 6 = 3; z – 10 = -2
⇒ x = 1; y = -3; z = 8
Thus, coordinates of B are (1, -3, 8).

Question 2.
A die is rolled. If the outcome is an even number, what is the probability that it is a prime number?
OR
A player has 7 cards in hand of which 5 are red and among these five, 2 are kings. A card is drawn at random. Find the probability that it is a king, if being known that it is red. (2)
Answer:
Sample space, S = { 1, 2, 3, 4, 5, 6}
Let A be the event of “getting an even number”, and B be the event of “getting a prime number”,
n (A) = {2, 4, 6}, n(B) = {2}, n (B ∩ A) = {2}
P(A) = \(\frac{3}{6}=\frac{1}{2}\)
And, P(B ∩ A) = \(\frac{1}{6}\)
[∵ 2 is the only even prime number from 1 to 6]
Now,
Required probability = P(B/A)
\(\frac{P(B \cap A)}{P(A)}=\frac{1 / 6}{1 / 2}=\frac{1}{3}\)

OR
Let A be the event of “card being red”, and B be the event of “card being king”.
P(A) = \(\frac{5}{7}\) And P(B ∩ A) = \(\frac{2}{7}\)
Now, required probability = P(B/A)
= \(\frac{P(B \cap A)}{P(A)}\)
= \(\frac{2 / 7}{5 / 7}=\frac{2}{5}\)

CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions

Question 3.
Find the vector and the cartesian equations of a line passing through the points (3, -2,-5) and (3, – 2, 6). (2)
Answer:
The direction ratios of the line passing through the points (3, -2, – 5) and (3, -2, 6) are (3 – 3, – 2 + 2, 6 + 5) i.e., (0, 0, 11).
Also, the required line passes through the point (3,-2,-5).
So, the cartesian equation of the required line is
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 1
And, its vector equation is
\(\vec{r}\) = (3î – 2ĵ – 5k̂) + λ(11k̂)

Question 4.
Evaluate ∫02| 1 – x | dx. (2)
Answer:
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 2

Question 5.
A die marked 1,2,3 in red and 4,5,6 in green is tossed. Let A be the event “the number is even” and B be the event “the number is red”. Are A and B independent? Give reasons for your answer. (2)
Answer:
We have, A = Event that the number is even.
∴ A = {2, 4, 6}
P(A) = \(\frac{3}{6}=\frac{1}{2}\)

Also, B = Event that the number is red.
∴ B = {1, 2, 3}
P(B) = \(\frac{3}{6}=\frac{1}{2}\)

And, A ∩ B = event that number is even and red
⇒ A ∩ B = {2}
P(A ∩ B) = \(\frac{1}{6}\)

∵P(A) × P(B) = \(\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}\) ≠ P(A n B)
Hence, the two events A and B are not independent.

Question 6.
Sketch the region bounded by curves y = x2 and y = |x|. (2)
Answer:
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 3
Hence, y = x2 is an equation of parabola which open upwards, towards positive side of y-axis, with its vertex at the origin.
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 4

Section – B
(Section – B has 4 short answer type (SA-2) questions of 3 marks each.)

Question 7.
Find the area of the region bounded by the curve y2 = 4x, the lines x = 1 and x = 4 and the x-axis in the first quadrant.
OR
Find the area of the region bounded by the curve y = |x + 3|, the lines x = -6 and x = 0. (3)
Answer:
y2 = 4x represents a parabola whose vertex is at the origin, axis of symmetry is x-axis, focus on the positive direction of x-axis and it opens to the right
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 5
= \(\frac{4}{3}\)[(4)3/2 – (1)3/2]
= \(\frac{4}{3}\)(8 – 1)
= \(\frac{28}{3}\) sq.units
OR
We have, y = |x + 3|
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 6
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 7

CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions

Question 8.
Find the area of a parallelogram whose adjacent sides are determined by vectors \(\vec{a}\) = î – ĵ + 3k̂ and b = 2î – 7ĵ + k̂ respectively. (3)
Answer:
Let ABCD be the parallelogram with \(\overrightarrow{\mathrm{AB}}=\vec{a}\) = î – ĵ + 3k̂ and \(\overrightarrow{\mathrm{BC}}=\vec{b}\) = 2î – 7ĵ + k̂.
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 8
∴ Area of Parallelogram ABCD = \(|\overrightarrow{A B} \times \overrightarrow{B C}|\)
Now,
\(\overrightarrow{A B} \times \overrightarrow{B C}=\left|\begin{array}{ccc}
\hat{i} & \hat{j} & \hat{k} \\
1 & -1 & 3 \\
2 & -7 & 1
\end{array}\right|\)
= î(-1 + 21) – ĵ(1 – 6) + k̂(-7 + 2)
= 20î + 5ĵ – 5k̂

∴ \(|\overrightarrow{A B} \times \overrightarrow{B C}|=\sqrt{(20)^{2}+(5)^{2}+(-5)^{2}}\)
= \(\sqrt{450}\)
= 15√2

Question 9.
Evaluate ∫02 x\(\sqrt{2-x}\)dx.
OR
Evaluate ∫\(\frac{\sin x}{1+\sin x}\) dx. (3)
Answer:
Let I = ∫02 x\(\sqrt{2-x}\)dx.
Put 2 – x = t
⇒ -dx = dt
For x= 0, t= 2 – 0 = 2
For x = 2, t= 2 – 2 = 0
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 9
OR
Let I = ∫\(\frac{\sin x}{1+\sin x}\) dx
= ∫\(\frac{\sin x(1-\sin x)}{1-\sin ^{2} x}\)dx
= ∫\(\frac{\sin x-\sin ^{2} x}{\cos ^{2} x}\) dx
= ∫(tan x sec x – tan2 x)dx
= ∫[tan x sec x – (sec2 x – 1)] dx
= ∫(tan x sec x – sec2 x + 1)dx
= sec x – tan x + x + C

Question 10.
Let \(\vec{a}, \vec{b}, \vec{c}\) be the three vectors such that | \(\vec{a}\) | = 3, | \(\vec{b}\) | = 4 and | \(\vec{c}\) | = 5 and each one of them being perpendicular to the sum of the other two. Find | \(\vec{a}+\vec{b}+\vec{c}\) |. (3)
Answer:
It is given that each vector is perpendicular to the sum of other two vectors.
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 10

Section – C
(Section – C has 4 long answer type questions (LA) of 4 marks each.)

Question 11.
Four defective bulbs are accidentally mixed with six good ones. If it is not possible to just look at a bulb and tell whether or not it is defective, then find the probability distribution of the number of defective bulbs, if four bulbs are drawn (without replacement) at random from this lot. (4)
Answer:
Let X be the discrete random variable defined as the number of defective bulbs.
Then, X can take values 0,1, 2, 3, 4.
Now, P(X = 0) = P (all the bulbs are good ones)
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 11
P(X = 1) = P(1 defective and three good ones)
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 12
P(X = 2) = P(2 defective and two good ones)
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 13
P(X = 3) = P(3 defective and one good one)
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 14
P(X = 4)= P (All the four defective bulbs)
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 15
Thus, the probability distribution of X is
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 16

CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions

Question 12.
Solve the differential equation:
\(\frac{d y}{d x}=\frac{x+y+7}{2 x+2 y+3}\)
OR
Solve the differential equation: du
sin x \(\frac{d y}{d x}\) + y cos x = x sin x
Answer:
Given differential equation is:
\(\frac{d y}{d x}=\frac{x+y+7}{2 x+2 y+3}\) …(i)

Put (x + y + 7) = z
⇒ 1 + \(\frac{d y}{d x}=\frac{d z}{d x}\)
Substituting these values in (i), we get
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 17
where, C1 = 9C
or, 6y – 3x – 11 log (3x + 3y + 10) = C2, where
C2 = C1 – 42.

which is the required solution of the given differential equation.
OR
The given differential equation can be rewritten dy
as \(\frac{d y}{d x}\) + cotx.y = x dx

It is a linear differential equation in the form
\(\frac{d y}{d x}\) + P(x).y = Q(x) dx
where, P(x) = cot x and Q(x) = x

Integrating Factor (I.F.) = e∫Pdx
= e∫cot x dx
= elogsin x
= sin x

Thus, the solution to the given differential equation is:
y.(I.F.) = ∫Q(x).(I.F.)dx
⇒ y.sin x = ∫x.sin x dx
⇒ y.sin x = x∫sin x dx – ∫[\(\frac{d y}{d x}\)(x)∫sin xdx]dx
⇒ y. sin x = -x cos x + sin x +C
⇒ y. sin x + x cos x = sin x + C
which is the required solution of the given differential equation.

Question 13.
Evaluate ∫cos{2 cot-1\(\sqrt{\frac{1-x}{1+x}}\)}dx. (4)
Answer:
Let I = ∫cos{2 cot-1\(\sqrt{\frac{1-x}{1+x}}\)}dx.
Put x = cos t
⇒ dx = -sin t dt
I = -∫cos{2 cot-1\(\sqrt{\frac{1-\cos t}{1+\cos t}}\)}sin tdt
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 18

CASE-BASED/DATA-BASED

Question 14.
Rohan and Rohit are two friends, and they are going to a road trip on their motorcycles. Their motorcycles are running at the speed more than the allowed speed on the road along the lines \(\vec{r}\) = λ(î + 2ĵ – k̂) and \(\vec{r}\) = 3î + 3ĵ + μ(2î + ĵ + k̂) respectively.
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 19
Based on the above information, answer the following two questions:
(A) Find the direction ratios of the line along which (i) motorcycle A is running (ii) motorcycle B is running. (2)
(B) Find the shortest distance between the two lines. (2)
Answer:
(A) (i) Direction ratios of the line along which the motorcycle A is running are <1, 2, – 1>.
(ii) Direction ratios of the line along which the motorcycle B is running are <2, 2, 1>.

(B) On comparing the given equations with equations \(\vec{r}=\overrightarrow{a_{1}}+\lambda \overrightarrow{b_{1}}\) and \(\vec{r}=\overrightarrow{a_{2}}+\lambda \overrightarrow{b_{2}}\)
we have
\(\overrightarrow{a_{1}}=\overrightarrow{0}\)
b2 = î + 2î – k̂
\(\overrightarrow{a_{2}}\) = 3î + 3î
b2 = 2i + ĵ + k̂
CBSE Sample Papers for Class 12 Maths Term 2 Set 7 with Solutions 20

CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions

Students can access the CBSE Sample Papers for Class 12 Maths with Solutions and marking scheme Term 2 Set 6 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions:

  • This question paper contains three sections-A. B and C. Each part is compulsory.
  • Section-A has 6 short answer type (SA1) questions of 2 marks each.
  • Section-B has 4 short answer type (SA2) questions of 3 marks each.
  • Section-C has 4 long answer type questions (LA) of 4 marks each.
  • There is an Internal choice in some of the questions.
  • Q14 is a case-based problem having 2 sub parts of 2 marks each.

Section – A
(Section – A has 6 short answer type (SA-1) questions of 2 marks each.)

Question 1.
Evaluate ∫sin-1\(\left(\sqrt{\frac{1-\cos 2 x}{2}}\right)\)dx. (2)
Answer:
Let I = ∫sin-1\(\left(\sqrt{\frac{1-\cos 2 x}{2}}\right)\)dx
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 1

Question 2.
Check whether the differential equation (4x + 6y + 5)dx – (3x + 2y + 4) dy = 0 is homogeneous or not.
OR
Find the solution of \(\frac{d y}{d x}\) = 2y-x. (2)
Answer:
We have.
(4x + 6y + 5)dx – (3x + 2y + 4)dy = 0
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 2
The given differential equation is not homogeneous.
OR
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 3
⇒ -2y + 2-x = c log 2
⇒ 2-x – 2y = k where k = c Log 2
Hence, the required solution is 2-x – 2y = k.

CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions

Question 3.
Find a unit vector in the direction of \(\overrightarrow{\mathrm{PQ}}\), where P and Q have coordinates (5, 0, 8) and (3, 3, 2) respectively. (2)
Answer:
We have, position vector of P = \(\overrightarrow{\mathrm{OP}}\) = 5î + 8k̂
and the position vector of Q = \(\overrightarrow{\mathrm{OQ}}\) = 3î + 3ĵ + 2k̂
\(\overrightarrow{\mathrm{PQ}}=\overrightarrow{\mathrm{OQ}}-\overrightarrow{\mathrm{OP}}\)
= (3î + 3ĵ + 2k̂) – (5î + 8k̂)
= -2î + 3ĵ – 6k̂
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 4
Now, unit vector in the direction of vector \(\overrightarrow{\mathrm{OP}}\)
= \(\frac{\overrightarrow{\mathrm{PQ}}}{\overrightarrow{\mid \mathrm{PQ}} \mid}\)
= \(\frac{1}{7}\)(-2î + 3ĵ – 6k̂)

Question 4.
Let \(\vec{a}\) and \(\vec{b}\) be two vectors such that |\(\vec{a}\)| = 3 and |\(\vec{a}\)| = \(\frac{\sqrt{2}}{3}\) Show that will be a unit vector, if the angle between them is \(\frac{\sqrt{2}}{3}\). (2)
Answer:
Let θ be the angle between the given two vectors \(\vec{a}\) and \(\vec{b}\).
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 5

Question 5.
Two dice are thrown. Find the probability that the numbers shown have a sum of 8, if it is known that the second die always exhibits 4. (2)
Answer:
Let A be the event of “occurrence of 4 always on second die” and B be the event of “occurrence of such numbers on both the dice whose sum is 8”.
∴ A = {(1,4), (2, 4), (3, 4), (4, 4), (5, 4), (6,4)}
And, B = {(2, 6), (3, 5), (4,4), (5, 3), (6, 2)}
∴P(A) = \(\frac{6}{36}=\frac{1}{6}\)
And P(B ∩ A) = \(\frac{1}{36}\)
Now,
Required Probability = P(B/A)
= \(\frac{P(B \cap A)}{P(A)}\)
= \(\frac{1 / 36}{1 / 6}=\frac{1}{6}\)

Question 6.
Two dice are rolled simultaneously. Find whether the following two events, are independent or not:
E = {(x, y): x + y = 11}; F = {(x, y): x ≠ 5} (2)
Answer:
We have,
E = {(x, y) : x + y = 11
∴ E = {(5, 6), (6, 5)}
Also, F = {(x, y) : x ≠ 5}
∴ F = {(1, 1), (1, 2), (1, 3),(1, 5), (1, 6), (2,1), (2, 2), (2, 4), (2, 5), (2, 6), (3, 1), (3, 3), (3, 4), (3, 5), (3, 6), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} – {(5, 1), (5, 2), (5, 3) (5, 4), (5,5), (5, 6)}
n (E) = 2. n (F) = 30, n (E ∩ F) = 1

And,
P(E) = \(\frac{2}{36}=\frac{1}{18}\)
P(F) = \(\frac{30}{36}=\frac{5}{6}\)
and P(E ∩ F) = \(\frac{1}{36}\)

= P(E) × P(F)= \(\frac{1}{18} \times \frac{5}{6}=\frac{5}{108}\)
Since. P(E) × P(E) ≠ P(E ∩ F)
So, the two events E and F are not independent.

Section – B
(Section – B has 4 short answer type (SA-2) questions of 3 marks each.)

Question 7.
If ∫abx3 dx = 0 and ∫ab x2 dx = \(\frac{2}{3}\) Values of a and b.
OR
1ex3 logx dx (3)
Answer:
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 6
⇒ b4 – a4 = 0 and b3 – a3 = 2
Now, b4 – a4 = 0
⇒ (b2 – a2)(b2 + a2) = 0
⇒ (b – a) (b + a) (b2 + a2) = 0
⇒ (b + a) (b2 + a2) = 0 [∵ b ≠ a]
⇒ (b + a) = 0 [∵ b2 + a2 = 0]
⇒ a = -b
Substituting these values in b3 – a3 = 2, we get
a = -1,b = 1
OR
Let I = ∫1ex3 logx dx
= ∫1ex3 1. logx dx
= log x∫1.dx – ∫[\(\frac{d}{d x}\)(log x).∫1dx]dx
(By Integration b parts formula)
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 7
= (e.log e – e) – (1 log 1 – 1)
= (e – e) – (0 – 1)
= 1

Question 8.
Find the cartesian equation of a line passing through (1, 2, 3) and parallel to the line \(\frac{x+2}{-1}=\frac{y+3}{7}=\frac{2 z-6}{3}\). (3)
Answer:
Given equation of line can be rewritten as
\(\frac{x+2}{-1}=\frac{y+3}{7}=\frac{2 z-6}{3}\)

∴ Its direction ratios: (-1, 7, \(\frac{3}{2}\))

Since, required line is parallel to the given line, so their direction ratios will be proportional.
∴ Direction ratios of required line = (-λ, 7λ, \(\frac{3}{2}\)λ)

Also the required line passes through the point (1, 2, 3).
∴ Cartesian equation of the required line is:
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 8

CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions

Question 9.
Solve the differential equation:
sin-1\(\left(\frac{d y}{d x}\right)\) = x + y
OR
Solve the differential equation: du
tan x\(\frac{d y}{d x}\) + 2y = secx (3)
Answer:
Given differential equation can be rewritten as:
\(\frac{d y}{d x}\) = sin (x + y) …(i)
Put (x + y) = t

Differentiating w.r.t. x, we get
1 + \(\frac{d y}{d}=\frac{d t}{d}\)

Substituting these values in eq. (i), we get
\(\frac{d t}{d x}\) – 1 = sin t

⇒ \(\frac{d t}{d x}\) = 1 + sin t
or
\(\frac{d x}{d t}=\frac{1}{1+\sin t}\)
= \(\frac{1-\sin t}{\cos ^{2} t}\)
= (sec2t – tan t sec t)
⇒ dx = (sec2t -tan t sec t) dt

Integrating both sides, we get
∫dx = ∫ (sec2 t – tan t sec t)dt
⇒ x = tan t – sec t + C
or, x = tan(x + y) – sec(x + y) + C
which is the required solution of the given differential equation.
OR
The given differential equation can be rewritten as:
\(\frac{d y}{d x}\) + 2cotx.y = cose cx

It is a linear differential equation in the form
\(\frac{d y}{d x}\) + P(x).y = Q(x) dx
where, P(x) = 2 cot x and Q(x) = cosec x

Integrating Factor (I.F.)
= e∫P(x).dx
= e∫cot x.dx
= e2logsinx
= elogsin2x
= sin2 x

Thus, the solution to the given differential equation is:
y – (I.F.) = ∫Q(x).(I.F.)dx
⇒ y.sin2x= ∫ cosec x.sin2x dx
⇒ y .sin2x = ∫ sinx dx
⇒ y sin2 x = – cos x + C
or y sin2x + cos x = C,
which is the required solution of the given differential equation.

Question 10.
Find the distance between the parallel planes \(\vec{r}\).(2î – 3ĵ + 6k̂) = 5 and \(\vec{r}\).(6î – 9ĵ + 18k̂) + 20 = 0. (3)
Answer:
Let \(\overrightarrow{r_{1}}\) be the position of any point on the plane \(\vec{r}\).(2î – 3ĵ + 6k̂) = 5
Then, \(\overrightarrow{r_{1}}\).(2î – 3ĵ + 6k̂) = 5
or \(\overrightarrow{r_{1}}\).(6î – 9ĵ + 18k̂) = 15

Now, the length of the perpendicular from \(\overrightarrow{r_{1}}\) to the other plane \(\vec{r}\).(6î – 9ĵ + 18k̂) + 20 = 0
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 9
Thus, the distance between the given parallel planes is \(\frac{5}{3}\) units.

Section – C
(Section – C has 4 long answer type questions (LA) of 4 marks each.)

Question 11.
Evaluate ∫0asin-1\(\sqrt{\frac{x}{a+x}}\)dx. (4)
Answer:
Let I = ∫0asin-1\(\sqrt{\frac{x}{a+x}}\)dx.
Put x = a tan2 t
⇒ dx = 2a tan t sec2 t dt
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 10

Question 12.
Using integration, find the area of the region bounded by a triangle whose vertices are A(2, 0), B(4, 5), C(6, 3).
OR
Sketch the bounded region and find the area bounded by the curve x = √y, the line x – y + 2 = 0 and the y-axis. (4)
Answer:
Given points are A(2, 0), B(4, 5) and C(6, 3).
We know, equation of a line with two given points, namely, (x1, y1) and (x2, y2) is given as:
y – y1 = \(\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)\)(x – x1)
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 11
Equation of side AB of triangle ABC is:
y – 0 = \(\frac{5-0}{4-2}\)(x – 2)
⇒ 2y = 5x – 10

Equation of side BC of triangle ABC is:
y – 5 = \(\frac{3-5}{6-4}\)(x – 4)
⇒ y = 9 – x

Equation of side AC of triangle ABC is:
y – 0 = \(\frac{3-0}{6-2}\)(x – 2)
⇒ 4y = 3x – 6

Now, required area of ∆ABC = ar(region APBA) + ar(region BPQB) – ar(region AQCA)
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 12
OR
x = √y, or x2 = y is an equation of a parabola which open upwards with its vertex at origin.
To find the point of intersection of x2 = y and x – y + 2 = 0, put y = x + 2 in x2 = y.
∴ x2 = x + 2
⇒ x2 – x – 2 = 0
⇒ (x – 2) (x + 1) = 0
⇒ x = 2, -1
For x = 2, y = 4
For x = -1, y = 1
∴ Points of intersection are (2, 4) and (-1, 1). Also, the area common to the curve x2 = y, line y = x + 2 and the y-axis is shown shaded in the figure.
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 13
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 14

CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions

Question 13.
A bag contains 5 red marbles and 3 black marbles. Three marbles are drawn one by one without replacement. What is the probability that at least one of the three marbles drawn be black, if the first marble is red? (4)
Answer:
Here, R = red marble and B = black marble For the condition that at least one of the three marbles drawn be black, if first marble is red, then following are the possibilities:
(A) Second marble is black and third is red (E1)
(B) Second marble is black and third is also black (E2)
(C) Second marble is red and third is black (E3)
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 15

Case-Based/Data-Based

Question 14.
Three slogans on chart paper are to be placed on a school bulletin board at the points A, B and C displaying A, B and C The coordinates
of these points are A(2. 5, 1),B(3, – 3, 2)and C(- 2, 4, 7) respectiveLy. Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be the position vectors of A, B, and C respectively
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 16
Based on the above information, answer the following two questions:
(A) Find the unit vector in the direction of \(\vec{b} \times \vec{c}\) (2)
Answer:
Here,
\(\vec{b} \times \vec{c}=\left|\begin{array}{ccc}
\hat{i} & \hat{j} & \hat{k} \\
3 & -3 & 2 \\
-2 & 4 & 7
\end{array}\right|\)
= (- 21 – 8)î – (21 + 4)ĵ + (12 – 6)k̂
= – 29î – 25ĵ + 6k̂
So, unit vector in the direction of \(\vec{b} \times \vec{c}\)
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 17

(B) Find the area of ∆ABC. (2)
Answer:
Area of ∆ABC = \(\frac{1}{2}|\overrightarrow{A B} \times \overrightarrow{A C}|\)
Now, \(\overrightarrow{A B}\)=(3 – 2)î + (-3 – 5)ĵ + (2 – 1)k̂
= î – 8ĵ + k̂
and \(\overrightarrow{A C}\) =(-2 – 2)î + (4 – 5) ĵ+(7 – 1)k̂
= -4î – ĵ + 6k̂
CBSE Sample Papers for Class 12 Maths Term 2 Set 6 with Solutions 18