Category: CBSE Sample Papers

Students can access the CBSE Sample Papers for Class 12 Accountancy 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 Accountancy Standard Term 2 Set 5 with Solutions

Time Allowed: 2 Hours
Maximum Marks: 40

General Instructions

• This question paper comprises two Parts A and B. There are 12 questions in the question paper. All questions are compulsory.
• Question nos. 1 to 3 and 10 are Short Answer Type I Questions carrying 2 marks each.
• Question nos. 4 to 6 and 11 are Short Answer Type II Questions carrying 3 marks each.
• Question nos. 7 to 9 and 12 are Long Answer Type Questions earning 5 marks each.
• There is no overall choice. However, an internal choice has been provided in 3 questions of three marks and 1 question of five marks.

Maximum Marks : 40
Time : 2 Hours

Part A
(Accounting for Not-for-Profit Organisations, Partnership Firms and Companies)

Short Answer (SA) Type I Questions (2 Marks)
Question 1.
Pass necessary journal entries for recording the following transactions at the time of dissolution of the firm
(i) Z, a partner agreed to pay-off his wife’s loan ₹ 20,000.
(ii) Y who undertakes to carry out the dissolution proceedings is allowed ₹ 2,000 for the same.
Answer:

Question 2.
State the reasons for the following
(i) When an asset is taken over by a partner, his capital account is debited.
(ii) Cash or bank account is not transferred to realisation account on dissolution of firm.
Answer:
(i) When an asset is taken over by a partner, his capital account is debited because the value of the
assets is charged from his capital, thus his capital account is reduced.
(ii) Cash or bank account will not be transferred to realistation account because it is already realised and can be distributed in its present form.

Question 3.
Rajeev, Manish and Mahesh were three partners in a firm who were sharing profits in the ratio of 5 : 3 : 2 as at 31st March, 2020. Due to poor health, Rajeev decided to retire on 31st March, 2020. All his dues were fully paid to him on his retirement. Balance sheet of Rajeev, Manish and Mahesh as at 31st March, 2020 was as follows


It was agreed that
(i) Fixed assets are to be depreciated by ₹ 5,500.
(ii) Make a provision for doubtful debts at 5% on debtors.
(iii) New profit sharing ratio of Manish and Mahesh will be 2 : 3.
(iv) A liability for claim, included in creditors of ₹ 22,000 is settled at ₹ 17,600.
Prepare revaluation account.
Answer:

Short Answer (SA) Type II Questions (3 Marks)
Question 4.
X Ltd. purchased the assets of Y Ltd. for ₹ 1,00,000 payable in fully paid 9% debentures of ₹ 100 each. What entries will be passed in the books of X Ltd, if such issue is
(i) at par (ii) at a premium of 25%
Or
Priya Services Pvt. Ltd. issued 15,000, 6% debentures of ₹ 10 each at a premium of 10% on 1st January, 2020, these debentures are redeemable after 3 years at a premium of 10%. Company spent ₹ 35,000 as a expense on issue of these debentures, which is written-off immediately in same year of issue. Pass the journal entries for expenses incurred on issuing debentures and writing-off these expenses and loss on issue of debentures in same year in which it is incurred.
Answer:

Working Notes
1. Number of debentures issued = \(\frac{1,00,000}{100}\) = 1,000 Debentures
2. Number of debentures issued = \(\frac{1,00,000}{100+25}\) = 800 Debentures
Or

Working Notes
1. Loss on Issue of Debentures = Premium on Redemption of Debentures (15,000 × 1) = ₹ 15,000
2. Securities Premium Reserve available balance from issue of debentures (15,000 × 1) = ₹ 15,000

Question 5.
X, Y and Z are partners sharing profits and losses in the ratio of 2 : 2 : 1. Y retires from the firm on 31st March, 2020. On the date of Y’s retirement, the following balances
Advertisement Suspense Account – ₹ 25,000
Contingency Reserve – ₹ 15,000
Workmen’s Compensation Reserve – ₹ 20,000
Loss in Business Account – ₹ 15,000
Pass the necessary journal entries for the adjustment of these items on Y’s retirement.
Or
X, Y and Z were partners in a firm sharing profits in 2 : 2 : 1 ratio. X died on 1st July, 2020. On that date, the goodwill of the firm was valued at ₹ 22,500. On the death of a partner, his share of profit in the year of death was to be calculated on the basis of the average profits of the last four years.
The profit for the last four years were
2016-17 – ₹ 80,000;
2017-18 – ₹ 72,000
2018-19 – ₹ 84,000;
2019-20 – ₹ 56,000 (Loss)
Pass necessary journal entries.
Answer:

Or

Working Notes
1. X’s Share of Goodwill = 22,500 × 2/5 = ₹ 9,000 (to be adjusted by Y and Z in the ratio 2 : 1)
2. Four Years Average Profit = \(\frac{80,000+72,000+84,000+(56,000)}{4}\) = ₹ 45,000
X’s share of profit = 45,000 × \(\frac{2}{5} \times \frac{3}{12}\) = ₹ 4,500

Question 6.
Ishu and Nishu are partners sharing profits and losses in the ratio of 2 : 1. On 31st December, 2019, the partners decided to dissolve the firm. Complete the realisation account and partners’ capital account.

Answer:

Long Answer (LA) Type Questions (5 Marks)
Question 7.
Following is the receipts and payments account of Green Club for the year ended 31st March, 2020

Additional Information
(i) The club owned furniture ₹ 12,000 and books ₹ 5,600 on 1st April, 2019.
(ii) Salary and rent were outstanding ₹ 480 and ₹ 960 on 31st March, 2020.
(iii) Subscription outstanding on 31st March, 2019 was ₹ 1,600 and on 31st March, 2020 was ₹ 2,000.
Prepare income and expenditure account and balance sheet for the year ending 31st March, 2020.
Answer:


Working Note
Accured Interest on Invesments = 16,000 × \(\frac{9}{100} \times \frac{9}{12}\) – 360 = 1,080 – 360 = ₹ 720

Question 8.
ABC Ltd. issued 20,000, 9% debentures of ₹ 100 each at a discount of 4% payable ₹ 30 on application and the balance on allotment. The debentures are redeemable after 5 years. Give necessary journal entries for the issue of debentures and write-off discount on issue of debentures in same year of issue, if company has a balance of ₹ 1,00,000 in securities premium reserve account.
Or
Malakar Ltd. issued 10,000, 6% debentures of ₹ 100 each to the public on 1st April, 2019 at a discount of ₹ 10 per debenture. Pass the necessary journal entries regarding issue of debentures in the books of the company in the following cases
(i) These debentures are redeemable after 9 years at 10% premium.
(ii) These debentures are redeemable after 9 years at par.
Also, write-off loss on issue of debentures in same year of issue assuming there is no balance of securities premium reserve.
Answer:

Or

Question 9.
Following are the details furnished by Youth Club. You are required to prepare balance sheet as at 31st March, 2019 and 31st March, 2020.

Additional Information

Answer:


Working Note

Part B
(Analysis of Financial Statements)

Short Answer (SA) Type I Question (2 Marks)
Question 10.
Classify the following activities into cash flows under operating, investing or financing,
(i) Purchase of fixed assets
(ii) Redemption of debentures
Answer:
(i) Purchase of fixed assets is outflow of cash from investing activity.
(ii) Redemption of debentures is outflow of cash from financing activity.

Short Answer (SA) Type II Question (3 Marks)
Question 11.
From the following information, prepare comparative statement of profit and loss of Malakar Pvt. Ltd.

Or From the following information, prepare comparative balance sheet of Malishka Ltd.

Answer:

Or

Long Answer (I.A) Type Question (5 Marks)
Question 12.
From the following balance sheet of ABS Ltd as at 31st March, 2019 and 2020, prepare cash flow statement for the year ended 31st March, 2020.

Additional Information
(i) Depreciation charged on fixed assets was ₹ 1,62,000.
(ii) Interim dividend of 15% paid on equity shares. Additional shares issued at 31st March, 2020.
(iii) Preference shares were redeemed at a premium of 15%.
(iv) Fixed assets with a book value of ₹ 1,08,000 were sold at ₹ 67,500.
(v) Preference dividend paid ₹ 64,800.
(vi) Debentures interest paid during the year ₹ 37,800.
Answer:

Working Notes

Students can access the CBSE Sample Papers for Class 12 Accountancy 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 Accountancy Standard Term 2 Set 7 with Solutions

Maximum Marks: 40
Time allowed: 2 Hours

General Instructions:

• This question paper comprises two Parts -A and B. There are 12 questions in the question paper. J All questions are compulsory.
• Question nos. 1 to 3 and 10 are Short Answer Type I Questions carrying 2 marks each.
• Question nos. 4 to 6 and 11 are Short Answer Type II questions carrying 3 marks each.
• Question nos. 7 to 9 and 12 are Long Answer Type Questions carrying 5 marks each.
• There is no overall choice. However, an internal choice has been provided in 3 questions of three marks and 1 question of five marks.

Part A
(Accounting for Not-for-Profit Organisations, Partnership Firms, and Companies)

Short Answer (SA) Type I Questions (2 Marks)

Question 1.
V, W and X were carrying out a business as partners and sharing profits in the ratio of 2:1:1. Their balance sheet as at 31st December 2019 is as follows
Balance Sheet
as at 31st December 2019

V died due to Covid-19 on 31st December 2019. In this regard, following adjustments were agreed upon
(i) The value of buildings to be increased to ₹ 96,000.
(ii) The provision for bad and doubtful debts on debtors to be maintained at 3%.
(iii) Plant and machinery should be valued at 20% less.
You are required to prepare revaluation account.
Answer:

Question 2.
Why do firms revalue assets and reassess their liabilities on retirement or on the event of death of a partner?
Answer:
At the time of retirement of a partner, the assets and liabilities are revalued, so that the profit/loss on revaluation up to the date of retirement/death of a partner may be ascertained and adjusted in all partners’ capital accounts in their old profit sharing ratio because such profit or loss on revaluation relates to pre-retirement period.

Question 3.
From the following information, calculate the amount of subscriptions outstanding as at 31st March, 2020.
A club has 250 members each paying an annual subscription of ₹ 1,000. The receipts and payments account for the year showed a sum of ₹ 2,82,000 received as subscriptions.
The following additional information is provided

Answer:

Short Answer (SA) Type II Questions (3 Marks)

Question 4.
On 1st April 2020, Khushi Ltd. issued 50,000,10% debentures of ₹ 100 each at a discount of 10%. These debentures were redeemable at a premium of 5% after four years. Pass necessary journal entries for issue of debentures.
Or
Arihant and Company Ltd. issued 6,000,12% debentures of ₹ 100 each to its vendor Suraj and Sons. These debentures are issued @ 15% premium for the consideration of plant purchased. A cheque of ₹ 3,50,000 was also issued to that vendor. Pass the necessary journal entries of the above-given information.
Answer:


Working Notes
1. 12% Debentures account = 6,000 x 100 = ₹ 6,00,000
2. Securities Premium Reserve Account =6,000 x 15= ₹ 90,000
3. Payable to Suraj and Sons =6,00,000 + 90,000 + 3,50,000 = ₹ 10,40,000

Question 5.
Following is the balance sheet of Hari, Ram, and Shyam as at 31st December 2019.
Balance Sheet
as at 31st December 2019

Ram retires on 31st March 2020. Under the partnership agreement, he was entitled to the following amounts.
(i) Amount standing to the credit of his capital account.
(ii) Interest on capital, which amounted to ₹ 62.50.
(iii) His share of goodwill ₹ 3,500.
Draw up Ram’s account.
Or
What journal entries would be passed for the following transactions on the dissolution of a firm of partners Raju and Priya after various assets and third-party liabilities have been transferred to realisation account?
(i) Workmen compensation reserve stood at ₹ 6,000 and liability in respect of it was ascertained at ₹ 6,000.
(ii) There was no workmen compensation reserve and firm had to pay ₹ 1,500 as compensation to the workers.
(iii) Building (Book value ₹ 50,000) sold for ₹ 80,000 through a broker who charged 2% commission.
(iv) Investments (Book value ₹ 4,000) realised 150%.
Answer:

Working Notes:
1. Ram’s share of goodwill, i.e., ₹ 3,500 to be distributed between Hail and Shyam in 1 : 1 ratio i.e.,
Hari =3,500 x \(\frac{1}{2}\) = ₹ 1,750, Shyani = 3,500 x \(\frac{1}{2}\) =₹ 1,750
2. Reserve Fund =3200 x \(\frac{1}{3}\) = ₹ 1066.67.

Question 6.
Following is the receipts and payments account of Star Club for the year ending 31st March 2020.
Receipts and Payments Account

Additional Information
(i) On 1st April, 2019 the club had investments ₹ 64,000, machinery ₹ 4,800, books ₹ 8,000.
(ii) Salary outstanding 31st March, 2019 ₹ 416 and 31st March, 2020 ₹ 528.
Prepare income and expenditure account for the year ending 31st March, 2020.
Answer:

Long Answer (LA) Type Questions (5 Marks)

Question 7.
A, B and C were partners sharing profits in the ratio of 2: 2 :1. The balance sheet on 31st March 2020, when they dissolved the firm was as follows
Balance Sheet
as at 31st March 2020

It was agreed that
(i) B is to take over all stock for ₹ 17,000 and some sundry assets at ₹ 72,000 (being 10% less than the book value).
(ii) The expenses of realization were ₹ 2,700. The remaining debtors were sold to a debt collecting agency at 50% of the value.
(iii) A to take over furniture at ₹ 8,000 and debtors amounting to ₹ 1,20,000 at ₹ 1,17,200 and the creditors of ₹ 16,000 were to be paid by him at this figure.
(iv) C to take over remaining sundry assets at 80% of the book value and assume the responsibility of discharge of loan together with accrued interest of ₹ 2,300.
Prepare necessary accounts to close the books of the firm.
Answer:


Working Notes
1. Book value of the sundry assetstaken over by B =72000 x \(\frac{100}{90}\) = 80,000
Remaining sundry assets = 1,17,000-80,000 = ₹ 37,000
Sundry assets taken over by C = 37,000 x \(\frac{80}{100}\) = ₹ 29,600

2. Book value of the debtors taken over by A = ₹ 1,20,000
Remaining debtors =1,24,200 – 1,20,000 = ₹ 4,200
Debtors collected by agency = 4200 x \(\frac{50}{100}\) = ₹ 2,100

Question 8.
From the following receipts and payments account of Sonic Club and from the given additional information prepare income and expenditure account for the year ending 31st December 2020 and the balance sheet as on 31st December 2019 and 31st December 2020.
Receipts and Payments Account

Additional Information
(i) The club had received ₹ 10,000 for subscription in 2019 for 2020.
(ii) Salaries had been paid only for 11 months.
(iii) Stock of sports equipment on 31st December 2019 was ₹ 1,50,000 and on 31st December 2020 ₹ 3,25,000.
Answer:


Working Note
The value of investments has been calculated as below
If interest is 8, the value of investments =100
If interest, is 20,000, the value of investments = \(\frac{100}{8} \) x 20,000 = ₹ 2,50,000

Question 9.
ABC Ltd. purchased assets of the book value of 8,00,000 and took over the liabilities of ₹ 1,00,000 for XYZ Ltd.
It was agreed that the purchase consideration settled at ₹ 7,60,000, be paid by issuing debentures of ₹ 100 each.
What journal entries will be made in the following cases, if debentures are issued
(i) at par
(ii) at a discount of 10%
(iii) at a premium of 10%
It was agreed that any fraction of debentures be paid in cash.
Or
Pass the journal entries for issue of debentures in following cases
(i) Raghu Ltd. issued 35,000, 9% debentures of ₹ 100 each payable on application and redeemable at premium of 10% after 5 years.
(ii) Raghu Ltd. issued 3,000,10% debentures of ₹ 100 each issued at a premium of 10% and redeemable at a premium of 10%.
(iii) Raghu Ltd. issued 4,000,11% debentures of ₹ 100 each issued at a discount of 10% and redeemable at a premium of 10%.
Answer:

Working Notes
1. No. of debentures =\(\frac{7,60,000}{90}\) = 8,444.44
Taking 8,444 debentures only and rest take paid in cash.
2. No. of debentures = \(\frac{7,60,000}{110} \)  = 6,909.090
Taking 6,909 debentures only and rest paid in cash.

Part B
(Analysis of Financial Statements)

Short Answer (SA) Type I Question (2 Marks)

Question 10.
State whether the following amounts to investing, operating or financing activity
(i) Sale of a fixed asset.
(ii) Receipts from the sale of goods and services.
Answer:
(i) Sale of fixed assets is investing activity. Investing activity relates to acquiring and selling of fixed assets.
(ii) Receipts from the sale of goods and services is an operating activity. Operating activities are the
primary activities of a business and involves manufacturing, distributing, selling, marketing etc.

Short Answer (SA) Type II Question (5 Marks)

Question 11.
Following is the balance sheet of Shri Ram Fabrics Ltd. who are engaged in the production and supply of green energy in the rural areas of India. Using the below information, prepare comparative balance sheet.

Or
From the following balance sheets of Drishti Ltd. prepare cash from operating activities for the year ended 31st March 2020.


Additional Information
(i) Debentures were issued on 31st March 2020.
(ii) Non-current investments were purchased on 31st March 2020.
(iii) Rate of interest on investments is 10% p.a.
Answer:


Long Answer (LA) Type Questions (5 Marks)

Question 12.
The summarised balance sheet of RK Ltd. as at 31st March 2019 and 2020 were as under Balance Sheet
as at 31st March 2019 and 2020

Additional Information
(i) Investments costing ₹ 4,000 were sold during the year 2019-20 for ₹ 4,250.
(ii) Provision for taxation made during the year was ₹ 4,500.
(iii) During the year, part of the fixed assets costing ₹ 5,000 was sold for ₹ 6,000 and the profit was induded in the statement of profit and loss.
(iv) Dividend paid during the year amounted to ₹ 20,000. You are required to prepare the cash flow statement.
Answer:

Students can access the CBSE Sample Papers for Class 12 Economic 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 Economics Term 2 Set 9 with Solutions

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.

Maximum Marks: 40
Time: 2 Hours

Short Answer (SA) Type I Questions (2 Marks)

Question 1.
If the Real GDP is ₹400 and Nominal GDP is ₹450, calculate the Price Index, (base = 100).
Or
Find Gross Value Added at Factor Cost.

Item	₹ (in crores)
Units of Output Sold	2,000
Price Per Unit of Output	20
Depreciation	2,000
Change-in-stock	(-) 500
Intermediate Cost	15,000
Subsidy	3,000

Answer:
Real GDP = ₹400; Nominal GDP = ₹450
Price Index = \(\frac{\text { Nominal GDP }}{\text { Real GDP }} \times 100=\frac{450}{400}\) x 100 = 112.5
Or
Gross Value Added at Factor Cost (GVAFC) = (Output Sold x Price Per Unit) + Change-in-stock – Intermediate Cost + Subsidy
= (2,000 x 20) + (- 500) -15,000 + 3,000
= 4,000 – 15,500 + 3,000
= ₹27,500 crore

Question 2.
Given below is the consumption function of an economy.
C = 100 + 0.5Y
With the help of a numerical example, show that in this economy as income increases, Average Propensity to Consume (APC) will decrease.
Answer:
C = 100 + 0.5 Y, substituting the values of Y as 400, 500 and 600, we get the schedule as below

y	C	APC = \(\frac{C}{Y}\)
400	300	0.75
500	350	0.70
600	400	0.67

In the given schedule, we can observe that as income rises, APC declines from 0.75 to 0.67.

Thus, as income is increasing, APC is decreasing.

Question 3.
Write a short note on the Great Proletarian Cultural Revolution of China.
Or
Mention any two failures in the structural reforms of Pakistan.
Answer:
Great Proletarian Cultural Revolution (1966-76) In 1965, Mao Tse Tung started a cultural revolution on a large scale. In this revolution, students and professionals were sent to work and learn from the countryside. Unlike GLF, campaign the cultural revolution did not have an explicit economic rationale.
Or
Failures of structural reforms in Pakistan are

• Growth rate of GDP and its sectoral constituents have fallen in 1990s.
• Poverty and unemployment are still areas of major concerns.

Question 4.
Observe the data given below carefully and answer the question.

Stunting and Underweight (%) among Children Below Age 5 Prevalence of Stunting and Underweight among Children Below 5 Years at State-level, 2014

Source Annual Health Survey Report, A Report on Clinical, Anthropometric and Bio-Chemical Survey (Part II)

Name two states that have highest percentage of underweight children in the country under 2 SD category. What does it indicate?

Or
The problem of land degradation in India is increasing. What are the factors responsible for it?
Answer:
Jharkhand and Uttar Pradesh have highest underweight children population in the mentioned category. This indicates the poor health infrastructure of these states and unequal distribution of resources.
Or
Land in India suffers from varying degrees and types of degradation mainly due to excessive use and inappropriate management practices.

The factors responsible for land degradation in India are (any two)

• Loss of vegetation occurring due to deforestation.
• Unsustainable fuel, wood and fodder extraction.
• Shifting cultivation.

Question 5.
What changes will take place to bring an economy in equilibrium if planned savings are greater than planned investment?
Answer:
In such a situation, the following changes will occur

• Stocks of the producers would be in excess of the desired limit.
• Profits will start shrinking.
• The desired level of output for the subsequent year will face a cut.
• Levels of income and employment will tend to shrink to the point where S = I.

Thus, the economy will come back to a state of equilibrium.

Short Answer (SA) Type II Questions (3 Marks)

Question 6.
Name and explain the various types of factor incomes.
Answer:
Factor incomes are broadly classified as under
(i) Compensation of Employees It includes wages and salaries in cash and facilities such as free education to children, free medical facilities, housing, free uniform, etc. employer’s contribution to social security scheme and pension on retirement.

(ii) Operating Surplus It refers to income from one’s property and entrepreneurship.
It includes the following items

• Rent
• Interest
• Profit

Profit is further split into three components as a dividend, corporate profit tax and retained earnings.

(iii) Mixed-Income It refers to the incomes of the self-employed persons using their own labour, land, capital and entrepreneurship to produce goods and services.

Question 7.
Complete the following table

Or
Draw the straight line saving curve for an economy and derive from it the consumption curve, explaining the method of derivation. Show a point on the consumption curve at which Average Propensity to Consume (APC) is equal to 1.
Answer:

Below diagram clearly depicts, savings at zero level of income is negative and equal to OA. It implies that consumption at zero level of income is positive and equal to OB. Therefore, consumption curve starts from B.

At OY₁, level of savings is equal to zero which implies consumption is equal to income. So, the consumption curve must pass through Y line (sloped 45°). It cuts Y at E. Now, joining Band £ and extending it forward, we get consumption curve.

Diagram Showing Derivation of Consumption Curve

Here, straight line consumption curve shows level of consumption at zero level of income and C = Y at Y₁ level of income. Now, APC = \(\frac{C}{Y}\)

∴ APC is equal to 1, when consumption is equal to income i.e., C = Y. This occurs at point E.

Question 8.
Observe the graphs carefully and answer the question.
Source Health Statistics, Statistical Report 2912, RGI

Note HP – Himachal Pradesh, AP – Andhra Pradesh, TN – Tamil Nadu, UP – Uttar Pradesh, WB – West Bengal, J&K – Jammu & Kashmir

Health sector in India is affected by urban-rural and rich-poor divide. Briefly explain how?

Direction Read the following text carefully and answer questions 9 and 10 given below Global warming and climate change have the potential to alter biological systems. More specifically, changes to near-surface air temperatures will likely influence ecosystem functioning and thus the biodiversity of plants, animals, and other forms of life. The current geographic ranges of plant and animal species have been established by adaptation to long-term seasonal climate patterns. As global warming alters these patterns on timescales considerably shorter than those that arose in the past from natural climate variability, relatively sudden climatic changes may challenge the natural adaptive capacity of many species.

A large fraction of plant and animal species are likely to be at an increased risk of extinction if global average surface temperatures rise another 1.5 to 2.5 °C (2.7 to 4.5 °F) by the year 2100.

Species loss estimates climb to as much as 40 percent for a warming in excess of 4.5 °C (8.1 °F)-a level that could be reached in the IPCC’s higher emissions scenarios. A 40 percent extinction rate would likely lead to major changes in the food webs within ecosystems and have a destructive impact on ecosystem function.

Surface warming in temperate regions is likely to lead changes in various seasonal processes-for instance, earlier leaf production by trees, earlier greening of vegetation, altered timing of egg laying and hatching, and shifts in the seasonal migration patterns of birds, fishes, and other migratory animals. In high-latitude ecosystems, changes in the seasonal patterns of sea ice threaten predators such as polar bears and walruses; both species rely on broken sea ice for their hunting activities.

Also in the high latitudes, a combination of warming waters, decreased sea ice and changes in ^ ocean salinity and circulation is likely to lead to reductions or redistributions in populations of algae and plankton. As a result, fish and other organisms that forage upon algae and plankton may be threatened. On land, rising temperatures and changes in precipitation patterns and drought frequencies are likely to alter patterns of disturbance by fires and pests.

Numerous ecologists, conservation biologists and other scientists studying climate warn that rising surface temperatures will bring about an increased extinction risk. In 2015, one study that examined 130 extinction models developed in previous studies predicted that 5.2 percent of species would be lost with a rise in average temperatures of 2 °C (3.6 °F) above temperature benchmarks from before the onset of the Industrial Revolution. The study also predicted that 16 percent of Earth’s species would be lost if surface warming increased to about 4.3 °C (7.7 °F) above preindustrial temperature benchmarks.

Other likely impacts on the environment include the destruction of many coastal wetlands, salt marshes, and mangrove swamps as a result of rising sea levels and the loss of certain rare and fragile habitats that are often home to specialist species that are unable to thrive in other environments.

For example, certain amphibians limited to isolated tropical cloud forests either have become extinct already or are under serious threat of extinction. Cloud forests – tropical forests that depend on persistent condensation of moisture in the air-are disappearing as optimal condensation levels move to higher elevations in response to warming temperatures in the lower atmosphere.

Source https://zvww.britannica.com/science/global-warming/Environmental-consequences-of-global- warming
Answer:
It is correctly said that health sector in India suffers from urban-rural and rich-poor divide. 70% population is living in rural areas but only 20% of the total hospitals are located in rural areas. In other words, 80% of total hospitals are available for only 30% of urban population.

There are only 0.36% hospitals for one lakh people in rural areas whereas it is 3.6 % hospitals per one lakh population in urban areas, i.e. number of hospitals in urban areas is 10 times the number of hospitals in rural areas. In villages, specialised medical care is completely missing like pediatrics, gynecology, anesthesia and obstetrics.

PHCs located in rural areas do not have even X-ray or blood test facilities. 20% of doctors passing, leave the country for better prospects. Many others are interested in urban areas, rare are the ones interested in rural areas. The poorest one-fifth spends 12% of their income on health while rich spend only 2% of their income on health.

Question 9.
Over the past few decades, the detrimental impact of global warming has impacted the mankind in a big way, state its impact on mankind.
Answer:
The gradual increase in the average temperature of Earth’s lower atmosphere is called global warming. It occurs due to greenhouse gases such as carbon dioxide, methane etc.

The following are the effects of global warming (any three)

• During the past century, the atmospheric temperature has risen by 1.10°F or 0.60°C.
• This has led to the melting of polar ice, resulting in an increase in sea levels. This has further led to the risk or coastal flooding.
• Disruption of drinking water supplies is dependent on the melting of snow.
• It has led to the extinction of certain species.
• It has led to more frequent tropical storms.

Question 10.
Briefly explain few measures to control environmental degradation.
Answer:
The following measures are needed to prevent environmental degradation (any three)
(i) Population Control Rising population is a threat, especially for developing countries like India as it possess threat on the environment. Therefore, it is absolutely essential to check the rising population if the environment is to be protected.

(ii) Social Awareness must be spread among the people to understand the negative consequences of pollution. This will help in reducing overuse of environmental resources.

(iii) Water Management For the protection of environment, provisions must be made to supply clean drinking water to the people. Also we need to make people aware of the judicial use of available fresh water. Also, people need to reduce misuse of ground water.

(iv) Improvement in Housing For the protection of environment, living places of the people should be made neat and clean. Houses should be constructed keeping in view the environmental challenges.

Long Answer (LA) Type Questions (5 Marks)

Question 11.
What are the various means by which countries are trying to strengthen their own domestic economies?
Answer:
The following are the various means through which the nations are trying to strengthen their own domestic economies
(i) Nations are forming various regional and economic groupings like SAARC, European Union, G-8, G-20, ASEAN, etc. in order to strengthen their economies through economic cooperation among the countries in the group to safeguard their common interests.

(ii) They are also trying to know and analyse the developmental process adopted by their neighboring nations, so as to evaluate their strengths and weaknesses and formulate policies accordingly.

(iii) Nations have also resorted to liberalising their economies by minimising government interference in economic activities. The economy is governed by market forces that promote efficiency and strengthen the economy.

(iv) Nations have also adopted the process of globalisation to integrate their economies with other economies of the world in order to provide wide international market for their domestic producers and attract foreign investment.

(v) In recent past, India managed to establish good domestic industries, that has not only helped in development of infrastructure but also led to increase in outsourcing services and inflow of foreign exchange.

Question 12.
From the following data, calculate the Net National Product at Market Price (NNPMP) by
(i) Expenditure method
(ii) Income method

Items	₹ (in crores)
Personal Consumption Expenditure	700
Wages and Salaries	700
Gross Business Fixed Investment	60
Gross Residential Construction Investment	60
Inventory Investment	20
Profits	100
Government Final Consumption Expenditure	200
Rent	50
Exports	40
Imports	20
Interest	40
Net Factor Income from Abroad	(-) 10
Depreciation	20
Subsidies	10
Indirect Taxes	20
Mixed-Income of Self-employed	140

Or
Find out the Net Value Added at Factor Cost (NVAFC) of a producing unit from the following data. What will be the value of national income in this situation?

Items	₹ (in lakhs)
Total Sales	24,000
Closing Stock	4,200
Opening Stock	3,000
Indirect Taxes	1,200
Subsidies	900
Depreciation	1,800
Purchase of Raw Material from Other Firms	6,000

Answer:
(i) Net National Product at Market Price (NNP_MP) by Expenditure Method
Gross Domestic Product at Market Price (GDP_MP) = Private Final Consumption Expenditure + Government Final Consumption Expenditure + Gross Domestic Capital Formation (Gross Business Fixed Investment + Gross Residential Construction Investment + Inventory Investment) + Net Exports
= 700 + 200 (60 + 60 + 20) + 20
= ₹1,060 crore
NNP_MP = GDP_MP + Net Factor Income from Abroad – Depreciation
= 1/160 + (-10) – 20 = 1,060 – 30
= ₹1,030 crore

(ii) Net National Product at Market Price (NNPmp )by Income Method
Net Domestic Product at Factor Cost
(NDP_FC) = Compensation of Employees + Operating Surplus + Mixed Income
= 700 + (100 + 50 + 40) + 140
= 700 + 190 + 140
= ₹1,030 crore

NNP_MP = NDP_FC + Net Indirect Tax (Indirect Tax – Subsidies) + Net Factor Income from Abroad
= 1,030 + (20 – 10) + (-10)
= 1,030 + 10 – 10
= ₹1,030 crore

Or

Gross Value Added at Market Price (GVA_MP) = Value of Output [Sales + Change-in-stock (Closing Stock – Opening Stock)] – Intermediate Consumption
GVA_MP = 24,000 + (4,200 – 3 D00) – 6,000
GVA_MP = 25,200 – 6,000
= ₹19,200 lakhs

Net Value Added at Factor Cost (NVA_FC)
= GVA_MP – Depreciation – Net Indirect Tax (Indirect Tax – Subsidies)
= 19,200 – 1,800 – (1,200 – 900)
= 19,200 – 2,100
= ₹17,100 lakh

National income is NNP_FC. So, NNP_FC = NVA_FC + NFIA. As in this case NFIA is not given, so, assuming it to be zero, value of NNP_FC will became equal to the value of NVA_FC i.e., ₹17,100 lakhs.

Question 13.
(i) Briefly explain the components of aggregate supply.
(ii) If national income is ₹90 crore and consumption expenditure is ₹81 crore, find out Average Propensity to Save. When income rises to ₹100 crore and consumption expenditure to ₹88 crore, what will be the Marginal Propensity to Consume and Marginal Propensity to Save?
Answer:
(i) The two main components of AS are

• Consumption expenditure (C)
• Saving (S)

A major portion of income is spent on consumption of goods and services and the balance is saved.

Aggregate Supply/National Income = Consumption + Savings or Y = AS = C + S

(ii) Here, in first condition, Y = ₹90 crore C = ₹81 crore
Average Propensity to Save
\(\mathrm{APS}=\frac{S}{Y}=\frac{Y-C}{Y}=\frac{90-81}{90}=0.10\)
Again, when the income and consumption expenditure rise,
Y = ₹100 crore
C = ₹88 crore
ΔC = 88 – 81 = ₹7 crore
ΔY = 100 – 90 = ₹10 crore
Marginal Propensity to Consume (MPC)
\(=\frac{\Delta C}{\Delta Y}=\frac{7}{10}=0.70\)
Again, Marginal Propensity to Save (MPS)
= 1 – MPC = 1 – 07 = 0.30

Students can access the CBSE Sample Papers for Class 12 Economic 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 Economics Term 2 Set 8 with Solutions

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.

Maximum Marks: 40
Time: 2 Hours

Short Answer (SA) Type I Questions (2 Marks)

Question 1.
Give the differences between ex-ante savings and ex-post savings.
Or
What do you understand by frictional unemployment and structural unemployment? Explain briefly.
Answer:
Differences between ex-ante and ex-post savings are (any two)

Basis	Ex-ante (Planned) Savings	Ex-post (Actual) Savings
Meaning	It refers to the desired level of savings.	It refers to the realised level of savings.
Reaction with Investments	In an accounting year, planned savings may or may not be equal to planned investment.	In an accounting year, actual savings is always equal to actual investment. (This is according to the principle of National Income Accounting).
Determination of Income	Equilibrium level of income is determined where planned savings is equal to planned investment.	Actual savings has no relevance in the determination of equilibrium level of income.

Or
(i) Frictional Unemployment It is that unemployment which arises due to immobility of labour, shortage of raw material, power, wear and tear of machinery, search of jobs. It is generally associated with changing jobs in the economy.

(ii) Structural Unemployment It is that unemployment which results from long-term decline of certain industries. It arises when there is change in production technique. It also arises when labourers are trained in old and decaying industries and are not adequately equipped for new industries.

Question 2.
An increase of ₹250 crore in investment in an economy resulted in total increase in income of ₹1,000 crore. Calculate Marginal Propensity to Consume (MPC).
Answer:
Calculation of Marginal Propensity to Consume
Multiplier (K) = \(\frac{1}{1-\mathrm{MPC}}\)
4 = \(\frac{1}{1-\mathrm{MPC}}\) (∵ Multiplier is 4 as income increased 4 times due to increase in investment)
4 (1- MPC) = 1
4 – 4MPC = 1
4 – l = 4MPC
\(\frac{3}{4}\) = 0.75 = MPC
i.e., Marginal propensity to consume = 0.75

Question 3.
Whether the following items will be included in national income or not? Give reasons for your answer.
(i) Bonus to employees
(ii) Purchase of books by a student
Or
Briefly describe money flow.
Answer:
(i) Bonus to Employees It will be included. Bonus paid to the employees is a factor payment and thus included in national income.

(ii) Purchase of Books by a Student It will be included. Purchase of books by a student is included in private final consumption expenditure.
Or
In money flow, factor services by the households are exchanged for monetary compensations by the firms. The below circular flow ought to explain money flow in a two-sector economy without the presence of financial market.

Money flow in a two-sector economy without financial market

Question 4.
Write a short note on Special Economic Zone (SEZ).
Answer:
A Special Economic Zone (SEZ) is an area in a country that is subject to different economic regulations than other regions within the same country.

Its aim includes increased trade balance, employment, increased investment, job creation and effective administration. To encourage businesses to set up in the zone, financial policies are introduced.

Question 5.
“Low employment among women is a reflection of economic backwardness of a country.” Suggest some measures to increase employment opportunities for women.
Or
Explain what role do trade unions play in the protection of workforce, keeping in view that the worker participation rate is low in country.
Answer:
I shall suggest the following measures to increase the employment opportunities for women (any two)

1. Education and training opportunities for women should be further expanded, diversified and made easily accessible.
2. Residential accommodation for working mothers should be increased.
3. There should be much more facilities of creches and child care during the working hours of mothers.
4. There should be large scale publicity and building of public opinion in favour of employment of women.

Or

Trade unions are voluntary organisations of workers formed to promote and protect the interests of workers through collective action.

The formation of trade unions was a reaction against the mechanisms of pauperisation, low pay, long working hours, child labour and generally appalling working conditions. Thus, the role of trade unions is to fight against poverty of workers, exploitation and the violation of their basic human dignity and to promote social justice in the global economy.

Short Answer (SA) Type II Questions (3 Marks)

Question 6.
State whether the following statements are true or false. Give reason in support of your answer.

(i) The value of Average Propensity to Save (APS) can be negative.
(ii) The value of Marginal Propensity to Save (MPS) can be negative.
Or
State any three causes of deficient demand.
Answer:
(i) True, because in a condition when consumption is greater than income, then Average Propensity
to Save (APS) is negative due to dissavings. This relation can be expressed as
C > Y ⇒ APS > 1
(ii) False, because Marginal Propensity to Save (MPS) is ratio between additional savings and additional income which is always positive. Infact, MPS can never be negative.
Or
Deficient demand occurs due to following causes (any three)

• Reduction in propensity to consume which reduces private consumption expenditure is a cause of deficient demand.
• Sometimes, instead of making fresh investments, government resort to disinvestment causing fall in aggregate demand.
• Decline in exports and rise in imports is yet another cause of deficient demand.
• High rate of inflation is also a cause of deficient demand.

Question 7.
Why are exports included in the estimation of domestic product by the expenditure method?
Answer:
According to expenditure method, national income is measured in terms of expenditure on purchase of final goods and services in the economy during an accounting year.

Net exports is the difference between exports and imports during an accounting year. If goods exported exceed the goods imported, then this will result in increase in the income of the country.

With increased income, the expenditure will also increase, because of this reason exports are included in the estimation of domestic product by expenditure method.

Question 8.
Observe the data given below carefully and answer the question
The 10 Most Affected Countries in 2019

Source https://www.hindustantimes.com/india-news/india-seventh-most-ajfected-by-climate-change- in-2019-globally-report-101611552192319.html

As per the data given above, India is at number 7 in the list of top 10 countries that are most affected by the environmental changes. What contributed to the India’s environmental crisis?

Direction Read the following text carefully and answer questions 9 and 10 given below

Infrastructure is regarded as a core support system that enables an economy to grow and develop. Generally, the term infrastructure means technical structure such as roads, transport, communication, bridges, dams, power, public institutions like schools, hospitals, etc. These structures not only serve as basic input for various economic activities like production, investment, but also enable an economy to break the shackles of traditional and primitive social structures and customs.

The difference between a developed country and an underdeveloped country can be mainly attributed to the lack of sufficient and technically advanced infrastructure in the latter.

Infrastructure has two-fold benefits-as an input and as a support system. Infrastructure as an input (roads, bank and power) facilitates the production process and attracts investment from domestic as well as from foreign investors.

Infrastructure as a support system (such as schools, hospital) develops the quality of human capital by imparting quality and technical education and health facilities. This raises the standard and quality of living and helps the economy to eradicate major economic problems like poverty, unemployment and inequality. Hence, it can be concluded that the presence of quality and sufficient infrastructure is a necessary and sufficient condition for accomplishing economic growth and development.

However, the expansion of the private sector in India has forced the passages of a number of regulations to promote quality of care and protect consumers. This has expanded the role of government in developing and enforcing regulations in three areas of the health sector: drugs, medical practice and health facilities. These regulations have been promulgated by both national and state governments.

The challenge for the future will be to ensure the quality and efficiency of health services in both the public and private sectors through these regulatory mechanisms while seeking to promote national health objectives. Eighty per cent of spending on health in India is from personal funds, but existing laws do not ensure that private medical services maintain even minimum standards, says the report.

“Powerful medical lobbies have opposed government efforts to regulate the private sector,” it says, adding that India’s medical councils are not enforcing laws relating to registration and licensing of medical practitioners. In a section on private healthcare services, the report acknowledges problems that consumer health organisations have long complained about doctors over prescribing drugs, recommending unnecessary investigations and treatment, and failing to provide appropriate information for patients.

“The Indian Medical Association has consistently opposed any kind of regulation,” said Ravi Duggal, coordinator of Mumbai’s Centre for Enquiry into Health and Allied Themes, a non-governmental organisation that has long been campaigning for minimum standards.

A survey in Mumbai in the mid-1990s showed gross deficiencies in the quality of medical services. “There were clinics operating out of residential flats, with kitchens turned into operating theatres,” said Dr Abhay Shukla, project coordinator at the centre.

Source https://www.ncbi.nlm.nih.gov/pmclarticleslPMC314535l(Modified)
Answer:
The environmental problems which may arise in India due to population growth, increased industrial and agricultural activities and depletion of natural resources in the next 25 years, are discussed here. Selected aspects of problems which require special attention are treated with particular emphasis on rural situations. The present status of the various aspects of human settlement such as quality of air, water, sanitation, health and housing as well as aspects of conservation of forests, soils and wildlife, is outlined as far as possible in a quantitative manner. It is visualised that environmental management will have to be more serious and of growing dimensions in the coming years.

Question 9.
In your view, is it essential for the government to regulate the fee structure in healthcare institutions? If so, why?
Answer:
Health is the basic requirement of human beings, so that they may be able to live a life of dignity. It is the responsibility of government to ensure health facilities to even the poorest of the poor.

For this purpose, either the government should itself provide these services through government . hospitals or encourage private sector participation in these sectors.

As India has a vast population which still lacks healthcare, it does not seem feasible for government alone to fulfill the requirement in this sector due to lack of resources.

Hence, private sector is allowed to operate in this sector. But private sector works with profit as the primary motive and so, if government does not regulate the fee structure in healthcare institutions, the fee may become too high to be in affordable limits of common people.

Question 10.
Why infrastructure is called the support system on which depends the efficient working of a modern economy?
Answer:
Infrastructure is the basic fundamental structure of the economy that is required for economic development. It increases the productivity of the factors of production and improves the quality of life of its people. Also, efficient working of a modem economy depends on development of infrastructure.

Agricultural production depends largely on the adequate expansion and development of irrigation facilities and power supply needed for the same. Industrial production increase depends on the development of power and electricity generation, transport and communication. Thus, high productivity is possible only when the country have a strong support system in terms of infrastructural facilities.

Long Answer (LA) Type Questions (5 Marks)

Question 11.
State the similar developmental strategies pursued by India and Pakistan on their path to development.
Answer:
India and Pakistan have followed following similar strategies in their respective development plans

1. India and Pakistan both started their development process on the basis of economic planning after getting independence in 1947.
2. Both of them have adopted the mixed economic system involving the co-existence of both the public and the private sector.
3. Both the countries relied more on the public sector for initiating the process of growth and development.
4. Both of them introduced economic reforms around the same time to strengthen their economies. Pakistan initiated reforms in 1988 and India followed in 1991.
5. They both have announced Five Year Plans for growth and development.

Question 12.
(i) From the following data, calculate national income by income method.

Items	₹ (in crores)
Government Final Consumption Expenditure	400
Subsidies	40
Rent	800
Wages and Salaries	2,400
Indirect Tax	240
Private Final Consumption Expenditure	3,200
Gross Domestic Capital Formation	480
Social Security Contributions by Employer	220
Royalty	100
Net Factor Income Paid to Abroad	120
Interest	80
Net Domestic Capital Formation	440
Profits	520
Net Export	280

(ii) Can Gross Domestic Product (GDP) be greater than Gross National Product (GNP)? Explain.
Or
(i) What is the difference between depreciation and depreciation reserve fund?
(ii) Assuming real income to be ₹200 crore and price index to be 135, calculate nominal income.
Answer:
(i) National Income by Income Method
Net National Product at Factor Cost (NNP_FC) = Rent + Wages and Salaries + Social Security Contribution by Employer + Royalty + Interest + Profits – Net Factor Income paid to Abroad
= 800 + 2,400 + 220 +100 + 80 + 520 – 120
= ₹ 4,000 crores

(ii) Gross Domestic Product (GDP) can be greater than Gross National Product (GNP), if net factor income from abroad is negative.

Net factor income from abroad will be negative if factor payments from abroad are less than factor payments to abroad.
Or
(i) Difference between depreciation and depreciation reserve fund.

Basis	Depreciation	Depreciation Reserve Fund
Concept	It is the loss of value of fixed assets in use, on account of normal wear and tear.	It is a provision of funds created by producers to cope up with depreciation losses.
Effect	It leads to correct computation of profit.	These funds are used for the replacement of fixed assets when these are worn out.
Reason	Expected or foreseen obsolescence, normal wear and tear.	Obsolete/outdated assets need to be replaced.

(ii) Given,
Real Income = ₹200 crores and Price Index = 135, Nominal Income = ?
We know that, Price Index = \(\frac{\text { Nominal Income }}{\text { Real Income }} \times 100\)

On substituting the vanables, we get, 135 = \(\frac{\text { Nominal Income }}{\text { 200 }} \times 100\)

⇒ Nominal Income 135 x 2 = 270 or ₹ 270 crore.

Question 13.
(i) In an economy, total savings are ₹2,000 crore and the ratio of average propensity to save and average propensity to consume is 2 : 7. Calculate the level of income in an economy.
(ii) How bank rate is different from repo rate? Which instrument is more effective for term goals to curb inflation?
Answer:
(i) Here,
S = ₹2,000 crore
\(\frac{\mathrm{APS}}{\mathrm{APC}}\) = \(\frac{2}{9}\), APS = \(\frac{S}{Y}\)
Here, S = APS x Y = \(\frac{2}{9}\) x Y (Where, Y = Income)
or 2,000 = \(\frac{2}{9}\) x Y
or Y = \(\frac{2}{9}\) x 2,000
So, National Income = ₹19,000 crore

(ii) Bank rate is the rate at which RBI lends to commercial bank for a period of more than 90 days, however repo rate is the rate at which RBI lends funds to commercial banks for a period ranging from 1 to 14 days. Repo rate is more effective tool to curb inflation in short-run.

Students can access the CBSE Sample Papers for Class 12 Maths with Solutions and marking scheme Term 2 Set 3 will help students in understanding the difficulty level of the exam.

CBSE Sample Papers for Class 12 Maths Term 2 Set 3 with Solutions

Maximum Marks : 40
Time : 2 Hours

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

Question 1.
A bag contains 5 red, 7 green and 4 white balls. Three balls are drawn one after the other without replacement. Find the probability that the balls drawn are white, green and green respectively.
Answer:
A bag has 5 red, 7 green and 4 white balls.
So, Total balls = 5 + 7 + 4 = 16
P(White, green and green) = P(White). P(green/white).P(green/white and green)
\(\frac{4}{16} \times \frac{7}{15} \times \frac{6}{14}=\frac{1}{20}\)

Question 2.
Find the direction cosines of the line passing through the two points (-1, 2, 3) and (2, -3, 5).
Answer:
We know that the direction cosines of a line joining two points P and Q are given by

Thus, the direction cosines of the line joining two points is
\(\frac{3}{\sqrt{38}}, \frac{-5}{\sqrt{38}}, \frac{2}{\sqrt{38}}\)

Question 3.
Find: ∫ cos 6x \(\sqrt{1+\sin 6 x}\) dx.
OR
Find ∫\(\left(x+\frac{1}{x}\right)^{2}\)dx
Answer:
We have I = ∫ cos 6x \(\sqrt{1+\sin 6 x}\) dx.
Put t = 1 + sin 6x, so that dt = 6 cos 6x dx

Therefore ∫ cos 6x \(\sqrt{1+\sin 6 x}\) dx = \(\frac{1}{2}\)∫t^1/2 dt
= \(\frac{1}{6} \times \frac{2}{3}\)(t)^3/2 + C
= \(\frac{1}{9}\)(1 + sin6x)^3/2 + C

OR

Let I = ∫\(\left(x+\frac{1}{x}\right)^{2}\)dx

Question 4.
From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being queens?
Answer:
Total number of ways of getting two cards,
n(S) = ⁴C₂ = \(\frac{52 \times 51}{2 \times 1}\) = 1326

Let E be the event of getting two queens out of 4.

Question 5.
\(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) are unit vectors such that 2\(\vec{a}\) + 3\(\vec{b}\) + 4\(\vec{c}\) = 0 and the angle between \(\vec{a}\) and \(\vec{b}\) is θ, find the value of (4cosθ – 1).
Answer:
2\(\vec{a}\) + 3\(\vec{b}\) + 4\(\vec{c}\) = 0
2\(\vec{a}\) + 3\(\vec{b}\) = – 4\(\vec{c}\)

Taking dot product with itself

⇒ 4 + 9 + 12.cos θ = 16
⇒ 12 cos θ = 3
⇒ cos θ = \(\frac{1}{4}\)
Now, 4 cos θ – 1 = 4 × \(\frac{1}{4}\) – 1
= 0

Question 6.
Find the order and degree of the following differential equation:
\(\left\{1+\left(\frac{d y}{d x}\right)^{2}\right\}^{3 / 2}=k \frac{d^{2} y}{d x^{2}}\)
Answer:
The highest derivative occuring in the differential equation:

Which is of order 2. Hence the order of the differential equation is 2.
The equation

as a polynomial in derivative.
Raising both sides of the powre 2 we have,

The exponent of the highest order derivative, i.e.,\(\frac{d^{2} y}{d x^{2}}\) is 2. Thus the degree of the equation is 2.

Section – B

Question 7.
Find the shortest distance between the following pairs of lines:
\(\frac{x-8}{3}=\frac{y-5}{-2}=\frac{z-10}{7}\) and \(\frac{x-15}{3}=\frac{y+1}{8}=\frac{z-5}{-5}\)
Answer:
Given equation of two lines
\(\frac{x-8}{3}=\frac{y-5}{-2}=\frac{z-10}{7}\) ……….(1)
and
\(\frac{x-15}{3}=\frac{y+1}{8}=\frac{z-5}{-5}\) …….(2)

Line (1) passes through (8, 5, 10) and has direction ratios proportional to 3, -2, 7, So its vector equation is
\(\overrightarrow{r_{1}}=\overrightarrow{a_{1}}+\lambda \overrightarrow{b_{1}}\)

Where \(\overrightarrow{a_{1}}\) = 8î + 5ĵ + 10k̂ and \(\overrightarrow{b_{1}}\) = 3î + 2ĵ + 7k̂
Line (2) passes through (15, – 1, 5) and has direction ratios 3, 8, -5, so its vector equation is
\(\overrightarrow{r_{2}}=\overrightarrow{a_{2}}+\lambda \overrightarrow{b_{2}}\)

Where \(\overrightarrow{a_{2}}\) = 15î – ĵ + 5k̂ and \(\overrightarrow{b_{2}}\) = 3î + 8ĵ – 5k̂

The shortest distance between the lines

OR

Given equation of lines are
\(\frac{x+5}{5 \lambda+2}=\frac{2-y}{5}=\frac{1-z}{-1}\)
and \(\frac{x}{1}=\frac{2 y+1}{4 \lambda}=\frac{1-z}{-3}\)

Above equation can be written as

Comparing equations (i) and (ii) with one point form of line \(\frac{x-x_{1}}{a}=\frac{y-y_{1}}{b}=\frac{z-z_{1}}{c}\) we get
a₁ = 5λ + 2, b₁ = -5, c₁ = 1
and a₂ = 1, b₂ = 2λ, c₂ = 3

Since, two lines are perpendicular,
∴ a₁a₂ + b₁b₂ + c₁c₂ = 0
⇒ 1(5λ + 2) + 2λ(-5) + 3(1) = 0
⇒ 5λ + 2 – 10λ + 3 = 0
⇒ -5λ + 5 = 0
⇒ 5λ = 5
⇒ λ = 1

Question 8.
Evaluate ∫\(\frac{(3 x+4)}{x^{2}+12 x+32}\) dx
Answer:
Let I = ∫\(\frac{(3 x+4)}{x^{2}+12 x+32}\) dx
Let 3x + 4 = A(\(\frac{d}{d x}\)(x² + 12x + 32) + B
⇒ 3x + 4 = A(2x + 12) + B

On comparing the coefficients,
2A = 3
⇒ A = \(\frac{3}{2}\)
and 12A + B = 4
⇒ B = 4 – 12.\(\frac{3}{2}\)
= 4 – 18 = – 14

Putting x² + 12x + 32 = t in first integral

Question 9.
If \(\vec{a}\) = î + ĵ + k̂ and \(\vec{b}\) = ĵ – k̂, then find \(\vec{c}\) such that \(\vec{a} \times \vec{c}=\vec{b}\) and \(\vec{a} \cdot \vec{c}\) = 3
Answer:
Let \(\vec{a}\) = xî + yĵ + zk̂
and \(\vec{a}\) = î + ĵ + k̂, \(\vec{b}\) = ĵ – k̂

Given \(\vec{a} \times \vec{c}=\vec{b}\)
\(\left|\begin{array}{ccc}
\hat{i} & \hat{j} & \hat{k} \\
1 & 1 & 1 \\
x & y & z
\end{array}\right|\) = ĵ – k̂

⇒ î(z – y) – ĵ(z – x) + k̂(y – x) = ĵ – k̂
∴ z – y = 0 ……..(2)
x – y = 1 ………(3)

\(\vec{a} \cdot \vec{c}\) = 3

Again given,
(î + ĵ + k̂). (xî + yĵ + zk̂) = 3 ……….(4)
⇒ x + y + z = 3 ………..(5)

On adding equation (2) and (3), we get
2x – y – z = 2

Solving equation (4) and (5), we get
x = \(\frac{5}{3}\), y = \(\frac{2}{3}\) and z = \(\frac{2}{3}\)

Now, \(\vec{c}\) = \(\frac{5}{3} \hat{i}+\frac{2}{3} \hat{j}+\frac{2}{3} \hat{k}\)
= \(\frac{1}{3}\)(5î + 2ĵ + 2k̂)

Question 10.
Solve the differential equation:
x\(\frac{d y}{d x}\) – y + sin \(\left(\frac{y}{x}\right)\) = 0

OR

Find a particular solution:
\(\frac{d y}{d x}\) = y tanx; y = 1 when x = 0.
Answer:
The given differential equation is,
x\(\frac{d y}{d x}\) – y + sin \(\left(\frac{y}{x}\right)\) = 0

Intergrating both sides, we get

Intergrating both sides, we get
∫\(\frac{d y}{y}\) = ∫ tan x dx

⇒ log y = log(sec x) + log C
⇒ log y = log(C × sec x)
⇒ y = C × sec x ………(1)

Now, y = 1, when x = 0
⇒ 1 = C × sec 0
⇒ C = 1

Substituting C = 1 in equation (1), we get
y = sec x.

Section – C

Question 11.
Find ∫\(\frac{\sec x}{1+{cosec} x}\) dx
Answer:


For t = -1,
⇒ – 1 = A[1 + (- 1)] [1 – (- 1)] + B[1 – (-1)] + C(1 + (-1)]²
⇒ -1 = A × 0 + B × 2 + C(0)²
⇒ -1 = 2B
⇒ B = \(\frac{1}{2}\)

For t = 1,
⇒ 1 = A(1 + 1) (1 – 1) +B(1 – 1) +C (1 + 1)²
⇒ 1 = A × 0 + B × 0 + C (2)²
⇒ 1 = 4C
⇒ C = \(\frac{1}{4}\)

For t = 0,
⇒ 0 = A(1 + 0)(1 – 0) + B(1 – 0) + C(1 + 0)²
⇒ 0 = A(1)(1) + B(1) + C(1)²
⇒ 0 = A + B + C
⇒ 0 = A + \(\left(\frac{-1}{2}\right)+\frac{1}{4}\)
⇒ A = \(\frac{1}{4}\)

From (1), we get

Question 12.
Find the area of the region enclosed between the parabola y² = x and the line x + y = 2.
OR
Using integration, find the area of a triangle ABC, coordinates of whose vertices are A(4,l), B(6,6), C(8,4).
Answer:
Given, curve is y² = x ……….(1)
It is a right hand parabola whose vertex is (0, 0)

Given x + y = 2
⇒ y = 2 – x

From equation (1) and (2)
(2 – x)² = x
⇒ 4+ x² – 4x = x
⇒ x² – 5x + 4 = 0
⇒ x² – 4x – x + 4 = 0
⇒ x(x – 4) – 1(x – 4) = 0
∴ x = 1, 4.
Putting in equation (2), we get
if, x = 1 then y = 1 and
if, x = 4 then y = -2

OR

The given points are A(4, 1), B(6, 6), and C(8, 4)
Equation of AB is given by
⇒ y – 1 = \(\frac{6-1}{6-4}\)(x – 4)
⇒ y – 1 = \(\frac{5}{2}\)(x – 4)
⇒ y = \(\frac{5}{2}\)x – 9 ………….(1)

Equation of BC is given by
y – 6 = 1(x – 6)
⇒ y = -x + 12

Similarly, equation of AC is given by
y – 1 = \(\frac{3}{4}\)(x – 4)
⇒ y = \(\frac{3}{4}\)x – 2

Question 13.
Find the equation of the plane passing through the points (1, 0, – 2), (3, – 1, 0) and perpendicular to the plane 2x – y + z = 8. Also find the distance of the plane thus obtained from the origin.
Answer:
Given points, P(1, 0, -2), Q (3, -1, 0)
Given plane 2x – y + z = 8

Normal vector of given plane,
\(\overrightarrow{n_{1}}\) = 2î – ĵ + k̂

Now,
\(\overrightarrow{P Q}\) = 2î – ĵ + 2k̂

Normal vector of required plane,
\(\overrightarrow{n_{2}}=\left(\overrightarrow{n_{1}} \times \overrightarrow{\mathrm{PQ}}\right)\)

= \(\left|\begin{array}{ccc}
\hat{i} & \hat{j} & \hat{k} \\
2 & -1 & 1 \\
2 & -1 & 2
\end{array}\right|\)
= – 1.î – 2ĵ + 0k̂ = -i – 2ĵ

Required equation of plane,
-1(x – 1) + (-2)(y – 0) + 0(z + 2) = 0
⇒ -x + 1 – 2y + 0 = 0
⇒ x + 2y = 1

Therefore, the required equation of the plane is, x + 2y = 1.
Now, distance from origin (0,0,0) is,

Therefore, distance from origin is \(\frac{1}{\sqrt{5}}\) units.

Question 14.
Sanjay, Ajay and Vijay are three best friends. After completing their MBA from IIM Lucknow. They apply for the job in the same company for the post of manager in finance department. Chances of selection of Sanjay, Ajay and Vijay are in the same ratio of 1 : 2 : 4. The probabilities that Sanjay can increase the profits of the company by his efforts is 0.8 whereas probabilities for the sam task of Ajay and Vijay are 0. 5 and 0.3 respectively.
From the above information attempt the following questions:
(i) A be event of increase the profit then find if it is due to Ajay.
(ii) If E₁, E₂ and E₃, be events of not increase the profits, then find the probability that is due to the appointment of Vijay?
Answer:
Let E₁ be event of selecting Sanjay, E₂ be event of selecting Ajay and E₃ be event of selecting Vijay.
∴ P(E₁) = \(\frac{1}{7}\)
P (E₂) = \(\frac{2}{7}\)
P(E₃) = \(\frac{4}{7}\)

(i) A be event of increasing profits
P(\(\frac{\mathrm{A}}{\mathrm{E}_{1}}\))
P(\(\frac{\mathrm{A}}{\mathrm{E}_{2}}\))
P(\(\frac{\mathrm{A}}{\mathrm{E}_{3}}\))

(ii) Let P be the event of not increases in profits.