Bhagya

Students can Download Tamil Nadu 12th Accountancy Model Question Paper 3 English Medium Pdf, Tamil Nadu 12th Accountancy Model Question Papers helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

TN State Board 12th Accountancy Model Question Paper 3 English Medium

Instructions:

1. The question paper comprises of four parts.
2. You are to attempt all the parts. An internal choice of questions is provided wherever applicable.
3. All questions of Part I, II. III and IV are to be attempted separately.
4. Question numbers 1 to 20 in Part I are Multiple Choice Questions of one mark each. These are to be answered by choosing the most suitable answer from the given four alternatives and writing the option code and the corresponding answer.
5. Question numbers 21 to 30 in Part II are two-mark questions. These are to be answered in about 50 words.
6. Question numbers 31 to 40 in Part III are three-mark questions. These are to be answered in about 150 words.
7. Question numbers 41 to 47 in Part IV are five-mark questions. These are to be answered in about 250 words. Draw diagrams wherever necessary.

Time: 2.30 Hours
Max Marks: 90

PART – I

Answer all the questions. Choose the correct answer.[Answers are in bold] [20 x 1 = 20]

Question 1.
The total assets of the proprietor are ? 5,00,000. His liabilities ? 3,50,000. Then his capital in the business is
(a) Rs 8,50,000
(b) Rs 1,50,000
(c) Rs 3,50,000
(d) Rs 4,25;000
Answer:
(b) Rs 1,50,000

Question 2.
A firm has assets worth Rs 60,000 and capital 45,000; then its liabilities is
(a) Rs 45,000
(b) Rs 1,05,000
(c) Rs 60,000
(d) Rs 15,000
Answer:
(d) Rs 15,000

Question 3.
Income and expenditure accounts show
(a) Cash available to an organization
(b) Closing capital of an organization
(c) Cash available in the bank account
(d) Surplus or deficit for the current accounting period
Answer:
(d) Surplus or deficit for the current accounting period

Question 4.
On what basis the receipts and payments account is prepared
(a) Cash basis
(b) Credit basis
(c) Both
(d) None of these
Answer:
(a) Cash basis

Question 5.
The balance in the appropriation account is transferred to the partner’s capital account in the
(a) Agree ratio
(b) Sacrifice ratio
(c) Profit sharing ratio
(d) Old ratio
Answer:
(c) Profit sharing ratio

Question 6.
Amount invested by partners in the partnership business is called
(a) Owner’s capital
(b) Partners capital
(c) Profit and loss appropriation
(d) None of these
Answer:
(b) Partners capital

Question 7.
The profit earning capacity of the firm determines the value of its
(a) Balance Sheet
(b) good will
(c) Profit and Loss Account
(d) All of these
Answer:
(b) good will

Question 8.
Goodwill acquired by making payment in cash or kind is called
(a) Purchased goodwill
(b) Self-generated goodwill
(c) Average goodwill
(d) (a) and (b)
Answer:
(a) Purchased goodwill

Question 9.
A new partner may be admitted to a partnership
(a) with the consent of all the partners
(b) with the consent of any one partner
(c) with the consent of two-third of the old partners
(d) with the consent of three-fourth of the old partners
Answer:
(a) with the consent of all the partners

Question 10.
An incoming partner is liable for all the acts of the firms dare
(a) Before his admission
(b) After his admission
(c) From six months prior to his admission
(d) None of these
Answer:
(b) After his admission

Question 11.
The profit or loss arising therefrom is transferred to the capital accounts of all the partners in the
(a) New profit sharing ratio
(b) Old profit sharing ratio
(c) Gaining ratio
(d) Sacrificing ratio
Answer:
(b) Old profit sharing ratio

Question 12.
The settlement is to be done in the manner prescribed in the
(a) Partnership-at-will
(b) Partnership deed
(c) Both (a) and (b)
(d) None of these
Answer:
(b) Partnership deed

Question 13.
Company is a voluntary association of persons which has separate
(a) legal entity
(b) voluntary association
(c) common seal
(d) limited liability
Answer:
(a) legal entity

Question 14.
The liability of the shareholders of the company is limited to the extent of face value of the shares held by the
(a) share holders
(b) card holders
(c) debenture holders
(d) None of these
Answer:
(a) share holders

Question 15.
The term fund refers to
(a) working capital
(b) opening capital
(c) closing capital
(d) None of these
Answer:
(a) working capital

Question 16.
When figure relating to several years are considered for the purpose of analysis, the analysis is called
(a) Horizontal analysis
(b) vertical analysis
(c) Trend analysis
(d) Cash flow analysis
Answer:
(a) Horizontal analysis

Question 17.
Which ratios measure the firm’s ability to meet its short term obligations in time?
(a) Profitability Ratios
(b) Liquidity Ratios
(c) Activity Ratios
(d) None of these
Answer:
(b) Liquidity Ratios

Question 18.
For Calculating Quick Assets – and- are excluded from current assets
(a) Debtors and inventory
(b) Inventory and Bills payable
(c) Cash and Bank balances
(d) Inventory and Prepaid Expenses
Answer:
(d) Inventory and Prepaid Expenses

Question 19.
Ideal current Ratio is
(a) 1 : 1
(b) 1 : 2
(c) 2 : 1
(d) 3 : 1
Answer:
(c) 2 : 1

Question 20.
Which of the following options is used to view Trial Balance from Gateway of Tally?
(a) Gateway of Tally → Reports → Trial Balance
(b) Gateway of Tally → Trial Balance
(c) Gateway of Tally → Reports → Display → Trial Balance
(d) None of these
Answer:
(c) Gateway of Tally → Reports → Display → Trial Balance

PART – II

Answer any seven questions in which question no. 30 is compulsory. [7 × 2 = 14]

Question 21.
From the following particulars ascertain profit or loss?
Capital as on 1. 4. 2018 1,60,000
Capital as on 31. 3. 2019 1,50,000
Additional capital introduced 25,000
Drawings made during the year 30,000
Answer:
Statement of profit or loss for the year ended 31.3.2019

Question 22.
From the following particulars of Tamil Educational Society.
Prepare Receipts and Payments for the year ended 31.03.2019

Answer:

Question 23.
What is partners current account?
Answer:
Under fixed capital method, Capital account and current accounts are maintained. In current account all adjustments relating to partners are recorded on the credit side of current account viz: Interest on capital, Share of profits, Salary and commission etc are recorded.
On the debit side drawings interest on drawings, share of loss are recorded. Current account sometimes show credit or debit balance.

Question 24.
The following are the profits of a firm in the last five years 2014 – Rs 4,000, 2015 – Rs 3,000, 2016 – Rs 5,000, 2017 – Rs 4,500, 2018 – Rs 3,500. Calculate the value of goodwill at 3 years purchase of average profit of five year.
Answer:
Goodwill = Average profit × No. of years of purchase

Good will = Average profit × No. of years of purchase
= Rs 4,000 × 3
Goodwill = Rs 12,000

Question 25.
Mala and Vimala were partners sharing profit and losses in the ratio of 3 : 2. On 31.3.2017. Varshini was admitted as a partner. On the date of admission. The book of the firm showed a reserve fund of Rs 50,000. Pass the journal entry to distribute the reserve fund.
Answer:
Journal Entry

Question 26.
Mary, Vleena, Mariam are partners of a firm sharing profit and losses equally. Many retired from the partnership on 1.1.2019. On that date, their balance sheet showed accumulated loss of Rs 75,000. On the assets side of Balance Sheet. Give the journal entry to distribute the accumulated loss.
Answer:
Journal Entry

Question 27.
Anitha was holding 500 equity shares of Rs 10 each of Thanjavur Motors Ltd. issued at par. She paid Rs 3 on application Rs 5 on allotment but could not pay the first and final call of Rs 2. The directors forfeited the shares for non payment of call money. Give Journal Entry for forfeiture of shares.
Answer:
Journal Entry

Question 28.
What is working capital?
Answer:
Working capital statement or schedule of changes in working is prepared to disclose net changes in working capitals on two specific dates (generally two balance sheet dates). It is prepared from current assets and current liabilities.
Working Capital = Current Assets – Current Liabilities

Question 29.
What is meant by accounting ratio?
Answer:
Ratio is a mathematical expression of relationship between two related or interdependent items. It is the numerical or quantitative relation ship between two items. It is calculated by dividing one item by the other related item. When ratios are calculated on the basis of accounting information, these are called ‘accounting ratio’.

Question 30.
What are accounting reports?
Answer:
Accounting report is a compilation of accounting information that are derived from the accounting records of a business concern. Accounting reports may be classified as routine reports and special purpose reports.

PART – III

Answer any seven questions in which question No. 40 is compulsory. [7 x 3 = 21]

Question 31.
Following are the balances of Shanthi as on 31.12.2018

Answer:
Prepare a statement of affairs as on 31.12.2018 and calculate capital as at that date.

Question 32.
Compute income from subscription for the 2018 from the following particulars relatiiig to a club.

Answer:
Subscription received during the year 2018 Rs 1,50,000
Calculation of incomes from subscription for 2018

Question 33.
From the following information prepare capital accounts of partners Mannan and Sevagan when their capitals are fluctuating.

Answer:
Partners Capital Account

Question 34.
From the following information relating to Sridevi Enterprises, calculate the value of goodwill on the basis of 4 years purchase of the average profit of 3 years.
(a) Profits for the year ending 31st December 2016, 2017 and 2018 were Rs 1,75,000, 1,50,000 and Rs 2,00,000 respectively.
(b) A non – recuring income of Rs 45,000 is included in the profits of the year 2016.
(c) The closing stock of the year 2017 was overvalued by Rs. 30,000
Answer:
Calculation of adjusted profit

Goodwill = Average profit × Number of years of purchase
= 1,60,000 × 4
= Rs 6,40,000

Question 35.
A, B and C were partners. Sharing profits and losses in the ratio of 5 : 3 : 2. D is admitted into a partnership. The following adjustments are to be made.
(a) Increase the value of premises by Rs 60,000
(b) Depreciate stock by Rs 5,000; Furniture by Rs 2,000 and Machinery by Rs 2,500.
(c) Provide for an outstanding liabilities of Rs 500. Pass the journal entries.
Answer:
Journal Entries

Question 36.
Kavitha, Kumudha and Lalitha are partners sharing profit and losses in the ratio of 5 : 3 : 3 respectively. Kumudha retires on 31st Dec 2018. On the date of retirement, her capital account shows a credit balance of Rs 2,00,000 pass journal entries of
(i) The amount due is paid off immediately by cheque.
(it) The amount due is not paid immediately
(iii) Rs 70,000 is paid immediately by cheque
Answer:

Question 37.
Maruthu Ltd. forfeited 150 equity shares @ Rs 10 each for non-payment of final call of Rs 4/- per share of these 100 shares were reissued @ Rs 9/- per share. Pass journal entries for forfeiture and reissue.
Answer:
Journal entries

Forfeited shares:
150 shares = Rs 900
100 shares \(\frac{900}{150}\) × 100 = Rs 600
Gain or loss = Amount forfeited – loss on reissue
= Rs 600 – 100 = Rs 500

Question 38.
From the following particulars prepare comparative income statement of Mary Co. Ltd.

Answer:
Comparative income statement of Mary Co. Ltd. for the year ended 31st March 2016 and 31st March 2017

Note: Calculation of income tax
For 2015-16 = 2,00,000 × 20% = Rs 40,000;
For 2016-17 = 3,20,000 × 50% = Rs 1,60,000

Question 39.
Explain the objectives of ratio analysis?
Answer:
Following are the objectives of ratio analysis.

1. To Simplify accounting figures
2. To Facilitate analysis of financial statements
3. To analyses the operational efficiency of a business.
4. To help in budgeting and forecasting
5. To facilitate intro firm and inter firm comparison of performance.

Question 40.
Mention the commonly used voucher types in Tally ERP.9. Following are some of the major accounting vouchers used in an organisation.
Answer:

1. Receipt voucher
2. Payment voucher
3. Contra voucher
4. Purchase voucher
5. Sales voucher
6. Journal voucher

PART – IV

Answer all the following questions. [7 × 5 = 35]

Question 41 (a).
Raju does not keep proper books of accounts. Following details are taken from his records.

During the year introduced further capital of? 50,000 and withdraw ? 2,500 per month from the business for his personal use. Prepare statement of profit or loss with above information.
Answer:
Statement of affairs as on 1.1.2018

[OR]

(b) From the following particular calculate total purchases.

Answer:

Total Purchases = Cash Purchases + Credit Purchases
= Rs 3,20,000 + Rs 4,80,000
= Rs 8,00,000

Question 42(a).
From the following Receipts and Payments Account of Friends Football club for the year ending 31st March 2017. Prepare income and expenditure Account for the year ending 31.3.2017.

Additional information:
(i) The club had furniture of Rs 12,000 on 1.4.2016. Ignore depreciation on furniture
(ii) Subscription outstanding for 2016-17- Rs 600
(iii) Stock of sports material on 31.03.2017- Rs 100
(iv) Capital Fund as on 1st April 2016 was Rs 23,000
Answer:
Income and Expenditure Account for the year ended 31.03.17

[OR]

(b) From the following balance sheets of Brindha and Praveena who share profits and losses in the ratio of 3 : 4, calculate interest on capital at 6% p.a. for the year ending 31st December 2017.
Balance sheet as on 31st December 2017

On 1st July 2017, Brindha introduced an additional capital of Rs 6,000 and on 1st October 2017, Praveena introduced Rs 10,000. Drawings of Brindha and Praveena during the year were Rs 5,000 and Rs 7,000 respectively. Profit earned during the year was Rs 31,000.
Answer:

Profit credited = Profit earned Rs 31,000 – Balance profit as per balance sheet Rs 10,000 = Rs 21,000. This amount is distributed in their profit sharing ratio of 3 : 4.
Calculation of interest on capital:

Question 43(a).
Anand and Narayanan are partners in a firm sharing profits and losses in the ratio of 5 : 3. On 1st January 2018, their capitals were Rs 50,000 and Rs 30,000 respectively. The partnership deed specifies the following:
(a) Interest on capital is to be allowed at 6% per annum.
(b) Interest on drawings charged to Anand and Narayanan are Rs 1,000 and Rs 800 respectively.
(c) The net profit of the firm before considering interest on capital and interest on drawings amounted to Rs 35,000.
Give necessary journal entries and prepare profit and loss appropriation account as on 31st December 2018. Assume that the capitals are fluctuating.
Answer:

[OR]

(b) The following particulars are available in respect of a business carried on by a partnership firm:
(i) Profits earned: 2016: Rs 30,000; 2017: Rs 29,000 and 2018: Rs 32,000.
(ii) Profit of 2016 includes a non-recurring income of Rs 3,000.
(iii) Profit of 2017 is reduced by Rs 2,000 due to stock destroyed by fire.
(iv) The stock is not insured. But, it is decided to insure the stock in future. The insurance premium is estimated at Rs 5,600 per annum.
You are required to calculate the value of goodwill on the basis of 2 years purchase of average profits of the last three years.
Answer:

Goodwill = Average profit × Number of years of purchase
= 24,400 × 2 = Rs 48,800

Question 44(a).
Sri Ram and Raj are partners sharing profits and losses in the ratio of 2 : 1. Nelson joins as a partner on 1st April 2017. The following adjustments are to be made.
(i) Increase the value of stock by Rs 5,000
(ii) Bring into record investment of Rs 7,000 which had not been recorded in the books of the firm.
(iii) Reduce the value of office equipment by Rs 10,000
(iv) A provision would also be made for outstanding wages for Rs 9,500. Give journal entries and prepare revaluation account.
Answer:
Journal Entries

[OR]

(b) Kannan, Rahim and John are partners in a firm sharing profit and losses in the ratio of 5 : 3 : 2. The balance sheet as on 31st December, 2017 was as follows:

John retires on 1st January 2018, subject to following conditions:
(i) To appreciate building by 10%
(ii) Stock to be depreciated by 5%
(iii) To provide Rs 1,000 for bad debts
(iv) An unrecorded liability of Rs 8,000 have been noticed
(v) The retiring partner shall be paid immediately
Prepare revaluation account, partners capital account and the balance sheet of the firm after retirement.
Answer:

Question 45(a).
Sudha Ltd. offered 1,00,000 shares of Rs 10 each to the public payable Rs 3 on application, Rs 4 on share allotment and the balance when required. Applications for 1,40,000 shares were received on which the directors allotted as:
Applicants for 60,000 shares – Full
Applicants for 75,000 shares – 40,000 shares (excess money will be utilised for allotment)
Applicants for 5,000 shares – Nil
All the money due was received. Pass journal entries upto the receipt of allotment.
Answer:
In the books of Sudha Ltd. Journal entries

Working note

[OR]

(b) Prepare common-size statement of financial position for the following particulars of Rani Ltd.

Answer:
Common Size Balance sheet of Rani Ltd. as on 31st March 2016 to 31st March 2017

Question 46(a).
Lalitha Ltd. offered 30,000 equity shares of Rs 10 each to the public payable Rs 2 per share on application, Rs 3 on share allotment and the balance when required. Applications for 50,000 shares were received on which the directors allotted as:
Applicants for 10,000 shares – Full
Applicants for 35,000 shares – 20,000 shares (excess money will be utilised for allotment)
Applicants for 5,000 shares – Nil
All the money due was received. Pass journal entries upto the receipt of allotment.
Answer:
Journal Entries

[OR]

(b) From the following particulars of Neithal Ltd, calculate trend percentages.

Answer:
Trend analysis for Neithal Ltd

Question 47 (a).
From the following particulars, calculate the trend percentages of Babu Ltd.

Answer:
Trend Percentage of Babu Ltd. (In Thousands)

[OR]

(b) Calculate
(i) Inventory turnover ratio
(ii) Trade receivable turnover ratio
(iii) Trade payable turnover ratio and
(iv) Fixed assets turnover ratio from the following information obtained from Delphi Ltd.

Additional information:
Revenue from operations for the year Rs 10,50,000
Purchases for the year Rs 4,50,000
Cost of revenue from operations Rs 6,00,000
Assume that sales and purchase are for credit
Answer:

Students can Download Tamil Nadu 12th Accountancy Model Question Paper 2 English Medium Pdf, Tamil Nadu 12th Accountancy Model Question Papers helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

TN State Board 12th Accountancy Model Question Paper 2 English Medium

Instructions:

1. The question paper comprises of four parts.
2. You are to attempt all the parts. An internal choice of questions is provided wherever applicable.
3. All questions of Part I, II. III and IV are to be attempted separately.
4. Question numbers 1 to 20 in Part I are Multiple Choice Questions of one mark each. These are to be answered by choosing the most suitable answer from the given four alternatives and writing the option code and the corresponding answer.
5. Question numbers 21 to 30 in Part II are two-mark questions. These are to be answered in about 50 words.
6. Question numbers 31 to 40 in Part III are three-mark questions. These are to be answered in about 150 words.
7. Question numbers 41 to 47 in Part IV are five-mark questions. These are to be answered in about 250 words. Draw diagrams wherever necessary.

Time: 2.30 Hours
Max Marks: 90

PART-I

Answer all the questions. Choose the correct answer. [Answers are in bold] [20 × 1 = 20]

Question 1.
In case of net worth method of single entry system profit is ascertained by
(a) Comparing the capital in the beginning of the accounting period and the capital at the end of the accounting period
(b) Preparing profit and loss account
(c) Preparing a balance sheet
(d) Representative Personal Account
Answer:
(a) Comparing the capital in the beginning of the accounting period and the capital at the end of the accounting period

Question 2.
Profit = capital at the end + ? – capital introduced – capital in the beginning ………
(a) Sales
(b) Drawing
(c) Net purchases
(d) Revenue expenditure
Answer:
(b) Drawing

Question 3.
From the incomplete records, it is possible to prepare…………
(a) Ledger Accounts
(b) Trial Balance
(c) Statement of Affairs
(d) Personal Account
Answer:
(c) Statement of Affairs

Question 4.
Which of the following is to be recorded in an income and expenditure account?
(а) Purchase of a fixed asset
(б) Capital expenditure incurred in a fixed asset
(c) Profit on the sale of fixed asset
(d) Sale of a fixed assets
Answer:
(c) Profit on the sale of fixed asset

Question 5.
Subscription due but not yet earned is considered as an…………
(a) Asset
(b) Liability
(c) Income
(d) Expenditure
Answer:
(a) Asset

Question 6.
In India partnership firms are governed by the Indian Partnership act ………….
(a) 1932
(b) 1930
(c) 1992
(d) 1986
Answer:
(a) 1932

Question 7.
The maximum number of partners in a partnership firm is……….
(a) 25
(b) 10
(c) 30
(d) 50
Answer:
(d) 50

Question 8.
The monetary value of such advantage is termed as………..
(a) Goodwill
(b) Bank overdraft
(c) Capital
(d) Cash
Answer:
(a) Goodwill

Question 9.
Goodwill helps in earning more profit and attracts more…………
(a) Customers
(b) Producers
(c) Competitors
(d) Suppliers
Answer:
(a) Customers

Question 10.
When are unrecorded liabilities is brought into books is results in …………
(a) Profit
(b) loss
(c) income
(d) expense
Answer:
(b) loss

Question 11.
The revaluation profit or loss is transferred to the old partner’s capital accounts in their……..
(a) Old ratio
(b) New ratio
(c) Sacrifice ratio
(d) Gain ratio
Answer:
(a) Old ratio

Question 12.
A partner who retires from the firm is called an……….
(a) outgoing partner
(b) admitted partner
(c) death of a partner
(d) none of these
Answer:
(a) outgoing partner

Question 13.
Profits and loses of previous years which are not distributed to the partners are known as ………
(a) Accumulated profit and losses
(b) General reserve
(c) Reserve fund
(d) Workmen compensation fund
Answer:
(a) Accumulated profit and losses

Question 14.
The money raised by issuing shares is called………
(a) Share capital
(b) Dividend
(c) Equity capital
(d) Share application
Answer:
(a) Share capital

Question 15.
Profits are distributed among the shareholders in the form of………..
(a) Share
(b) Dividends
(c) Both
(d) None of these
Answer:
(b) Dividends

Question 16.
Which statements are involve personal judgements in certain cases?
(a) Financial statements
(b) Income statements
(c) Profit and loss account statements
(d) None of these
Answer:
(a) Financial statements

Question 17.
Different tools are used for analysing the…………
(a) Balance sheet
(b) Financial statement
(c) Income statement
(d) None of these
Answer:
(b) Financial statement

Question 18.
If the two items in a ratio are from income statement it is classified as ………….
(a) Balance sheet ratio
(b) Income statement ratio
(c) Inter-statement ratio
(d) None of these
Answer:
(b) Income statement ratio

Question 19.
If a ratio is computed with one item from income statement and another item from balance sheet it is called ……….
(a) Inter-statement ratio
(b) Balance sheet ratio
(c) Income statement ratio
(d) None of these
Answer:
(a) Inter-statement ratio

Question 20.
Transactions are to be recorded through………….
(a) Journal entries
(b) Voucher entries
(c) Accounting entries
(d) None of these
Answer:
(b) Voucher entries

PART – II

Answer any seven questions in which question no. 30 is compulsory. [7 × 2 = 14]

Question 21.
What are the possible reasons for keeping in complete records?
Answer:
(i) Simple method:
Proprietor, who do not have the proper knowledge of accounting principles. Find it much convenient and easier to maintain their business records under this system.
(ii) Less expensive:
It is an economical mode of maintaining records as there is no need to appoint specialised accountant.

Question 22.
What are the features of not- for-profit organisation?
Answer:

1. They are the organisations which function without any profit motive.
2. Their main aim is to provide services to a specific group or the public at large.
3. They do not undertake business or trading activities.

Question 23.
Mannan and Ramesh share profit and losses 3 : 1. The capital of Rs 80,000 and Rs 60,000 and their current accounts show a credit balance of Rs 10,000 and Rs 5,000 respectively. Calculate interest on capital at 5% p.a. for the year ending 31st march 2018 and show the journal entries.
Answer:
Interest on capital = amount of capital × rate of interest
Interest of Mannan’s capital = 80,000 × \(\frac{5}{100}\) = Rs 4,000
Interest of Ramesh’s capital = 60,000 × \(\frac{5}{100}\) = Rs 3,000
Note:
Balance of current account will not be considered for calculation of interest on capital.

Question 24.
The following are the profit of a firm in the last five years 2014 – Rs 8,000, 2015 – Rs 6,000, 2016 – Rs 10,000, 2017 – Rs 9,000, 2018 – Rs 7,000. Calculate the value of goodwill at 3 years purchase of average profits of five year.
Answer:
Goodwill = Average profit × No. of years of purchase

Goodwill = Average profit × No. of years of purchase
= Rs 8,000 × 3
Goodwill = Rs 24,000

Question 25.
What is the journal entries of transferring of accumulated profit and reserves?
Answer:

Question 26.
Kiran, vinoth and vimal are partners sharing profits in the ratio 5 : 3 : 2. Kiran retires and the new profit sharing ratio between vinoth and vimal is 2 : 1. Calculate the gaining ratio.
Answer:
Share gained = New share – Old Share

Question 27.
What is the journal entry forfeiture of shares?
Answer:
Journal Entry

Question 28.
What is analysis of Financial statement?
Answer:

1. Methodical classification of the data given in the financial statement.
2. Explaining the meaning and significance of the relationship between various financial factor,
3. Comparison of these relationship.

Question 29.
Calculate quick ratio of Ananth construction ltd from the following given below. Total current liabilities Rs 1,00,000, Inventories Rs 50,000,
Total current assets Rs 25,000, prepaid expenses Rs 15,000.
Answer:

= Current assets – Inventories – Prepaid expenses
= 2,50,000 – 50,000 – 15,000
= Rs 1,85,000

Question 30.
What are accounting reports?
Answer:
Accounting report is a compilation of accounting information that are derived from the accounting records of a business concern. Accounting reports may be classified as routine reports and special purpose reports.

PART – III

Answer any seven questions in which question No. 40 is compulsory. [7 × 3 = 21]

Question 31.
Following are the balances in the books of Thomas as on 31st march 2019.

Answer:

Question 32.
From the following particulars of Tamil Educational society. Prepare Receipts and payments account for year ended 31st march 2019.

Answer:

Question 33.
Mr A and B started a business on 1.4.2014 with capital of Rs 60,000, Rs 50,000 respectively. On 1st July 2014 Mr A withdrawal of Rs 8000 from his capital. Mr. B introduced additional capital Rs 10,000 on 30.9.2014. Calculate interest on capital at 5% p.a. for the year ending 31.03.2015.
Answer:

Question 34.
A firm has decided to value its goodwill at 3 years purchase of the average profits of 4 years using weighted average methods. Profits of past 4 years & respective weights are as follows.

compute the value of good will.
Answer:

Goodwill = Weighted Average profit × Number of years of purchase
= 24,800 × 3 = Rs 74,400

Question 35.
Sri Ram and Raj are partners sharing profit and losses in the ratio of 2 : 1. Nelson joins as a partner on 1.4.17.
The following adjustments are to be made.
(i) Increase the value of stock Rs 5,000
(ii) Bring into record investments of Rs 7,000, which had not been recorded in the books of the firm.
(iii) Reduce the value of office equipment by Rs 10,000.
(iv) A provision would also be made for outstanding wages for Rs 9,500. Give the journal entries.
Answer:
Journal Entries

Question 36.
Rahul, Ravi and Rohit are partners, sharing profits and loss in the ratio of 5 : 3 : 2. Rohit retires and the share is taken by Rahul and Ravi in the ratio of 3 : 2. Find out the new profit sharing ratio and gaining ratio.
Answer:
Rohit share = \(\frac{2}{10}\)
Share gained = Retiring partner share × Proportion of share gained

New share of continuing partners = old share + share gained

Question 37.
Anu company forfeited 200 equity shares of Rs 10 each issued at par held by thiyagu for non-payment of the final call of Rs 3 per share. The shares were reissued to laxman at Rs 6 per share, show the journal entries.
Answer:
In the books of Anu Company Journal entries

Question 38.
From the following prepare comparative income statement of Tharun & Co. Ltd.

Answer:
Comparative incomp statement of Tharun Co. Ltd. for the year ended 31st March 2017 and 31st March 2018

Tutorial note: Computation of percentage increase for revenue from operations.

Question 39.
Calculate operating profit ratio under the following cases,
Case 1: Revenue from operation Rs 20,00,000 operating profit Rs 3,00,000
Case 2: Revenue from operation Rs 30,00,000 operating cost Rs 24,00,000
Case 3: Revenue from operation Rs 40,00,000 gross profit 30% on revenue from
operations expenses Rs 8,00,000.
Answer:

Operating profit = Revenue from operation – operating cost
= 30,00,000 – 24,00,000 = Rs 6,00,000

Operating profit = Gross profit – Operating expenses
= 12,00,000 – 8,00,000 = Rs 4,00,000

Question 40.
What are the salient features of computerised Accounting system?
Answer:
(i) Simplicity:
They are easy to set up and simple to us.
(ii) Speed:
They are capable to generation instant and accurate report.
(iii) Power:
They are capable of maintaining accounts of multiple companies and with unlimited levels of classification.
(iv) Flexibility:
They provide flexibility to generate instant reports for giving period.

PART – IV

Answer all the following questions. [7 × 5 = 35]

Question 41(a).
From the following particulars calculate total purchase.

Answer:
Bills payable account

Total Purchases = Cash purchases + credit Purchase
= 7 3,20,000 + 74,80,000 = 7 8,00,000

[OR]

(b) From the following receipts and payments account of yercaud youth Association. Prepare income and expenditure Account for the year ended 31st march 2019 and the balance sheet as on that date.

Additional information:
(i) Opening capital fund Rs 20,000
(ii) Stock of books on 1.4.2018 Rs 9,200
(iii) Subscription due but not received Rs 1,700
(iv) Stock of stationery on 1.4.2018 Rs 1,200; stock of stationery on 31.3.2019 Rs 2,000.
Answer:
Income and Expenditure Account for the year ended 31.3.2019

Question 42(a).
Miss. Soniya sport equipment does not keep proper records from the following informations. Find out profit or loss and also prepare balance sheet for the year ended 31st December 2017.

Drawing Rs 10,000 per month for personal use, additional capital introduced during the year Rs 2,00,000. A bad debts Rs 2,000 and a provision of 5% to be made in debtors. Outstanding salary Rs 2,600 prepaid insurance Rs 700 depreciation changed as furniture at 10% P.a.
Answer:
Statement of affairs as on 31st December 2016

Balance sheet as on 31.3.2017

[OR]

(b) From the following Receipts and Payment account of Neyveli Science Club for the year ended 31st December 2018.

Additional information:
(i) Opening capital fund Rs 6,400
(ii) Subscription includes Rs 600 for the year 2019
(iii) Science equipment as on 1.1.2018 Rs 5,000
(iv) Surplus on account of exhibition should be kept in reserve for new auditorium.
Prepare income and expenditure account for the year ended 31st December 2018 and the balance sheet as on that date.
Answer:
Income and Expenditure Account for the year ended 31st Dec. 2018

Question 43(a).
Arulappan and Nallasamy are partners sharing profit and losses in the ratio 4 : 1. On 1st January 2018 their capitals were Rs 20,000 and Rs 10,000 respectively. The partnership deed specifies the following.
(а) Interest on capital is to he allowed at 5%P.a
(b) Interest on drawings charged to Arulappan and Nallasamy are Rs 200 and Rs 300 respectively.
(c) The net profit of the firm before considering interest on capital and interest on drawings amounted to Rs 18,000.
Give the journal entries and prepare profit and loss appropriation account for the year ending 31st December 2018. Assume that the capitals are fluctuating.
Answer:
Journal Entries

[OR]

(b) From the following information compute the value of goodwill by super profit method & capitalising method
(i) Capital employed is Rs 4,00,000
(ii) Normal rate of return is 10%
(iii) Profit for 2016 : Rs 62,000; 2017 : Rs 61,000 and 2018 : Rs 63,000
(iv) Super profit method:
Answer:

Normal profit = capital employed × Normal rate of return
= 400000 × \(\frac{10}{100}\)
= 40000
Super profit = Average profit – Normal profit = Rs 62,000 – 40,000
= Rs 22,000

Goodwill = Total capitalised value of the average profit – Capital employed = Rs 6,20,000 – 4,00,000
= Rs 22,000

Question 44(a).
Calculate the value of goodwill of the partnership firm of 2 partners
(а) At the 3 years purchase of average profits
(b) At the 3 years purchase of super profits
(c) On the basis of capitalisation of super profits
(d) On the basis of capitalisation of average profits
(i) Average capital employed Rs 7,00,000
(ii) Net trading results of the firm 2014 – Rs 1,47,600, 2015 – Loss Rs 1,48,100, Profit for 2016 – Rs 4,48,700
(iii) Interest on capital @ 18%
(iv) Remuneration Rs 500 per month.
Answer:
Calculation of Average profit and super profit
Total profit = Rs 1,47,600 – Rs 1,48,100 + Rs 4,48,700 = Rs 4,48,200

Super profit = Average profit – Normal profit
= 1,37,400 – 1,26,000
Super profit = Rs 11,400
(a) Average profit method:
Average profit × No. of years purchase
= Rs 1,37,400 × 3 = Rs 4,12,200
(b) Super profit method:
Super profit × No. of years purchase
= Rs 11,400 × 3 = Rs 34,200

[OR]

(b) Sri Ram and Raj are partners sharing profits in the ratio 2 : 1. Nelson joins as a partner on 1st April 2017. The following adjustments are to be made.
(i) Increase the value of Rs 10,000
(ii) Bring into record investment of Rs 14,000 which had not been recorded in the books of the firm.
(iii) Reduce the value of office equipment by Rs 20,000
(iv) A provision would also be made for outstanding wages for Rs 19,000. Give journal entries and prepare revaluation account.
Answer:
Journal Entries

Question 45(a).
Raj an and selva are partners sharing profit and losses in the ratio of 3:1. sheet as on 31st march 2017.

On 1.4.2017 they admit Ganesan as a new partner on the following arrangements
(i) Ganesan brings 10,000 as capital for 1/5 share of profit.
(ii) Stock and furniture is to be reduced by 10% a reserve of 5% on debtors for doubtful debts is to be created.
(iii) Appreciate building by 20%
Prepare revaluation account, partners capital account and the balance sheet of the firm after admission.
Answer:

[OR]

(b) The balance sheet of Rekha and mary on 31.12.2018 as

They share the profit and losses in the ratio 3 : 1. They agreed to admit kavitha into the partnership firm for 1/4 share of profits which she gets entirely gets from Rekha. Following are the conditions,
(i) Kavitha has to bring Rs 20,000 as capital. Her share of goodwill is valued at 4,000. She could not bring cash towards goodwill.
(ii) Depreciate buildings by 10%
(iii) Stock to be the revalued at Rs 6,000
(iv) Create provision for doubtful debts @ 5% on debito?
Prepare necessary ledger accounts and the balance sheet after admission.
Answer:

Question 46(a).
Charles, Muthu and sekar are partners sharing profits in the ratio 3 : 4 : 2. Their balance sheet as on 31st december 2018 is as under.

(i) On 1.1. 2019 Charles retired from the partnership firm on the following arrangements. Stock to be appreciated by 10%
(ii) Furniture to be depreciated by 5%
(iii) To provide Rs 1000 for bad debts
(iv) There is an outstanding repair of Rs 11,000 not yet recorded.
(v) The final amount due to Charles was paid.
Prepare revaluation account, capital account and the balance sheet of partner’s frim after the retirement.
Answer:

Balance sheet

[OR]

(b) Thangam Ltd issued 50,000 shares of Rs 10 each at a premium of Rs 2 per share payable as follows.
On application Rs 5, on allotment Rs 5 (including premium) on first and final call Rs 2.
Issue was fully subscribed and the amounts due were received except priya to whom 500 shares were allotted who faded to pay the allotment money and first and final call money. Her shares were forfeited. All the forfeited shares were reissued to devi Rs 8 per share. Pass journal entries.
Answer:
Journal Entries

Question 47(a).
Compute trend percentage for the following particular of Boomi Ltd.

Answer:

[OR]]

(b) Calculate-
(i) inventory turnover ratio
(ii) Trade receivable turnover
(iii) Trade payable turnover ratio
(iv) Fixed assets turnover ratio
(v) Gross profit ratio from the following,

Additional information:
Revenue from operations for the year Rs 10,50,000
Purchases for the year Rs 4,50,000
Cost of revenue from operations RS 6,00,000
Assume that sales and purchase are for credit
Answer:


Gross profit = Revenue from operations – Cost of revenue from operations
= 10,50,000 – 6,00,000
= 7 4,50,000

Students can Download Tamil Nadu 12th Accountancy Model Question Paper 1 English Medium Pdf, Tamil Nadu 12th Accountancy Model Question Papers helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

TN State Board 12th Accountancy Model Question Paper 1 English Medium

Instructions:

1. The question paper comprises of four parts.
2. You are to attempt all the parts. An internal choice of questions is provided wherever applicable.
3. All questions of Part I, II. III and IV are to be attempted separately.
4. Question numbers 1 to 20 in Part I are Multiple Choice Questions of one mark each. These are to be answered by choosing the most suitable answer from the given four alternatives and writing the option code and the corresponding answer.
5. Question numbers 21 to 30 in Part II are two-mark questions. These are to be answered in about 50 words.
6. Question numbers 31 to 40 in Part III are three-mark questions. These are to be answered in about 150 words.
7. Question numbers 41 to 47 in Part IV are five-mark questions. These are to be answered in about 250 words. Draw diagrams wherever necessary.

Time: 2.30 Hours
Max Marks: 90

Part -I

Answer all the questions. Choose the correct answer. [Answers are in bold] [20 × 1 = 20]

Question 1.
Capital in the beginning of the accounting year is ascertained by preparing
(a) Debtors A/c
(b) Cash A/c
(c) Opening statement of affairs
(d) None of these
Answer:
(c) Opening statement of affairs

Question 2.
Single entry system can be adopted by
(a) Small firms
(b) Joint stock companies
(c) Co-op societies
(d) None of these
Answer:
(a) Small firms

Question 3.
An advance receipt of subscription from a member of the non-profit organisation is considered as an
(a) Expenses
(b) Liability
(c) Equity
(d) Assets
Answer:
(b) Liability

Question 4.
Income and expenditure account is based on
(a) Cash Accounting
(b) Government Accounting
(c) Management Accounting
(d) Accrual Accounting
Answer:
(d) Accrual Accounting

Question 5.
The name under which the business of a firm is carried on is called the
(a) Company name
(b) Firm name
(c) Partnership firm
(d) Partner’s name
Answer:
(b) Firm name

Question 6.
The profit or loss arising from the partnership business is shared by the partners ………. in the
(a) Old ratio
(b) New ratio
(c) agreed ratio
(d) Sacrifice ratio
Answer:
(c) agreed ratio

Question 7.
Which is the present value of a firm’s future excess earnings?
(a) Fixed assets
(b) Current assets
(c) Goodwill
(d) None of these
Answer:
(c) Goodwill

Question 8.
Goodwill is shown under fixed assets in the
(a) Trial balance
(b) Balance sheet
(c) Trading A/c
(d) P and L A/c
Answer:
(b) Balance sheet

Question 9.
Revaluation account is also called
(a) Accumulation profit and loss A/c
(b) Profit and loss adjustment A/c
(c) Profit and loss appropriation A/c
(d) None of these
Answer:
(b) Profit and loss adjustment A/c

Question 10.
When the value of assets increases it results in
(a) profit
(b) loss
(c) income
(d) expense
Answer:
(a) profit

Question 11.
When a partner leaves from a partnership firm, it is known as
(a) Admission
(b) Retirement
(c) Dissolution
(d) Death
Answer:
(b) Retirement

Question 12.
The firm is reconstituted and other partners continue the partnership firm with a new………..
(a) contract
(b) agreement
(c) start business
(d) none of these
Answer:
(b) agreement

Question 13.
In order to meet them production must be carried on a
(a) small scale
(b) large scale
(c) medium scale
(d) none of these
Answer:
(b) large scale

Question 14.
The capital of companies is divided into small unit is
(a) shares
(b) debentures
(c) dividend
(d) none of these
Answer:
(a) shares

Question 15.
Which statement are prepared by the business concerns at the end of the accounting period to ascertain the operating results and the financial position?
(a) Trend analysis
(b) Income statement
(c) Financial statement
(d) Balance sheet
Answer:
(c) Financial statement

Question 16.
Financial statements are prepared based on………..
{a) Past data
(b) Future cost
(c) Terminal cost
(d) Historical cost
Answer:
(d) Historical cost

Question 17.
The financial status and financial performance of business entities can be assessed through………..
(a) Financial analysis
(b) Managerial analysis
(c) Cash flow statement
(d) None of these
Answer:
(a) Financial analysis

Question 18.
If both items in a ratio are from balance sheet it is classified as………..
(a) Inter statement ratio
(b) Income statement ratio
(c) Balance sheet ratio
(d) All of these
Answer:
(c) Balance sheet ratio

Question 19.
CAS helps to compute various taxes and to deduct these and deposit the same to the………..
(a) Private A/c
(b) Company A/c
(c) Government A/c
(d) None of these
Answer:
(c) Government A/c

Question 20.
In 2009, Tally solutions introduced the software………..
(a) Tally ERP 9
(b) Tally ERP 10
(c) Tally ERP 6.0
(d) None of these
Answer:
(a) Tally ERP 9

PART – II

Answer any seven questions in which question No. 30 is compulsory. [7 × 2 = 14]

Question 21.
What shall be the profits of the concern? if,
Opening capital 3,20,000, Drawings 72,000
Closing capital 3,60,000, Additional capital 20,000
Statement of Profit or Loss
Answer:

Question 22.
How will the following items appear in income and expenditure account?

Answer:

Question 23.
What is partnership deed?
Answer:
Partnership deed is a documents in writting that contains the terms of agreement among the partners. It is not compulsory for a partnership to have a partnership deed as per the Indian partnership Act 1932.

Question 24.
What is normal rate of return?
Answer:
Normal rate of return refers to the rate at which profit is earned by similar business entities in the Industry under normal circumstances.

Question 25.
Give the Journal Entry for writing off existing goodwill at the time of admission of a new partner?
Answer:

Question 26.
A, B and C are partners sharing profits in the ratio of 3:2:1. A retires and the new profit sharing ratio between B and C is 2:3. Calculate the gaining ratio.
Answer:
Share gained = New share – old share

∴ The gaining ratio of B, C = 2 : 13

Question 27.
What are the methods of issue of equity shares?
Answer:
A public company may raise capital by issue of equity shares through the following ways:
Public issue
Private placement
Rights issue
Bonus issue

Question 28.
What are “Financial Statements”?
Answer:
Financial statements are the statements prepared by the business concern at the end of the accounting period to ascertain the operating results and the financial position. The basic financial statements prepared by business concerns are income statement and balance sheet.

Question 29.
Calculate quick ratio; Total current liabilities Rs 2,40,000; Total current assets Rs 4,50,000; Inventories Rs 70,000; prepaid expenses Rs 20,000.
Answer:
Current liabilities
Quick ratio = \(\frac{Quick assets}{Current liabilities}\)
Quick assets = Current assets – Inventories – Prepaid expenses
Rs 4,50,000 – 70,000 – 20,000
= Rs 3,60,000
Quick ratio = \(\frac{360000}{240000}\)
= 1.5 : 1

Question 30.
What are accounting reports?
Answer:
Accounting report is a compilation of accounting information that are derived from the accounting records of a business concern. Accounting reports may be classified as routine reports and special purpose reports.

PART – III

Answer any seven questions in which question No. 40 is compulsory. [7 x 3 = 21]

Question 31.
What are the features of incomplete records?
Answer:
(i) Nature:
It is an unscientific and unsystematic way of recording transactions. Accounting principles and accounting standards are not followed properly.
(ii) Lack of uniformity:
There is no uniformity in recording the transactions among different organisations. Different organisations record their transactions according to their needs and conveniences.
(iii) Suitability:
Only the business concerns which have no legal obligation to maintain books of accounts under double entry system may maintain incomplete records. Hence it may be maintained by small sized sole traders and partnership firms.

Question 32.
From the following particulars, show how the items “subscription” will appear in the income and expenditure account for the year ended 31.2.2018. Subscription received in 2018 is Rs 32,000; which includes Rs 3,000 for 2017 and Rs 5,000 for 2019. Subscription outstanding for the year 2018 is Rs 4,000; subscription of Rs 2,000 was received in advance for 2018 in the year 2017.
Answer:
Income and expenditure account for the year ended 31.12.2018

Question 33.
From the following information, prepare capital accounts of Mannan and Sevagan where their capitals and fluctuating.

Answer:

Question 34.
The following particulars are available in respect of a business carried on by a partnership firm.
a) Profits earned 2016 – 30,000; 2017 – 29,000; 2018 – 32,000.
b) Profit of 2016 includes a non-recurring income of Rs 3,000.
c) Profit of 2017 is reduced by Rs 2,000 due to stock destroyed by fire.
d) The stock is not insured. But it is decided to insure the stock in future. The insurance premium is estimated at Rs 5,600 p.a. You are required to calculate the value of goodwill on the basis of 2 years purchase of average profit of the last three years.
Answer:
Calculation of adjusted profit

Goodwill = Average profit × Number of years of purchase
= 24,400 × 2 = Rs 48,800

Question 35.
A and B are partners sharing profits in the ratio of 3 : 2. ‘C’ is admitted as a new partner and the new profit sharing ratio is decided as 5 : 3 : 2. The following revaluation are made. Pass journal entries.
(a) The value of building is increased by Rs 15,000
(b) The value of the machinery is decreased by Rs 4,000
(c) Provision for doubtful debtors is made for Rs 1,000
Answer:
Journal Entries

Question 36.
Rathna, Baskar and Ibrahim are partners sharing profit and losses in the ratio of 2 : 3 : 4, respectively. Rathna died on 31st December 2018. Final amount due to her showed a credit balance of 1,00,000. Pass journal entries, if
(а) The amount due is paid off immediately by cheque
(b) The amount due is not paid immediately
(c) Rs 60,000 is paid immediately by cheque.
Answer:

Question 37.
Anu company forfeited 200 equity shares of Rs 10 each issued at par held by Thiyagu for non-payment of the final call of Rs 3 per share. The shares were reissued to Laxman at Rs 6 per share. Show the journal entries for forfeiture and reissue.
Answer:
Journal entries

Question 38.
From the following particulars prepare comparative income statements of Tharun co Ltd.

Answer:

Question 39.
Calculate operating profit ratio under the following cases:
Case 1: Revenue from operations and Rs 10,00,000, operating profit Rs 1,50,000
Case 2: Revenue from operations and Rs 15,00,000, operating cost Rs 12,00,000
Case 3: Revenue from operations and Rs 20,00,000, gross profit 30%.
On revenue from operations, operating expenses Rs 4,00,000.
Answer:
case 1:
operating profit ratio =

case 2:
operating profit ratio =

Operating profit = Revenue from operation – operating cost
= 15,00,000 – 12,00,000
= Rs 3,00,000

case 3:
operating profit ratio =

Gross profit = 20,00,000 × \(\frac{30}{100}\) = Rs 6,00,000
Operating profit = Gross profit – operating expenses Operating profit
= 6,00,000 – 4,00,000
= Rs 2,00,000

Question 40.
Write a brief note on accounting vouchers?
Answer:
This type of a voucher basically analyses a business transactions from the accounting stand point and is used for recording purposes. These are commonly prepared by accountants on the basis of supporting voucher and approved by a different individual. They are further sub¬divided into two. Cash and non-cash voucher.
Example of cash type:

1. Credit vouchers
2. Debit vouchers

Example of Non-cash type:

1. Debit Note
2. Credit Note
3. Invoice

PART – IV

Answer all the questions. [7 × 5 = 35]

Question 41(a)
David does not keep proper books of accounts. Following details are given from his records.

During the year, he introduced further capital of Rs 45,000 and withdraw of Rs 2,500 per month from the business for his personal use. Prepare the statement of profit or loss with the above information.
Answer:
Statement of affairs as on 1.4.2018 and 31.03.2019

[OR]

(b) Arun and Selvan are partners who maintain their capital accounts under fixed capital method. From the following particulars prepare capital accounts of partner

Answer:

Question 42(a)
From the following receipts and payments account of friends football club for the year ending 31st March 2017. Prepare income and expenditure account for the year ending , 31st March 2017 and the balance sheet as on that date.
In the books of Friends Football Club

Additional information:
(i) The club had furniture of Rs 12,000 on 1st April 2016. Ignore depreciation on furniture.
(ii) Subscription outstanding for 2016-17 – Rs 600
(iii) Stock of sports materials on 31.3.2017 – Rs 100
(iv) Capital fund as on 1st April 2016 was Rs 23,000
Answer:
In the books of Friends Football Club

[OR]

(b) Calculate the value of goodwill at 5 years purchase of super profit from the following information.
(i) Capital employed: Rs 60,000.
(ii) Normal rate of return: 20%
(iii) Net profit for 5 years: 2014 – 1,00,000; 2015 – Rs 50,000; 2016 – 70,000; 2017 – 54,000; 2018 – 10,000.
(iv) Fair remuneration to the partners Rs 3,600 p.a
Answer:


Normal profit = Capital employed × Normal rate of return
= 60000 × \(\frac{20}{100}\)
= Rs 12,000
super profit = Average profit – Normal profit
= 53,200 – 12,000
= 41,200
Goodwill = Super profit × Number of years of purchased R
= 41,200 × 5
= Rs 2,06,000

Question 43(a)
Hari, Madhavan and Kesavan are partners sharing ratio of 5 : 3 : 2. As from 1st April 2017. Vanmathi is admitted into the partnership and the new profit ratio is decided 4 : 3 : 2 : 1. The following adjustments are to be made.
(a) Increase the value of premises by Rs 60,000.
(b) Depreciate stock by Rs 5,000; furniture by Rs 2000 and machinery by Rs 2,500.
(c) Provide for an outstanding liability of Rs 500.
Pass journal entries and prepare revaluation.
Answer:
Journal Entries

[OR]

(b) Sundar, Vivek, and Pandian are partners sharing profits in the ratio of 3 : 2 : 1. Their balance sheet as on 31st Dec 2018 is as under.

On 1.1.2019 Pandian died and on his death the following arrangements are made,
(i) Stock to be depreciated by 10%.
(ii) Land is to be appreciated by Rs 11,000.
(iii) Reduce the value of debtors Rs 3,000.
(iv) The final amount due to Pandian was not paid. Prepare revaluation account, partner’s capital A/c and the balance sheet of the firm after death.
Answer:

Question 44(a)
Vetri and Ranjit are partners sharing profit in the ratio of 3 : 2. Their balance sheet as on 31st December 2017 as under.

On 1.1.2018, they admit suriya into their firm as a partner on the following arrangements.
(i) Suriya brings Rs 10,000 as, capital for 1/4th share of profit
(ii) Stock to be depreciated by 10%
(iii) Debtors to be revalue at Rs 7,500
(iv) Furniture to be revaluted at Rs 40,000
(v) There is an outstanding wages Rs 4,500 not yet recorded. Prepare revaluation account, partner’s capital account and the balance sheet of the firm after admission.
Answer:

[OR]

(b) Prabu, Raju and Siva are partners sharing profit and losses in the ratio of 3 : 2 : 1. Prabu retires from partnership on 1.4.2017.
The following adjustments are to be made:
(i) Increase the value of building by Rs 12,000
(ii) Reduce the value of furniture by Rs 8,500
(iii) A provision would also be made for outstanding salary for Rs 6500.
Answer:
Journal Entries

Question 45(a)
Mani, Rama and Devan are partners in a firm sharing profit and losses in the ratio of 4 : 3 : 3. Their balance sheet as on 31st March 2019 is as follows:

Vlani retired from the partnership firm on 31.03.2019 subject to the following
adjustments:
(i) Stock to be depreciated Rs 5,000.
(ii) Provision for doubtful debtors to be created for Rs 1,000.
(ii) Buildings to be appreciated by Rs 16,000. The final amount due to Mani is not paid immediately. Prepare revaluation A/c and Capital Account of partners after retirement.
Answer:

[OR]

(b) Joy company issued 10,000 equity shares at Rs 10 per share payable Rs 5 on application, Rs 3 on allotment and Rs 2 on first and final call. The public subscribed for 9,000 shares. The directors allotted all the 9,000 shares and duly received the money. Pass the necessary journal entries.
Answer:
Journal Entries

Question 46(a)
Thangam Ltd issued 50,000 shares of Rs 10 each at a premium of Rs 2 per share payable as follows:
On application Rs 5, on allotment Rs 5 (including premium), on first and final call Rs 2. Issue was fully subscribed and the amount due were received except Priya to whom 500 shares were allotted who failed to pay the allotment money and first and final call money. Her shares were forfeited. All the forfeited share were reissued to devi Rs 8 per share.
Answer:
Journal Entries

[OR]

(b) From the following particulars of Neithal Ltd. Calculate trend percentage.

Answer:

Question 47 (a)
From the following balance sheet of Gupta Ltd, prepare comparative balance sheet as on 31st March 2017 and 31st March 2018.

Answer:
Comparative balance sheet as on 31st March 2017 and 31.3.2018

[OR]

(b) Calculate
(i) inventory turnover ratio
(ii) Trade receivable (or) turnover ratio
(iii) Trade payable turnover ratio
(iv) Gross profit ratio
(v) Fixed assets turnover ratio.
From the following information obtained from Delphi Ltd.

Additional information:
Revenue from operations for the year – 10,50,000
Purchases for the year – 4,50,000
Cost of revenue from operations – 6,00,000
Assume that sales and purchases are for credit
Answer:

Gross profit ratio = Revenue from operation – Cost of revenue from operation
Gross profit ratio = 10,50,000 – 6,00,000 = Rs 4,50,000

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 4 Inverse Trigonometric Functions Ex 4.1 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.1

Question 1.
Find all the values of x such that
Solution:
(i) sin x = 0
⇒ x = nπ
where n = 0, ±1, ±2, ±3, ……., ±10
(ii) sin x = -1
⇒ x = (4n – 1) \(\frac{\pi}{2}\), n = 0, ±1, ±2, ±3, 4

Question 2.
Find the period and amplitude of
Solution:
(i) y = sin 7x
For Amplitude use the form
y = a sin(bx – c) + d
Amplitude = |a|
a = 1, ∴ |a| = 1
Period using the formula = \(\frac{2π}{|b|}\) = \(\frac{2π}{|7|}\) = \(\frac{2π}{7}\)
∴ Amplitude = 1
Period = \(\frac{2π}{7}\)

(ii) y = -sin (\(\frac{1}{3}\)x)
a = -1, b = \(\frac{1}{3}\)
∴ Amplitude = |a| = |-1| = 1
Period = \(\frac{2π}{|b|}\) = \(\frac{2π}{| \frac{1}{3}|}\) = 3(2π) = 6π

(iii) y =4 sin (-2x)
a = 4, b = -2
Amplitude = |4| = 4
Period = \(\frac{2π}{|b|}\) = \(\frac{2π}{|-2|}\) = \(\frac{2π}{2}\) = π

Question 3.
Sketch the graph of y = sin (\(\frac{1}{3}\)x) for 0 ≤ x ≤ 6π
Solution:

Question 4.
Find the value of
(i) sin^-1 (sin(\(\frac{2π}{3}\)))
(ii) sin^-1 (sin(\(\frac{5π}{4}\)))
Solution:

Question 5.
For what value of x does sin x = sin^-1 x?
Solution:
sin x = sin^-1 x is possible only when x = 0 (∵ x ∈ R)

Question 6.
Find the domain of the following
(i) f(x) = sin^-1 (\(\frac{x²+1}{2x}\))
Solution:
f(x) = sin^-1 (\(\frac{x²+1}{2x}\))
Range of sin^-1x is [-1, 1]
-1 ≤ \(\frac{x²+1}{2x}\) ≤ 1
Multiply by 2x² ≥ 0

∴ solution is [-1, 1]

(ii) g (x) = 2 sin^-1 (2x – 1) – \(\frac{π}{4}\)
Range of 2 sin^-1 x is [-1, 1]
-1 ≤ 2x – 1 ≤ 1
2x – 1 ≤ 1 (or) 2x – 1 ≥ -1
2x ≤ 2 (or) 2x ≥ -1 + 1
x ≤ 1 (or) 2x ≥ 0 ⇒ x ≥ 0
x ≥ 0 and x ≤ 1
∴ solution is [0, 1]

Question 7.
Find the value of
(sin\(\frac{5π}{9}\) cos\(\frac{π}{9}\) + cos\(\frac{5π}{9}\) sin\(\frac{π}{9}\))
Solution:
sin (A + B) = sin A cos B + cos A sin B

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 3 Theory of Equations Ex 3.7 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 3 Theory of Equations Ex 3.7

Choose the most suitable answer.

Question 1.
A zero of x³ + 64 is:
(a) 0
(b) 4
(c) 4i
(d) -4
Solution:
(d) -4
Hint:
x³ = -64
x³ = -4 × -4 × -4 = (-4)³
x = -4

Question 2.
If f and g are polynomials of degrees m and n respectively, and if h(x) = (f o g) (x), then the degree of h is:
(a) mn
(b) m + n
(c) mⁿ
(d) n^m
Solution:
(a) mn
Hint:
Let f(x) = x^m and g(x) = xⁿ
degree = m, degree = n
(f o g) (x) = f(g(x)) = f(xⁿ) = (xⁿ)^m =x^mn
degree = mn

Question 3.
A polynomial equation in x of degree n always has:
(a) n distinct roots
(b) n real roots
(c) n imaginary roots
(d) at most one root.
Solution:
(a) n distinct roots

Question 4.
If α, β and γ are the roots of x³ + px² + qx + r, then Σ \(\frac{1}{α}\) is:
(a) –\(\frac{q}{r}\)
(b) –\(\frac{p}{r}\)
(c) \(\frac{q}{r}\)
(d) –\(\frac{q}{p}\)
Solution:
(a) –\(\frac{q}{r}\)
Hint:
x³ + px² + qx + r = 0
α, β, γ are the roots
α + β + γ = -p
αβ + βγ + γα = q
αβγ = -r
Σ \(\frac{1}{α}\) = \(\frac{1}{α}\) + \(\frac{1}{β}\) + \(\frac{1}{γ}\) = \(\frac{βγ+αβ+αγ}{αβγ}\) = –\(\frac{q}{r}\)

Question 5.
According to the rational root theorem, which number is not possible rational root of 4x⁷ + 2x⁷ – 10x³ – 5?
(a) -1
(b) \(\frac{5}{4}\)
(c) \(\frac{4}{5}\)
(d) 5
Solution:
(c) \(\frac{4}{5}\)
Hint:
By rational root of theorem,
\(\frac{p}{q}\) is a root of a polynomial a₀ = -5, a_n = 4 and (4, -5) = 1, then p must divide 5 and q must divide 4.
Possible values of p are +1, -1, +5, -5
Possible values of q are +1, -1, 4, -4
∴ \(\frac{4}{5}\) is not possible rational roots.

Question 6.
The polynomial x³ – kx² + 9x has three real roots if and only if, k satisfies:
(a) |k | ≤ 6
(b) k = 0
(c) |k| > 6
(d) |k| ≥ 6
Solution:
(d) |k| ≥ 6
Hint:
Δ ≥ 0
k² – 4(1)(9) ≥ 0
k² ≥ 36
|k| ≥ 6

Question 7.
The number of real numbers in [0, 2π] satisfying sin⁴x – 2 sin²x + 1 is:
(a) 2
(b) 4
(c) 1
(d) ∞
Solution:
(a) 2
Hint:
sin⁴x – 2sin²x + 1 = 0
Put sin²x = t [t² – 2t + 1 = 0 ⇒ (t – 1)² = 0]
t = 1, t = 1
sin²x = 1
sin x = ± 1
∴ sin x = 1, sin x = -1
sin x = sin \(\frac{π}{2}\), sin x = sin (π + \(\frac{π}{2}\))
x = \(\frac{π}{2}\), x = \(\frac{3π}{2}\)
Number of real numbers in [0, 2, π] is 2.

Question 8.
If x³ + 12x² + 10ax + 1999 definitely has a positive root, if and only if:
(a) a ≥ 0
(b) a > 0
(c) a < 0
(d) a ≤ 0
Solution:
(c) a < 0
Hint:
∴ If a < 0, then only we can get one sign change.

Question 9.
The polynomial x³ + 2x + 3 has:
(a) one negative and two real roots
(b) one positive and two imaginary roots
(c) three real roots
(d) no solution
Solution:
(a) one negative and two real roots
Hint:
p(x) = x³ + 2x + 3, no sign changes ⇒ no positive real roots.
p(-x) = -x³ – 2x + 3, one sign changes ⇒ one negative real roots.
∴ It has 1 negative root and 2 imaginary roots.

Question 10.
The number of positive roots of the polynomials \(\sum_{r=0}^{n}\) ⁿC_r (-1)^r x^r is
(a) 0
(b) n
(c) <n
(d) r
Solution:
(b) n
Hint:
\(\sum_{r=0}^{n}\) ⁿC_r (-1)^r x^r = xⁿ – ⁿC₁ x^n-1 + ⁿC₂ x^n-2 + …. + (-1)ⁿ
P(x) has n changes
∴ It has n positive changes
P(-x) has no changes
∴ no negative roots.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 3 Theory of Equations Ex 3.5 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 3 Theory of Equations Ex 3.5

Question 1.
Solve the following equations
(i) sin² x – 5 sin x + 4 = 0
Solution:
sin²x – 5sinx + 4 = 0
Let y = sin x
(y² – 5y + 4 = 0
(y – 1) (y – 4) = 0
(y – 1) = o or (y – 4) = 0
y = 1 or y = 4
sin x = 1 or sin x = 4 [not possible since sin x ≤ 1]
sin x = sin \(\frac{\pi}{2}\)
x = nπ + (-1)ⁿ α, n ∈ z.
x = nπ + (-1)ⁿ \(\frac{\pi}{2}\)

(ii) 12x³ + 8x = 29x² – 4 = 0
Solution:
12x³ – 29x² + 8x + 4 = 0

12x² – 5x – 2 = 0
12x² – 8x + 3x – 2 = 0
4x(3x – 2) + 1(3x – 2) = 0
(3x – 2)(4x + 1) = 0
3x = 2, 4x = -1
x = \(\frac{2}{3}\) or x = –\(\frac{1}{4}\)
The roots are 2, \(\frac{2}{3}\), –\(\frac{1}{4}\).

Question 2.
Examine for the rational roots of
(i) 2x³ – x² – 1 = 0
Solution:
Sum of co-efficients = 2 – 1 – 1 = 0
⇒ x = 1 is a factor.

Which is imaginary root
∴ x = 1 is rational root.

(ii) x⁸ – 3x + 1 = 0
Solution:
a_n = 1; a₀ = 1
If \(\frac{p}{q}\) is a root of the polynomial. (p, q) = 1
By rational root theorem, it has no rational roots.

Question 3.
Solve: 8x^{\(\frac{3}{2n}\)} – 8x^{\(\frac{-3}{2n}\)} = 63.
Solution:
Put k = \(\frac{3}{2n}\) ∴ 8x^k – 8x^-k = 63
8x^k – \(\frac{8}{x^k}\) = 63
8x^2k – 8 = 63x^k
8x^2k – 63x^k – 8 = 0
(x^k – 8) (8x^k + 1) = 0
x^k – 8 = 0
x^k = 8
x^{\(\frac{3}{2n}\)} = 8
x = 8^{\(\frac{3}{2n}\)} (2³)^{\(\frac{3}{2n}\)} = (2²)ⁿ = 4ⁿ
∴ x = 4ⁿ is a root of the equation.

Question 4.
Solve: 2\(\sqrt{\frac{x}{a}}\) + 3\(\sqrt{\frac{a}{x}}\) = \(\frac{b}{a}\) = \(\frac{6a}{b}\)
Solution:
put \(\sqrt{\frac{x}{a}}\) = y

Question 5.
Solve the equations
(i) 6x⁴ – 35x³ + 62x² – 35x + 6 = 0
Solution:
This is Type I even degree reciprocal equation. Hence it can be rewritten as

(1) ⇒ 6(y² – 2) – 35y + 62 = 0
6y² – 12 – 35y + 62 = 0
6y² – 35y + 50 = 0

2x² + 2 – 5x = 0 (or) 3x² + 3 = 10x
2x² – 5x + 2 = 0 (or) 3x² – 10x + 3 = 0
x = 2, \(\frac{1}{2}\) (or) x = 3, \(\frac{1}{3}\)
Roots are 2, \(\frac{1}{2}\), 3 and \(\frac{1}{3}\)

(ii) x⁴ + 3x³ – 3x – 1 = 0
Solution:
(x – 1) and (x + 1) is a factor.

(x – 1)(x + 1)(x² + 3x + 1) = 0
x – 1 = 0 (or) x + 1 = 0 (or) x² + 3x + 1 = 0
x = 1 (or) x = -1 (or) x² + 3x = -1

Question 6.
Find all real numbers satisfying
Solution:
4^x – 3 (2^x+2) + 2⁵ = 0
⇒ (2²)^x – 3(2^x . 2²) + 2⁵ = 0
(2²)^x – 12 . 2^x+ 32 = 0
Let y = 2^x
y² – 12y + 32 = 0
⇒ (y – 4) (y – 8) = 0
y – 4 = 0 or y – 8 = 0
Case (i): 2^x = 4
⇒ 2^x = (2)²
⇒ x = 2
Case (ii): 2x = 8
⇒ 2^x = (2)³
⇒ x = 3
∴ The roots are 2, 3

Question 7.
Solve the equation 6x⁴ – 5x³ – 38x² – 5x + 6 = 0 if it is known that \(\frac{1}{3}\) is a solution.
Solution:
6x⁴ – 5x³ – 38x² – 5x + 6 = 0

6(y² – 2) – 5y – 38 = 0
6y² – 12 – 5y – 38 = 0
6y² – 5y – 50 = 0
6y² – 20y + 15y  – 50 = 0
2y(3y – 10) + 5(3y – 10) = 0
(3y – 10)(2y + 5) = 0
3y = 10, 2y = -5

3x² + 3 = 10x, 2x² + 2 = -5x
3x² – 10x + 3 = 0, 2x² + 5x + 2 = 0
(x – 3)(3x – 1) = 0, (2x + 1)(x + 1) = 0
x = 3, x = \(\frac{1}{3}\) or x = \(\frac{-1}{2}\), x= -2
The roots are 3, \(\frac{1}{3}\), -2, \(\frac{-1}{2}\).

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 3 Theory of Equations Ex 3.6 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 3 Theory of Equations Ex 3.6

Question 1.
Discuss the maximum possible number of positive and negative roots of the polynomial equation 9x⁹ – 4x⁸ + 4x⁷ – 3x⁶ + 2x⁵ + x³ + 7x² + 7x + 2 = 0.
Solution:
P(x) = 9x⁹ – 4x⁸ + 4x⁷ – 3x⁶ + 2x⁵ + x³ + 7x² + 7x + 2
The number of sign changes in P(x) is 4.
∴P(x) has at most 4 positive roots.
P(-x) = -9x⁹ – 4x⁸ – 4x⁷ – 3x⁶ – 2x⁵ – x³ + 7x² – 7x + 2
The number of sign changes in P(-x) is 3.
P(x) has almost 3 negative roots.
Since the difference between the number of sign changes in co-efficient P(-x) and the number of negative roots of the polynomial P(x) is even.
The number of negative roots = at most 2.

Question 2.
Discuss the maximum possible number of positive and negative roots of the polynomial equations x² – 5x + 6 and x² – 5x + 16 . Also, draw a rough sketch of the graphs.
Solution:
y = x² – 5x + 6
x = 1, y = 1 – 5 + 6 = 2
x = 2, y = 4 – 10 + 6 = 0
x = 0, y = 6
x = 3, y = 9 – 15 + 6 = 0
x = -1, y = 1 + 5 + 6 = 12
x = 4, y = 16 – 20 + 6 = 2

(1, 2), (0, 6), (-1, 12)
P(x) = (x² + 5x + 6) (x² – 5x + 16)
= x⁴ – 5x³ + 16x² – 5x³ + 25x² – 80x + 6x² – 30x + 96 = 0
= x⁴ – 10x³ + 47x² – 110x + 96 = 0
It has two sign changes
∴ It has two positive real roots
P(-x) = x⁴ + 10x³ + 47x² + 110x + 96
It has no sign change, no negative real roots
y = x² – 5x + 16

Question 3.
Show that the equation x⁹ – 5x⁵ + 4x⁴ + 2x² + 1 = 0 has atleast 6 imaginary solutions.
Solution:P(x) = x⁹ – 5x⁵ + 4x⁴ + 2x² + 1
(i) The number of sign changes in P(x) is 2. The number of positive roots is atmost 2.
(ii) P(-x) = -x⁹ + 5x⁵ + 4x⁴ + 2x² + 1. The number of sign changes in P(-x) is 1. The number of negative roots of P (x) is atmost 1. Since the difference of number of sign changes in P(-x) and number of negative zeros is even.
P(x) has one negative root.
(iii) 0 is not the zero of the polynomial P(x). So the number of real roots is almost 3.
∴ The number of imaginary roots at least 6.

Question 4.
Determine the number of positive and negative roots of the equation x⁹ – 5x⁸ – 14x⁷ = 0.
Solution:
P(x) = x⁹ – 5x⁸ – 14x⁷. It has only one sign change.
∴ It has one positive roots.
P(-x) = -x⁹ – 5x⁸ + 14x⁷. It has only one sign change.
It has one negative root.
∴ It has one positive and one negative roots.

Question 5.
Find the exact number of real roots and imaginary of the equation x⁹ + 9x⁷ + 7x⁵ + 5x³ + 3x.
Solution:
P(x) = x⁹ + 9x⁷ + 7x⁵ + 5x³ + 3x.
There is no change in the sign of P(x) and P(-x), P(x) has no positive and no negative real roots, but 0 is the root of the polynomial equation P(x).

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 3 Theory of Equations Ex 3.4 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 3 Theory of Equations Ex 3.4

Question 1.
Solve:
(i) (x – 5) (x – 7) (x + 6)(x + 4) = 504
Solution:
(x – 5) (x + 4) (x – 7) (x + 6) = 504
(x² – x – 20) (x² – x – 42) = 504
Let y = (x² – x)
(y – 20) (y – 42) = 504
⇒ y² – 42y – 20y + 840 = 504
⇒ y² – 62y + 336 = 0
⇒ (y – 56) (y – 6) = 0
⇒ (y – 56) = 0 or (y – 6) = 0
⇒ x² – x – 56 = 0 or x² – x – 6 = 0
⇒ (x – 8) (x + 7) = 0 or (x – 3) (x + 2) = 0
⇒ x = 8, -7 or x = 3, -2
The roots are 8, -7, 3, -2

(ii) (x – 4)(x – 2)(x- 7)(x + 1) = 16
Solution:
(x – 4) (x – 7) (x – 2) (x + 1) = 16
⇒ (x – 4) (x – 2) (x – 7) (x + 1) = 16
⇒ (x² – 6x + 8) (x² – 6x – 7) = 16
Let x² – 6x = y
(y + 8)(y – 7) = 16
⇒ y² – 7y + 8y – 56 – 16 = 0
⇒ y² + y – 72 = 0
⇒ (y + 9) (y – 8) = 0
y + 9 = 0
x² – 6x + 9 = 0
(x – 3)² = 0
x = 3, 3
or
y – 8 = 0
x² – 6x – 8 = 0

Question 2.
Solve:
(2x – 1)(x + 3)(x – 2)(2x + 3) + 20 = 0
Solution:
(x + 3)(x – 2) (2x – 1)(2x + 3) + 20 = 0
(x² + x – 6) (4x² + 6x – 2x – 3) + 20 = 0
(x² + x – 6) (4x² + 4x – 3) + 20 = 0
(x² + x – 6) (x² + 4x – \(\frac{3}{4}\)) + 20 = 0
(÷4) (x² + x – 6) (x² + x – \(\frac{3}{4}\)) + \(\frac{20}{4}\) = 0
Put y = x² + x

4y² – 27y – 38 = 0
4y² – 8y – 19y + 38 = 0
(4y – 19) (y – 2) = 0
y = 2 (or) y = \(\frac{19}{4}\)
x² + x = 2 (or) x² + x = \(\frac{19}{4}\)
x² + x – 2 = 0 (or) 4x² + 4x = 19
(x + 2)(x – 1) = 0 (or) 4x² + 4x – 19 = 0
x = -2 or x = 1

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 3 Theory of Equations Ex 3.3 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 3 Theory of Equations Ex 3.3

Question 1.
Solve the cubic equation: 2x³ – x² – 18x + 9 = 0 if sum of two of its roots vanishes.
Solution:
The given equation is 2x³ – x² – 18x + 9 = 0
\(x^{3}-\frac{x^{2}}{2}-9 x+\frac{9}{2}=0\)
Let the roots be α, -α, β
α – α + β = \(-\left(\frac{-1}{2}\right)\)
\(\Rightarrow \beta=\frac{1}{2}\)
(α) (-α) (β) = \(\frac{-9}{2}\)
\(\Rightarrow-\alpha^{2}\left(\frac{1}{2}\right)=\frac{-9}{2}\)
α² = 9
α = ±3
The roots are 3, -3, \(\frac { 1 }{ 2 }\)

Question 2.
Solve the equation 9x³ – 36x² + 44x – 16 = 0 if the roots form an arithmetic progression.
Solution:
Given the roots are in AP
Let the roots be a – d, a, a + d

Question 3.
Solve the equation 3x³ – 26x² + 52x – 24 = 0 if its roots form a geometric progression.
Solution:

3 + 3λ + 3λ² = 13λ
3λ² + 3λ – 13λ + 3 = 0
3λ² – 10λ + 3 = 0
(λ – 3) (3λ – 1) = 0
λ = 6 or λ = \(\frac{1}{3}\)

Question 4.
Determine k and solve the equation 2x³ – 6x² + 3x + k = 0 if one of its roots is twice the sum of the other two roots.
Solution:
Given cubic equation
2x³ – 6x² + 3x + k = 0
Let the roots be α, β, γ
Given α = 2(β + γ)
β + γ = \(\frac{α}{2}\) ………. (1)
Sum of roots α(β + γ) = 3
From (1) α + \(\frac{α}{2}\) = 3
\(\frac{3α}{2}\) = 3 ⇒ α = 2
Again αβ + βγ + γα = \(\frac{3}{2}\)
α = 2 ⇒ 2β + βγ + 2γ = \(\frac{3}{2}\)
from (1) 2(\(\frac{α}{2}\)) + βγ = \(\frac{3}{2}\)
βγ = \(\frac{3}{2}\) – 2 = \(\frac{3-4}{2}\) = \(\frac{-1}{2}\)
βγ = \(\frac{-1}{2}\) ………… (2)
product of roots α β γ = –\(\frac{k}{2}\)
α = 2 ⇒ 2βγ = –\(\frac{k}{2}\)
βγ = –\(\frac{k}{4}\) ………… (3)

Question 5.
Find all zeros of the polynomial x⁶ – 3x⁵ – 5x⁴ + 22x³ – 39x² – 39x + 135, if it is known that 1 + 2i and √3 are two of its zeros.
Solution:
(i) Given that 1 + 2i, √3
Another roots be 1 – 2i, -√3
sum of roots = 1 + 2i + 1 – 2i
product roots = (1 + 2i)(1 – 2i)
1² + 2² = 1 + 4 = 5
x² – 2x + 5 = 0

(ii) sum of roots = √3 – √3
product roots = (√3)(-√3)
x² – 0x – 3 = 0
x² – 3 = 0
(x² – 2x + 5)(x² – 3) = x⁴ – 2x³ + 2x² + 6x – 15
x⁶– 3x⁵ – 5x⁴ + 22x³ – 39x² – 39x + 135
= (x⁴ – 2x³ + 2x² + 6x – 15)  (x² + px – 9)
Equate of co-efficient of x on both sides
-39 = -54 – 15 p
-39 + 54 = -15 p
15 = -15 p
p = -1
∴ x² – x – 9 = 0

Question 6.
Solve the cubic equations:
(i) 2x³ – 9x² + 10x = 3,
2x³ – 9x² + 10x – 3 = 0
Solution:
(i) 2x³ – 9x² + 10x = 3
2x³ – 9x² + 10x – 3 = 0
sum of the coefficients 2 – 9 + 10 – 3 = 0
∴ x = 1 is one of the roots.

2x² – 7x + 3 = 0
(x – 3)(2x – 1) = 0
x = 3 or x = \(\frac{1}{2}\)
roots are 3, \(\frac{1}{2}\), 1

(ii) 8x³ – 2x² – 7x + 3 = 0
sum of the alternative coefficients are equal
8 – 7 = -2 + 3
1 = 1
∴ (x + 1) is a factor.

8x² – 10x + 3 = 0
(4x – 3) (2x – 1) = 0
4x  = 3 (or) 2x = 1
x = \(\frac{3}{4}\) (or) \(\frac{1}{2}\)
∴ The roots are \(\frac{3}{4}\), \(\frac{1}{2}\), -1

Question 7.
Solve the equation:
x⁴ – 14x² + 45 = 0
Solution:
Put t = x² ⇒ (x²)² – 14x² + 45 = 0
t² – 14t + 45 = 0
t² – 9t – 5t + 45 = 0
t(t – 9) – 5(t – 9) = 0
(t – 9)(t – 5) = 0
t – 9 = 0 or t – 5 = 0
t = 9 or t = 5
x² = 9 or x² = 5
x = ± 3 or y = ±√5
The roots are ±3, ±√5

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 3 Theory of Equations Ex 3.2 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 3 Theory of Equations Ex 3.2

Question 1.
If k is real, discuss the nature of the roots of the polynomial equation 2x² + kx + k = 0, in terms of k.
Solution:
The given quadratic equation is 2x² + kx + k = 0
a = 2, b = k, c = k
∆ = b² – 4ac = k² – 4(2) k = k² – 8k
(i) If the roots are equal
k² – 8k = 0
⇒ k(k – 8) = 0
⇒ k = 0, k = 8
(ii) If the roots are real
k² – 8k > 0
k(k – 8) > 0
k ∈ (-∞, 0) ∪ (8, ∞)
(iii) If this roots are imaginary
k² – 8k < 0
⇒ k ∈ (0, 8)

Question 2.
Find a polynomial equation of minimum degree with rational coefficients, having 2 + √3 i as a root.
Solution:
Let the root be 2 + i √3
Another root be 2 – i √3
Sum of the roots = 2 + i √3 + 2 – i √3 = 4
Product of the roots = (2 + i √3) (2 – i √3) = 2² + √3² = 4 + 3 = 7
x² – (SR)x + PR = 0
x² – 4x + 7 = 0

Question 3.
Find a polynomial equation of minimum degree with rational coefficients, having 2i + 3 as a root.
Solution:
Given roots is (3 + 2i), the other root is (3 – 2i);
Since imaginary roots occur in with real co-efficient occurring conjugate pairs.
x² – x(S.O.R) + P.O.R = 0
⇒ x² – x(6) + (9 + 4) = 0
⇒ x² – 6x + 13 = 0

Question 4.
Find a polynomial equation of minimum degree with rational coefficients, having √5 – √3 as a root.
Solution:
Let the root be √5 – √3,
Another root is √5 + √3
Sum of the roots = √5 – √3 + √5 + √3 = 2√5
Product of roots = (√5 – √3) (√5 + √3)
√5² – √3² = 5 – 3 = 2
x² – (SR)x + PR = 0
x² – 2√5 x + 2 = 0 which is not rational co-efficient.
to make rational co-efficient
(x² + 2√5 x + 2) (x² + 2 + 2√5 x) = 0
(x² + 2)² – (2√5x)² = 0
x⁴ + 4 + 4x² – 20x² = 0
⇒ x⁴ – 16x² + 4 = 0 is a rational co-efficient polynomial equation.

Question 5.
Prove that a straight line and parabola cannot intersect at more than two points.
Solution:
Let the standard equation of parabola y² = 4ax …..(1)
Equation of line be y = mx + c …(2)
Solving (1) & (2)
(mx + c)² = 4ax
⇒ mx² + 2mcx + c² – 4ax = 0
⇒ mx² + 2x(mc – 2a) + c² = 0
This equation can not have more than two solutions and
hence a line and parabola cannot intersect at more than two points.