Institute of Chartered Financial Analysts of India (ICFAI) University 2010 MS Finance Cfa - Question Paper

Model Question Paper Financial Accounting - II (MSF1A2)

   Answer all 75 questions.

   Marks are indicated against each question.

Total Marks:100

1. Which of the following statements is false with respect to goodwill?

(a)    It is normally represented by the capacity of a business to earn excess profits

(b)    For the calculation of goodwill, past profits will have to be adjusted in order to determine the future expected maintainable profit

(c)    It is an excess of acquisition cost over net assets acquired

(d)    It is an identifiable intangible asset

(e)    It can be defined as the present value of firms anticipated excess earnings.

²    Amortization of intangible assets, such as copyrights or patents, is the accounting process of

(a)    Determining the cash flow from operations for the current period

(b)    Systematically allocating the cost of the intangible assets to the period of use

(c)    Accumulating a fund for the replacement of the asset at the end of its useful life

(d)    Systematically reflecting the change in general price level over the current period

(e)    Asset valuation based on net realizable value at the statement of financial position.

³    Flier Ltd., issued 5,000, equity shares at Rs.25 each with par value of Rs.20 each, and all shares are subscribed and total amount duly received. The journal entry to record this transaction would include a

(a)    Debit to Cash for Rs. 1,00,000

(b)    Credit to Equity Share capital for Rs. 1,25,000

(c)    Debit to Securities premium for Rs.25,000

(d)    Credit to Equity Share capital for Rs. 1,00,000

(e)    Credit to Cash for Rs. 1,25,000.

⁴    Which of the following is false with regard to rights shares?

(a)    Rights shares are first offered to the existing shareholders

(b)    The price of rights shares offered is normally below the market price of the shares

(c)    Where the rights are offered at a price over the face value, the excess amount is credited to securities premium account

(d)    The number of rights shares offered need not be in proportion to the equity shares already held

(e)    Bank account is debited with the amount received and equity share capital account is credited with the face value of shares.

⁵    If forfeited shares are reissued at a premium, the amount of such premium will be credited to

(a)    Share forfeiture account

(b)    Securities premium account

(c)    Capital reserve account

(d)    Discount on issue of shares account

(e)    Share capital account.

⁶    If a company issues some of its common shares in exchange for assets other than cash, the transaction should be recorded at the

(a)    Current market value of the assets acquired

(b)    Stated value of the shares issued

(c)    Par value of the shares issued

(d)    Book value of the shares issued

(e)    Net realizable value of asset.

⁷    Unless the Board of Directors approve the allotment of shares, the application money received from public will remain with the company as a/an

(a)    Liability

(b)    Additional capital

(c)    Share capital

(d)    Securities premium

(e) Calls-in-advance.

⁸ The amount of capital, to describe the shares offered to public for subscription is

(a)    Authorized Capital

(b)    Issued Capital

(c)    Outstanding Capital

(d)    Subscribed Capital

(e)    Called up Capital.

9.

Which of the following signifies the difference between par value and an issue price below par?

(a)    Securities premium

(b)    Discount on issue of shares

(c)    Calls in arrear

(d)    Calls in advance

(e)    Rebate on shares.

¹⁰Tf a shareholder does not pay his dues on allotment, for the amount due, there will be a

(a)    Credit balance in share allotment account

(b)    Debit balance in share forfeiture account

(c)    Credit balance in share forfeiture account

(d)    Debit balance in share allotment account

(e)    Debit balance in share capital account.

H-The value of equity share of Good Strength Ltd., as per yield method is Rs.19.50 and as per fair value method is Rs.22.50. The value of share according to intrinsic value method is

(a)    Rs.21.00

(b)    Rs.25.50

(c)    Rs.19.50

(d)    Rs.22.50

(e)    Rs.26.50.

have the right to receive dividends in arrears, whenever earnings become adequate.

(a)    Cumulative preference shares

(b)    Participating preference shares

(c)    Convertible preference shares

(d)    Callable preference shares

(e)    Redeemable preference shares.

¹³-Red    Rock Ltd., issued 5,000, 15% Debentures of Rs.100 each at a discount of 5%, repayable after 5 years at a premium of 5%. The amount debited to loss on issue of debentures account is

(a)    Rs. 25,000

(b)    Rs. 50,000

(c)    Rs. 75,000

(d)    Rs.1,00,000

(e)    Nil.

¹⁴-The    interest on calls in advance is paid for the period from the

(a)    Date of receipt of application money to the date of appropriation

(b)    Date of receipt of allotment money to the date of appropriation

(c)    Date of receipt of advance to the date of appropriation

(d)    Date of appropriation to the date of dividend payment

(e)    Date of appropriation to the date of receipt of final call.

¹⁵-Which    of the following does not appear under the head share capital of a balance sheet?

(a)    Preference share capital

(b)    Minority interest in subsidiaries

(c)    Calls-in-arrear

(d)    Equity share capital

(e)    Shares forfeited account.

¹⁶-As    per SEBI guidelines, for a debenture issue having a maturity of more than 18 months, a Debenture

Redemption Reserve shall be created out of profits, prior to the commencement of the redemption, for a minimum percentage of debenture issue. Such minimum percentage is

(a)    25%

(b)    50%

(c)    10%

(d)    15%

(e)    5%.

¹⁷-At the end of the financial year, the cumulative total of interest on own debentures account is transferred to

(a) Profit and Loss account (b) Profit and Loss Appropriation account (c) Own Debentures account (d) Securities premium account (e) Bank account.

18-Premium    on issue of debentures account is transferred to

(a)    Capital reserve

(b)    General reserve

(c)    Securities premium account

(d)    Capital redemption reserve

(e)    Debentures account.

¹⁹-The    long term investments are accounted for in the balance sheet at

(a)    Cost price less depreciation

(b)    Cost price or market price, whichever is lower

(c)    Cost price

(d)    Replacement price

(e)    Net realizable value.

²⁰-Tax    deducted at source on the payments made by a company appears in the Balance Sheet of the company on the

(a)    Liabilities side under current liabilities

(b)    Liabilities side under provisions

(c)    Assets side under current assets

(d)    Assets side under loans and advances

(e)    Assets side under miscellaneous expenditure.

²¹-The    periodical interest received in respect of investments made on account of debenture redemption fund is transferred to

(a)	Interest income account
(b)	Debenture holders account
(c)	Debentures account
(d)	Debenture redemption fund account
(e)	Bank account.

²²-On    December 01, 2008, Lucas Ltd., purchased 5,000 of its 12% Debentures of Rs. 100 each at a price of Rs.98 ex-interest. Interest on debentures is payable on March 31 and September 30, every year. At the time of recording the purchase of debentures, the interest account will be debited by

(a)    Rs. 5,000

(b)    Rs. 100

(c)    Rs.15,000

(d)    Rs.10,000

(e)    Nil.

23-Which    of the following receipts is included in the profits for the purpose of calculating managerial remuneration?

(a)    Profits by way of premium on shares

(b)    Profits from sale of an undertaking

(c)    Profits by way of premium on debentures

(d)    Subsidies received from the Government

(e)    Profits on sales of forfeited shares by the company.

²⁴-The    gross profit and the administrative expenses of Payal Ltd., for 2006-07 was Rs.3,00,000 and Rs.2,00,000 respectively. In 2007-08 the gross profit increased by 20% and administrative expenses also increased by 10% from previous year. If the sales during 2007-08 were Rs.8,00,000, the net profit increased by

(a)    Rs.40,000

(b)    Rs.20,000

(c)    Rs.60,000

(d)    Rs.30,000

(e)    Rs.10,000.

²⁵-Uncalled    liability on shares partly paid is shown

(a)    As a current liability in the balance sheet of a company

(b)    As a miscellaneous expenditure in the balance sheet of a company

(c)    Under the head reserves on the liabilities side of the balance sheet of a company

(d)    By way of notes to the balance sheet of a company

(e)    In the Profit and Loss account of a company.

26-which    of the following statements is false with regard to special audit?

(a)    A special auditor shall submit a report to the Central Government

(b)    A special auditor cannot be the companys statutory auditor

(c)    The Board of Directors appoints the special auditor

(d)    The special auditors report has to be acted upon by the Central Government within four months from the date of its receipt

(e)    The expenses of audit will be determined by the Central Government and paid by the company.

²⁷-Which    of the following need not be stated in the Directors Report?

(a)    Technology absorption

(b)    Financial state of affairs of the company

(c)    Foreign exchange earnings of the company

(d)    Statement of accounting policies

(e)    Conservation of energy.

²⁸-Which    of the following is not a duty of the auditor of the company?

(a)    Scrutinize Loans and Advances

(b)    Scrutinize entries

(c)    Scrutinize expenses

(d)    Scrutinize investments

(e)    Scrutinize professional efficiency of management.

²⁹-If    the forfeited shares are issued at a discount, the amount of discount shall be debited to

(a)    Profit and loss account

(b)    Capital reserve account

(c)    Share forfeiture account

(d)    Securities premium account

(e)    Share capital account.

³⁰-If    no auditor is appointed or re-appointed at an Annual General Meeting, the company should inform the fact to the Central Government within

(a)    7 days

(b)    15 days

(c)    30 days

(d)    Three months

(e)    Six months.

³¹-If    proposed dividend declared out of pre-acquisition profits appears in the balance sheet of the subsidiary company, the proportionate share of the holding company in such proposed dividend should be

Debited to Profit and Loss Appropriation account of holding company

(b) Added to the cost of control (c) Shown under proposed dividend in the consolidated balance sheet (d) Credited to the investment account of the holding company (e) Credited to the consolidated Profit and Loss account. 32-Which of the following is treated as revenue profits by the holding company at the time of preparation of consolidated balance sheet? (a) Profits arising out of inter-company transactions (b) Reserves of the subsidiary company up to the date of acquisition (c) Current year profit of subsidiary company up to the date of acquisition (d) The profit on the revaluation of assets during acquisition (e) Profits earned by the subsidiary company after the date of acquisition. 33-Which of the following statements is false? (a) A bill drawn by the holding company and accepted by its subsidiary company is an outside obligation for holding company (b) A consolidated balance sheet shows the assets and liabilities of the holding company and its subsidiaries (c) A holding company can acquire control over its subsidiary company by controlling the composition of board of directors of the subsidiary company (d) A subsidiary company is excluded from consolidation, if the control is intended to be temporary (e) A group consists of parent and all its subsidiaries.

34-Hero Cycles Ltd., acquired 85% shares of Villan Cycles Ltd., for Rs.75,000. The balance sheet of Villan Cycles Ltd., as on March 31, 2008 was as follows:

Liabilities	Rs.	Assets	Rs.
Share capital: Equity shares of Rs.10 fully paid-up Current liabilities	80,000 20,000	Fixed assets Current assets	72.000 28.000
Total	1,00,000		1,00,000

The amount of goodwill to be shown in the consolidated balance sheet prepared by Hero Cycles Ltd., as on March 31, 2008 was

(a)    Rs.7,000

(b)    Rs.5,000

(c)    Rs.3,000

(d)    Rs.2,500

(e)    Rs.7,500.

³⁵-On January 01, 2008 Sayo Ltd., acquired 8,000 shares of Musi Ltd. The share capital of Musi Ltd., consists of 10,000 shares of Rs.100 each fully paid. Musi Ltd., furnished the following details:

Particulars	Rs.
Profit and Loss account (Cr.) as on April 01, 2007	1,50,000
Profit for the year 2007-08 (Cr.)	50,000
Dividends paid out of pre-acquisition profits on May 05, 2007	75,000

The share of revenue profit of Sayo Ltd., was

(a)    Rs.10,000

(b)    Rs.12,500

(c)    Rs.50,000

(d)    Rs.40,000

(e)    Rs.35,000.

³⁶-Double Ltd., acquired 70% shares of Single Ltd., on January 01, 2008. The book value of total assets of Single Ltd., on the date of acquisition was Rs.5,00,000 and during the acquisition the total assets were revalued at Rs.6,05,250. The share of Double Ltd., in the capital profit, to be shown in the Consolidated Balance Sheet as on March 31, 2008 was

(a)    Rs. 73,675

(b)    Rs. 55,250

(c)    Rs.1,05,250

(d)    Rs. 18,750

(e)    Rs.1,50,000.

³⁷-On    July 31, 2007 Nizam Ltd., acquired 70% shares of Orugallu Ltd., for Rs.6,50,000. The share capital of Orugallu Ltd., consists of 2,25,000 shares of Rs.100 each. The Profit and Loss account showed a balance of Rs.75,000 (Dr.) on April 01, 2007 and Rs.2,25,000 (Cr.) on March 31, 2008 respectively. The total amount of pre-acquisition profits was

(a)    Rs.25,000

(b)    Rs.16,667

(c)    Rs.91,667

(d)    Rs.75,000

(e)    Rs.26,667.

38-Which    of the following items should not be deducted to adjust the Gross profit, while calculating the Managerial Remuneration?

(a)    Any tax notified by the Central Government as being in the nature of a tax on abnormal profit

(b)    Any tax on business profits imposed for special reasons by the Central Government

(c)    Interest on unsecured loans

(d)    Compensation paid voluntarily

(e)    Bad debts written-off.

³⁹-Which    of the following is true with reference to dividends?

(a)    Dividends are an expense to the company

(b)    Dividends are deducted from revenue in the income statement

(c)    Dividends are always equal to net income

(d)    Dividends reduce both assets and owners equity

(e)    Dividends are paid out of capital.

⁴⁰-In    computation of gross value added, which of the following is not included?

(a)    Sales revenue

(b)    Income from royalties

(c)    Cost of all materials and services

(d)    Depreciation

(e)    Income from investments.

⁴¹-Which    of the following can be used as a means for introducing productivity linked bonus schemes for the employees?

(a)    Value added statement

(b)    Value added ratios

(c)    Economic value added

(d)    Market value added

(e)    Brand value added.

⁴²-The    shortcomings of Economic Value Added, calculated on the basis of historical costs can be overcome by using_in place of book values.

(a)    Current value

(b)    Replacement cost

(c)    Net realizable value

(d)    Standard cost

(e)    Marginal cost.

43. Which of the following statements is false regarding underwriting?

(a)    An underwriter guarantees that the shares underwritten by him will be sold

(b)    The company undertakes to pay an underwriting commission for the service rendered by underwriter

(c)    Underwriting commission need not be paid on shares required to be purchased by the underwriter as per agreement

(d)    Underwriting commission is allowed for undertaking the issue of debentures

(e)    If the public do not take up all the shares, the underwriter will himself purchase the remaining shares.

44.EVA    can be improved by

I.    Investing in high return projects.

II.    Increasing the rate of return for the same capital base.

III.    Downsizing unprofitable operations, units or by selling off sub standard assets.

(a)    Only (I) above

(b)    Only (III) above

(c)    Both (I) and (II) above

(d)    Both (II) and (III) above

(e)    All (I), (II) and (III) above.

45.Addition    of wealth made by the organization with the efforts of management and employees using capital is called

(a)    Value addition

(b)    Enterprise resource planning

(c)    Allocation

(d)    Appreciation

(e)    Utilization.

46.Economic    value addition can be computed as

(a)    Gross profit minus cost of debt

(b)    Net profit minus cost of capital

(c)    Sales minus gross profit

(d)    Net operating profit after tax minus weighted average cost of capital

(e)    Net operating profit before tax minus depreciation.

47.Shown below are selected data from income statement of Amitabh Ltd.:

Particulars	Rs.
Sales Other income (investment) Operating expenses Excise duty	5,00,000 1,20,000
	6,20,000 2,60,000 50,000

Considering the above data, the value added is

(a)    Rs.3,10,000

(b)    Rs.1,90,000

(c)    Rs.3,60,000

(d)    Rs.2,40,000

(e)    Rs.4,50,000.

⁴⁸-The net profits of Pfizer Ltd., after providing for taxation for the past five years were as follows:

Year ending profits	Rs.
2003-04	1,20,000
2004-05	1,50,000
2005-06	1,30,000
2006-07	1,80,000
2007-08	1,60,000

The average capital employed in the business was Rs.12,00,000 on which normal rate of return of 10% is expected. The amount of goodwill on 5 years purchase of super profits calculated on the basis of the average profits of the last 5 years was

(a)    Rs.1,50,000

(b)    Rs.1,48,000

(c)    Rs.1,40,000

(d)    Rs.1,20,000

(e)    Rs.1,00,000.

⁴⁹-Raghavan Ltd., proposed redemption of its preference shares at a premium of 10%. The data pertaining to it is as follows:

Particulars	Rs.
12% Preferential share capital	2,00,000

General reserve	30,000
Securities premium	10,000
Profit and Loss a/c (Cr.)	44,000

The required fresh issue of equity shares is worth

Rs.1,90,000 Rs.1,80,000 Rs.1,66,000 Rs.1,36,000 Rs.1,16,000.

following is the balance sheet of Trialblazer Ltd., as on March 31, 2008:

Liabilities Rs. Assets Rs. Equity share capital 7,500 Equity shares of Rs.10 each, fully paid General reserve Profit & Loss a/c Bank Loan (20%) Sundry creditors Provision for taxation 75.000 10.000 23.000 15.000 28.000 14,000 Goodwill Plant & Machinery Land &Building Stock-in-trade Sundry debtors Cash at bank Discount on issue of shares Preliminary expenses 3.000 60,000 25.000 11.000 40,000 9.000 2.500 14.500 1,65,000 1,65,000

Additional information:

The profits earned by the company after payment of tax at the rate of 40% in the last 4 years were as under:

Year 2004-05 2005-06 2006-07 2007-08 Profit (in Rs.) 11,000 12,000 14,000 15,000

The dividends paid by the company for the last 4 years were as follows:

Year 2004-05 2005-06 2006-07 2007-08 Dividend 11% 12% 14.5% 14.5%

The value of goodwill of the company by using the capitalization method (simple average) is

(a)    Rs.1,00,000

(b)    Rs. 88,000

(c)    Rs. 12,000

(d)    Rs. 13,000

(e)    Rs. 30,000.

⁵¹-ZED Consultancy Ltd., provides the following information:

Year ending	2005-06	2006-07	2007-08
Profit (Rs.)	48,000	57,600	24,000
Weights	1	2	3

The following information is provided:

1.    On April 1, 2005, the company purchased fixed assets of Rs.8,000 that were wrongly accounted as an expense in the year 2005-06. The company depreciates fixed assets @ 10% p.a. on Straight-line method.

2.    Non-recurring expenditure of Rs.9,000 is included in the Profit and Loss account of 2007-08.

3.    In 2006-07, dividend received from subsidiary company Rs.9,050 is included in the Profit and Loss account of 2006-07.

The average adjusted profit (weighted) for calculation of goodwill was

(a)    Rs.41,217

(b)    Rs.96,500

(c)    Rs.82,433

(d)    Rs.39,200

On first call	Rs.2
On final call	Rs.2.

Applications were received for 60,000 shares from the public. Applicants of 6,000 shares were refunded and remaining applicants were allotted the shares on pro-rata basis. All the calls were called up by the company. Call-in-arrears were as follows:

i.    Mr. Arun who was allotted 1,250 shares paid application money only.

ii.    Mr. Tarun who was allotted 2,500 shares did not pay calls money.

iii.    Mr. Pandit who was allotted 6,250 shares did not pay the final call money.

The total amount in calls-in-arrears account was

Rs.29,250 Rs.33,750 Rs.33,000 Rs.28,000 Rs.25,000.

⁵⁶-Gold Plated Ltd., invited applications for 2,00,000 equity shares of Rs.20 each, at a premium of Rs.4 per share. The entire issue was underwritten by three underwriters in the following percentages:

Siri	30%
Satya	40%
Narayana	30%

The details of marked and unmarked applications received are:

Marked applications of: Siri	44,000 shares
Satya	48,000 shares
Narayana	56,000 shares
Unmarked applications	32,000 shares

The final liability of Satya in terms of number of shares is

57-The Balance Sheet of Pashupathi Ltd., as on March 31, 2008 showed the following position:

Liabilities Rs. Assets Rs. Share capital: Fixed Assets: 30,000 shares of Rs.20 6,00,000 Factory premises 5,75,000 each, fully paid Plant and machinery 5,00,000 10,000 shares of Rs.20 1,60,000 each, Rs.16 per share paid 10,000 shares of Rs.20 1,40,000 each, Rs.14 per share paid General reserve 4,00,000 Current Assets: Profit and Loss account 1,75,000 Stock in hand 7,50,000 Current liabilities: Debtors 2,50,000 Bank overdraft 1,50,000 Creditors 2,00,000 Provision for taxation 2,50,000 Total 20,75,000 Total 20,75,000

Additional information:

   The market values of the assets were as follows:

Stock - Rs.7,75,000

Plant and machinery - Rs.5,20,000 and

Factory premises - Rs.6,41,500.

   Goodwill of the business has been valued at Rs.52,250.

The value of each fully paid equity share under intrinsic value method is

Rs.32.275 Rs.31.675 Rs.30.775 Rs.34.775 Rs.28.775.

following is an extract of the Balance Sheet of Sandeep Raja Ltd.:

Liabilities Rs. 60,000, Equity shares of Rs.20 each, fully paid-up General reserve Securities premium (includes Rs.20,000 on promoters shares) Capital reserve (includes a cash gain of Rs.1,20,000 on sale of machinery) Profit and Loss account 12,00,000 4.00.000 1.00.000 2,00,000 7,00,000

The directors decided to issue three bonus shares for every five shares held. It was decided to use capital reserve, securities premium, general reserve to the fullest extent possible and the deficit to be adjusted from Profit and Loss account. The amount to be adjusted from Profit and Loss account, for the issue of bonus shares is

(a)    Rs.3,00,000

(b)    Rs.1,80,000

(c)    Rs.2,40,000

(d)    Rs.1,20,000

(e)    Rs.1,00,000.

⁵⁹-Ahana    Ltd., issued 1,00,000 equity shares of Rs.10 each at par, payable as Rs.5 per share on application, Rs.2 per share on allotment and the balance on the first and final call. Call money on 2,000 shares were not received. These shares were forfeited. Out of the forfeited shares, 1,200 shares were reissued to Mr. Suraj at Rs.8 per share. Later, 200 shares were reissued to Ms. Basuli at par. The remaining shares were re-issued to Ms. Swathi at Rs.11 per share.

The amount transferred from shares forfeited account to capital reserve in respect of the shares reissued to Ms. Swathi is

(a)    Nil

(b)    Rs.9,600

(c)    Rs.2,400

(d)    Rs.4,200

(e)    Rs. 600.

⁶⁰-On    March 31, 2008, the balance of 12% Debentures of Rs.100 each of Tops Ltd., was Rs.6,00,000. The company reserves the right to redeem the debentures in any year by purchase in the open market. Interest on debentures is payable on September 30 and March 31, every year.

On July 1, 2008, the company purchased 1,200 of its 12% Debentures as investment at Rs.102 cum-interest.

The company cancelled 1,200 own debentures on September 01, 2008. The profit/loss on cancellation of own debentures is

(a)    Rs.4,800 (Profit)

(b)    Rs.4,800 (Loss)

(c)    Rs.3,600 (Loss)

(d)    Rs.1,200 (Loss)

(e)    Rs.1,200 (Profit).

⁶¹-Hilly    Ltd., has issued 25,000, 10% Preference Shares of Rs.100 each, fully paid and 2,50,000 Equity Shares at Rs.20 each fully paid, (par value at Rs.15 each). The profit for the year 2007-08 was Rs.21,68,000.

The company has to provide Rs.7,60,000 for taxation of the previous year 2006-07. The company declared an equity dividend of 10%. The total amount debited to Profit and Loss Appropriation account on account of the above decisions was

(a)    Rs. 4,60,000

(b)    Rs. 2,86,000

(c)    Rs.13,62,000

(d)    Rs.13,85,000

(e)    Rs.11,36,000.

⁶²-The Managing Director of Ortega Ltd., is entitled to a commission of 4% on net profits after charging such commission. The net profit of the company for the year ended March 31, 2008 was reported to be Rs.45,00,000. Subsequently, it was noticed that the following transactions were omitted:

Particulars	Rs.
Payment of Directors remuneration Sale of a plant (cost price Rs.3,00,000; written down value Rs.2,40,000) Payment of bonus to Production Executive Payment of income tax and super tax	1.50.000 3.30.000 75.000 30.000

The commission payable by the company to the managing director for the year 2007-08 was

(a)    Rs.1,66,731

(b)    Rs.1,74,205

(c)    Rs.1,77,406

(d)    Rs.1,73,661

(e)    Rs.1,78,200.

⁶³-The    Profit and Loss account of Urmila Ltd., for the year ended March 31, 2008 showed a debit balance of Rs.75,000. Subsequently, it was noticed that the following transactions were omitted:

   Goods worth Rs.3,000 returned to the supplier and were not recorded in the books.

   The rent of the godown is Rs.24,000 p.a. out of which only Rs.20,000 was paid. The rent accrued but not paid was not considered in the books of account.

   One cheque given by a customer for Rs.7,000 was dishonored and the fact of dishonor was not recorded in the books.

The profit/loss made by the company after considering the above transactions is

(a)    Rs.76,000 (Profit)

(b)    Rs.74,000 (Profit)

(c)    Rs.83,000 (Loss)

(d)    Rs.69,000 (Profit)

(e)    Rs.76,000 (Loss).

⁶⁴-Pavani    Ltd., was registered with an Authorised Capital of Rs.20,00,000 consisting shares of Rs.100 each. The following transactions were made during the year 2007-08:

   It acquired fixed assets worth Rs.8,80,000 from Kiran Bros. and the purchase consideration was paid in the form of shares at a premium of 10%.

   Further, the company allotted 1,000 shares to promoters in lieu of their services and the shares were issued at par to the promoters.

   The company offered to the public 3,000 shares at a premium of 10%, the entire share amount being payable on application. The issue was fully subscribed by the public.

The total of Balance Sheet of the company after considering the above transactions was

(a)    Rs.13,10,000

(b)    Rs.14,00,000

(c)    Rs.13,00,000

(d)    Rs.12,40,000

(e)    Rs.11,70,000.

⁶⁵-The    following balances were extracted from the books of Vaibhav Ltd., as on March 31, 2008:

Particulars	Rs.	Particulars	Rs.
Called-up share capital	6,00,000	Fixed assets	9,24,000
Secured loans	4,80,000	Calls in arrears	36,000
Loans to employees	61,440	Capital reserve	1,08,000
Cash	4,800	Profit and Loss account	60,000

Sundry debtors	1,32,000	(credit balance)
Stock	1,15,200	Sundry creditors	1,09,440
Bank balance	48,000	Preliminary expenses	36,000

The balance sheet total of Vaibhav Ltd., as on March 31, 2008, prepared in accordance with Part I of Schedule VI of the Companies Act, 1956 was

(a)    Rs.13,21,440

(b)    Rs.14,35,550

(c)    Rs.12,34,670

(d)    Rs.14,35,850

(e)    Rs.15,34,550.

⁶⁶ Alpha Ltd., furnished the following data as on March 31, 2008:

Debit Balances	Rs.	Credit Balances	Rs.
Investment (market value Rs.9,60,000) Establishment Charges Income tax paid for the year 2006-07 Depreciation	10,00,000 15,40,000 6,00,000 4,30,000	Equity Share Capital Commission Gross Profit Provision for Taxation (2006-07)	70,00,000 50,000 52,30,000 4,30,000

Additional information:

   Provision for income tax is to be created at 60%.

   Managing Director is to be paid commission at 5% of the annual net profit (before charging such commission)

The profit after tax of Alpha Ltd., was

(a)    Rs.33,10,000

(b)    Rs. 1,65,500

(c)    Rs.15,72,250

(d)    Rs.12,57,800

(e)    Rs.18,86,700.

^67.Following is the data pertaining LIMA Ltd., as on March 31, 2008 :

Particulars	Rs.
Authorized share capital (25,000 shares of Rs.100 each) Is sued/subscribed/called-up capital Calls-in-arrear Interim dividend declared Current year profit	25,00,000 12,35,000 10,000 49,000 3,75,000

If final dividend of 9% is declared (in addition to interim dividend), the amount that will have to be transferred to General Reserve in lieu of dividend declared (inclusive of interim dividend) out of current year profit would be

(a)    Nil

(b)    Rs.16,850

(c)    Rs.33,700

(d)    Rs.15,000

(e)    Rs.18,750.

⁶⁸-Strong Ltd., acquired 3,200 equity shares of Weak Ltd., on March 31, 2008. The summarized Balance Sheets of the two companies as on that date are given below:

Liabilities	Strong Ltd. (Rs.)	Weak Ltd. (Rs.)	Assets	Strong Ltd. (Rs.)	Weak Ltd. (Rs.)
Share capital (shares of Rs.100 each fully paid-up)	10,00,000	4,00,000	Fixed assets	7,80,000	6,78,800

General reserve 4,80,000 3,40,000 Investments in Weak Ltd. 6,80,000 Profit and Loss 1,14,400 72,000 Stocks 2,40,000 72,000 account Bills payable Sundry debtors 88,000 80,000 (including Rs.6,000 to Strong Limited) 16,800 Sundry creditors 2,54,400 18,000 Bills receivable (including Rs.6,000 from Weak Limited) Cash at bank 31,600 29,200 16,000 Total 18,48,800 8,46,800 Total 18,48,800 8,46,800

The additional information is as follows:

i.    Weak Ltd., made a bonus issue on March 31, 2008 of one equity share for every four shares held by its shareholders. This has not yet been accounted for.

ii.    Sundry creditors of Strong Ltd., included Rs.24,000 due to Weak Ltd.

If the value of goodwill was Rs.14,400, the total of assets side of Consolidated Balance Sheet was

(a)    Rs.40,40,000

(b)    Rs.20,00,000

(c)    Rs.21,30,000

(d)    Rs.23,60,000

(e)    Rs.34,60,000.

⁶⁹-Indrani    Ltd., issued 4,000 10% Preference shares of Rs.100 each at par, which are redeemable at a premium of 10%. For the purpose of redemption, the company issued 3,000 Equity Shares of Rs.100 each at a premium of 20% per share. At the time of redemption of Preference Shares, the amount to be transferred by the company to the Capital Redemption Reserve Account is

(a)    Rs.1,00,000

(b)    Rs. 80,000

(c)    Rs.4,00,000

(d)    Rs.4,40,000

(e)    Rs.1,40,000.

⁷⁰-Consider    the following Balance Sheets of Long Ltd., and Short Ltd., as on March 31, 2008:

Liabilities	Long Ltd. (Rs.)	Short Ltd. (Rs.)	Assets	Long Ltd. (Rs.)	Short Ltd. (Rs.)
Share Capital (Equity shares of Rs.10 each) Other Liabilities	24.000 12.000	12,000 6,000	Investment in Short Ltd. (960 Shares) Other Assets	9,600 26,400	18,000
	36,000	18,000		36,000	18,000

Long Ltd., has acquired the shares of Short Ltd., on March 31, 2008. The Minority interest shown in the Consolidated Balance Sheet was

(a)    Rs.2,400

(b)    Rs.2,500

(c)    Rs.5,000

(d)    Rs.3,000

^(e)    Rs.8,000.

⁷¹-Green Ltd., acquired 75% share in the Share Capital of Rs.75,000 of Yellow Ltd., at a price of Rs.1,05,000. The pre-acquisition profits and post-acquisition profits of the subsidiary company were Rs.38,000 and Rs.25,000 respectively. The amount of goodwill shown in the Consolidated Balance Sheet was

(a)    Rs.84,750

(b)    Rs.26,000

(c)    Rs.20,250

(d)    Rs.28,500

(e)    Rs.56,250.

⁷².Nippon    Batteries Ltd., issued 1,00,000 shares of Rs.100 each at a premium of 30% payable Rs.20 on application, Rs.50 (including premium) on allotment and the balance on calls. Applications were received for 1,92,000 shares and allotments were made as under:

   Applicants for 50,000 shares were allotted 35,480 shares on pro-rata basis.

   Applicants for 96,000 shares were allotted 38,400 shares on pro-rata basis.

   Applicants for 46,000 shares were allotted 26,120 shares on pro-rata basis.

The amount adjusted towards allotment money was

(a)    Rs.38,40,000

(b)    Rs.20,00,000

(c)    Rs.18,40,000

(d)    Rs.19,20,000

(e)    Rs.29,00,000.

⁷³.Maggy    Ltd., issued 5,000 shares of Rs.100 each at a premium of Rs.20 per share of which 4,500 shares are subscribed for. The amount to be paid is as follows:

Rs.50 - on application, including premium of Rs.20.

Rs.50 - on allotment.

Rs.20 - on first and final call.

Call money was not received on 500 shares. On forfeiture of these shares, the amount standing to the credit of securities premium account is

(a)    Rs.1,00,000

(b)    Rs. 90,000

(c)    Rs. 80,000

(d)    Rs. 70,000

(e)    Rs. 10,000.

⁷⁴.Zolor    Ltd., acquired the shares of Zeft Ltd. The closing stocks of two companies were Rs.44,000 and Rs.72,000 respectively. Closing stock of Zolor Ltd., included goods worth Rs.3,600 purchased from Zeft Ltd. Zeft Ltd., sells goods at a profit of 50% on cost. The net amount of closing stock appearing in the consolidated balance sheet was

(a)	Rs.1,14,800
(b)	Rs.1,14,200
(c)	Rs.1,12,400
(d)	Rs.1,20,000
(e)	Rs.1,16,400.

^75.According to which of the following accounting concepts, the consolidated financial statements are prepared when a parent-subsidiary relationship exists?

(a)	Going concern
(b)	Business entity
(c)	Materiality
(d)	Cost
(e)	Periodicity.

END OF QUESTION PAPER

Suggested Answers Financial Accounting - II (MSF1A2)

Answer    Reason

D Intangible assets are classified as either identifiable or unidentifiable. Goodwill (d), arising out of payment fo reputation, brand name, location, loyalty etc. is an unidentifiable intangible asset. Hence, alternative (d) i correct answer.

B Amortization is the accounting process of systematically allocating cost of intangible assets to the period o use. It is not the process of determining cash flow from operations. It is not creating any fund to replace th asset. It is not the process of adjusting the change of price level, and it is not the asset valuation process Hence (b) is correct.

^D The credit to equity share capital should be for Rs.1,00,000; the amount of the legal capital requirement a determined by the Rs.20 par value (5,000 shares x Rs.20 per share). The entire entry to record this transactio would be debit Cash, Rs.1,25,000; credit Share capital, Rs.1,00,000; and credit securities premium Rs.25,00( The journal entry is :

Cash a/c    Dr. Rs.1,25,000

To Equity share capital    Rs. 1,00,000

To Securities premium a/c    Rs. 25,000

D The number of rights shares offered is in proportion to the equity shares already held and they are no disproportionately issued.

B If the forfeited shares are reissued at a premium, the amount of such premium shall be credited to securitie premium account.

A If a company issues some of its common shares in exchange for assets other than cash, the transaction shoul be recorded at the current market value of the assets acquired.

A Unless the Board of Directors approve the allotment of shares, the application money received from publi will remain with the company as a liability.

B The amount of capital that is offered to the public for subscription is called issued capital. The value c shares taken up by the public is subscribed capital. The part of the capital that has been called up is called u capital. Thus the alternative (b) is the correct answer.

B When shares are issued at less than par value, the difference is the discount on issue of shares.

D If the allotment money is not paid by the shareholder, there will be a debit balance (of that unpaid money) i share allotment account. Other options, stated in (a), (b), (c) and (e) are not correct.

B Value as per fair value method is (value as per intrinsic value method + value as per yield method)/2 Value a per intrinsic value method is (2 x Rs.22.5) - Rs.19.5 = Rs.25.5.

A Cumulative preference shares have the right to receive dividends in arrears, whenever earnings becom adequate.

B The journal entry to be made for the issue is

Particulars		Rs.	Rs.
Bank Account	Dr.	4,75,000
Loss on issue of debentures	Dr.	50,000
To 15% Debentures A/c.			5,00,000
To Premium on Redemption of			25,000
Debentures

Hence the correct answer is (b).

14.    C The company may receive from the shareholders the amount uncalled on the shares held by them even thoug

the amount is not called for. In such a case the company is compelled to pay interest on the calls in advance a prescribed rate from the date of receipt of advance to the date of appropriation i.e. the date when the call i made and the advance received is appropriated from calls in advance account to the relevant call account. Hence the correct answer is (c).

15.    B Except minority interest in subsidiaries all other above mentioned items are included in owners equity of

balance sheet.

16. B As per SEBI guidelines, for debentures issued having a maturity of more than 18 months, a Debentur Redemption Reserve shall be created out of profits, prior to the commencement of the redemption, for minimum percentage of debenture issue. Such minimum percentage is 50%.

At the end of the financial year, the cumulative total of interest on own debentures account is transferred t

(a) Profit and Loss account.

The premium collected on issue of debentures is recorded in the debenture premium account and subsequently transferred to capital reserve. It is an income to the issuing company. There are no restrictions as to its use. It is not transferred to General reserve (b), capital redemption reserve (d). Securities premium account (c) reflects only premium on issue of shares. It is not a debt to be transferred to debentures (e). Thus the correct answer is (a).

The long term investments are accounted for in the balance sheet at cost price.

Tax deducted at source is the liability of the company towards the tax authority. It is also payable to the tax authority within a short period. Therefore, it is to be shown on liabilities side of the balance sheet under current liabilities Hence, (a) is correct answer.

The periodical interest received in respect of investments made on account of debenture redemption fund is credited to (d) Debenture redemption fund account. Hence, option (d) is the correct answer.

At the time of purchase of debentures, the interest account will be debited with

Interest = 5,00,000 x 12% x 2/12 = Rs. 10,000.

Subsidies received from the Government are included in the profits for the purpose of calculating managerial remuneration. Therefore, option (d) is the correct answer.

Increase in gross profit in 2007-08 = 3,00,000 x 20/100 = Rs.60,000

Increase in operating expenses in 2007-08= 2,00,000 x 10/100 = Rs.20,000

Increase in net profit = Rs.60,000 - Rs.20,000 = Rs.40,000.

A company should also show, by way of notes to the balance sheet, certain contingent liabilities listed below:

1.    Claims against the company not acknowledged as debts.

2.    Uncalled liability on shares partly paid.

3.    Arrears of fixed cumulative dividends.

4.    Estimated amount of contracts remaining to be executed on capital account and not provided for.

5.    Other money for which the company is contingently liable.

Therefore option (d) is the correct answer.

The Central Government appoints a Chartered Accountant or the company auditor as a special auditor, but not by the Board of Directors of the company.

Statement of accounting policies need not be stated in the Directors Report. It is to be stated in Auditors Report

Scrutinizing professional efficiency of management is not a duty of an auditor.

If a company reissues forfeited shares at a discount, that discount amount will be debited to share forfeited account. Hence (c) is the correct answer. According to the companies act the company cannot debit share capital account, profit and loss account, capital redemption reserve account and capital reserve account for the amount of discount allowed on the reissue of forfeited shares.

If no auditor is appointed or re-appointed at annual general meeting, the company should inform the Central Government within 7 days and the Central Government may appoint a person to fill-up the vacancy Therefore, alternative (a) is the correct answer

The amount of proposed dividend out of pre-acquisition profits of the subsidiary company belonging to the holding company is credited to the investment account of the holding company. Therefore option (d) is the correct answer.

Option (e) is the correct answer because profits earned after the date of acquisition are treated as revenue profits for a holding company.

Bills drawn or accepted either by the holding company or its subsidiary company is not an outside obligation for the holding company. The item Bills Receivable in one companys balance sheet and correspondin item Bills Payable in another companys balance sheet are to be eliminated under inter-compan transactions against each other. Hence option (a) is correct answer.

Particulars	Rs.
Cost of acquisition of shares Less: Nominal value of shares 80,000 x 85% Goodwill	75.000 68.000
	7,000.

Revenue Profits of Musi Ltd. = Rs.50,000 x 3/12 = 12,500 The share in revenue profit of Sayo Ltd. = Rs.12,500 x 80% = Rs.10,000 Total profit on revaluation of assets = Rs.6,05,250 - Rs.5,00,000 = Rs.1,05,250 Share of Double Ltd., in the capital profit = Rs.1,05,250 x 70% = Rs.73,675. Amount of profit for the year 2007-08 is Rs.2,25,000 + Rs.75,000 = Rs.3,00,000 Amount of profit for 4 months from April 01, 2007 to July 31, 2007 Rs.3,00,000

-x 4 = Rs. 1,00,000

12

Pre-acquisition profits = Rs.1,00,000 - Rs.75,000 = Rs.25,000.

Any compensation, damages or payments made voluntarily shall not be deducted from the gross profit whil calculating the managerial remuneration, except this all the other items should be deducted from the gros profit to calculate managerial remuneration. Hence the answer is (d).

Dividends are distributions of profits to the investors (stockholders) of the company. Dividends are not expenses and do not appear in the income statement They are appropriation of profits and appear in the profit and loss appropriation account. When dividends are declared and paid they reduce both the assets and owners equity.

Gross value added does not include depreciation.

Value added statement can be used as a means in introducing productivity linked bonus schemes for the employees.

Current value of assets can be used in place of historical costs to overcome the drawback in computing EVA on the basis of historical costs.

Option (c) is the correct answer because underwriting commission is paid on shares purchased by the underwriter as per agreement.

EVA can be improved by

I.    Investing in high return projects.

II.    Increasing the rate of return for the same capital base.

III.    Downsizing unprofitable operations, units or by selling off sub standard assets.

All are steps for improvement of EVA. Alternative (e), the combination of above, is the correct answer. Addition of wealth made by the organization with the efforts of management and employees using capital is called as value addition.

Economic value addition = Net operating profit after tax - Weighted average cost of capital.

Value added = Sales - Operating expenses - Excise duty

Value added = Rs.5,00,000 - Rs 2,60,000 - Rs.50,000 = Rs.1,90,000.

Year	Profits (Rs.)
2003-04 2004-05 2005-06 2006-07 2007-08	1,20,000 1.50.000 1.30.000 1.80.000 1,60,000
	7,40,000

Average annual profits = Rs.7,40,000 v 5 =

Less: 10% Return on Rs.12,00,000 (average capital employed) = Super profit

Goodwill = 5 x Rs.28,000 = Rs.1,40,000.

Particulars

Preference share capital

Add: Premium on redemption @ 10%

Amount required for redemption

Less: Amount available for redemption Rs.30,000 + Rs.10,000 +

Rs.44,000

Required fresh issue of shares

Computation of net tangible assets

Particulars	Rs.	Rs.
Plant & machinery Land & building Stock in trade Sundry debtors Cash at bank Less: Bank loan Sundry creditors Provision for taxation Net tangible assets	60,000 25.000 11.000 40,000 9,000	1,45,000 57,000
	15.000 28.000 14,000
		88,000

Computation of average maintainable profit

Average profit after tax = (11,000 + 12,000 + 14,000 + 15,000) / 4 = Rs.13,000 Average dividend paid = (11% + 12% + 14.5% + 14.5%) / 4 = 13%

Therefore, normal rate of dividend = 13%

Total value of the business = (Average maintainable profit / Normal rate of return) x 100 = Rs.13,000 / 13% = Rs.1,00,000

Goodwill = Total value of the business - Net tangible assets = Rs.1,00,000 - Rs.88,000 = Rs.12,000.

51. A

Particulars	Mar. 31, 2006	Mar. 31, 2007	Mar. 31, 2008
Profit as per books	48,000	57,600	24,000
Purchase of Fixed asset	8,000
(W.N.1)	-800	-800	-800
Non-recurring expenditure			9,000
Profits from subsidiary		-9,050
company	55,200	47,750	32,200
Adjusted Profit
Weights (assumed)	1	2	3
Weighted average profit	55,200	95,500	96,600

Weighted average profit = (55,200 + 95,500 + 96,600 ) / 1 + 2 + 3 = 2,47,300 / 6 = Rs.41,217.

52. A

Particulars	March 31, 2006 (Rs.)	March 31, 2007 (Rs.)	March 31, 2008 (Rs.)
Gross Profit Less: Other expenses Interest on debentures Pre-tax profit Less: Tax @35% Post-tax profits	2,50,000 60,000 48,000	3,25,000 72.000 48.000	4,80,000 80,000 48,000
	1,42,000 49,700	2,05,000 71,750	3,52,000 1,23,200
	92,300	1,33,250	2,28,800

Average post-tax profits = (Rs.92,300 + 1,33,250 + 2,28,800) / 3 = Rs.1,51,450 Goodwill = Rs.1,51,450 x 4 = Rs.6,05,800.

53. D

Particulars	Rs.
Total assets	3,87,500
Less: Profit and Loss account (loss)	30,000
Long-term loan	1,00,000
Creditors	25,000
Bank overdraft	12,500

Capital employed at the end	2,20,000
Less: Vi of the profit during the year	12,500
Average capital employed	2,07,500

Normal profit

= Average capital employed x normal rate of return = Rs.2,07,500 x 10% = Rs.20,750.

Year	PAT (Rs.)	Taxes (Rs.)	Directors Remuneration (Rs.)	Profit before tax and remuneration (Rs.)
2005-06	72,750	72,750	4,500	1,50,000
2006-07	87,300	87,300	5,400	1,80,000
2007-08	97,000	97,000	6,000	2,00,000
				5,30,000

Particulars	Rs.	Rs.
Average Profit before tax and directors remuneration Less: Additional Depreciation @ 10% on Rs.1,00,000 Directors Remuneration on Rs.1,66,667 @ 3% Less Income Tax @ 50% Future Maintainable Profits	10,000 5,000	1,76,667 15,000
		1,61,667 80,834
		80,833

Computation of total amount of calls-in-arrear:

Pro-rata ratio = 54,000 : 45,000 = 6 : 5

Mr. Arun who did not pay allotment

money applied for shares = 1,250 x 6 / 5 = 1,500 shares

Amount paid by Mr. Arun on application = Rs.3 x 1,500 shares

Amount adjusted against allotment = Rs.3 x 250 = Rs.750.

Amount due from Mr. Arun:

Due on allotment = Rs.5 x 1,250 Less: Amount adjusted from application    =

Due on calls = Rs.4 x 1,250 .*. Amount due from Mr. Arun Amount due from Mr. Tarun = Rs.2,500 x 4 Amount due from Mr. Pandit = Rs.6,250 x 2 Total amount of calls-in-arrear is

(No. of shares)

Particulars Siri Satya Narayana Total Liability Less: Unmarked applications in the ratio of 3 : 4 : 3 60,000 9,600 80,000 12,800 60,000 9,600 2,00,000 32,000 50,400 67,200 50,400 1,68,000 Less: Marked (Stamped) applications 44,000 48,000 56,000 1,48,000 Less: Division of Sunils surplus 6,400 19,200 (5,600) 20,000 (in the ratio of 3:4) 2,400 3,200 5,600 - Final liability of each underwriter 4,000 16,000 Nil 20,000

Valuation of shares under Intrinsic Value Method: Calculation of capital employed under net assets basis:

Particulars	Rs.	Rs.
Assets:

Particulars	Rs.	Rs.
Notional calls on partly paid shares 10,000 x Rs.4 10,000 x Rs.6	40.000 60.000	1,00,000
Funds available to Equity share holders		17,38,750

Number of shares    = 50,000

Intrinsic value of shares    = Rs.17,38,750 / 50,000 = Rs.34.775.

Intrinsic value fully paid share = Rs.34.775

Intrinsic value of partly paid share (Rs.16 paid per share) = Rs.34.775 - Rs.4 = Rs.30.775. Intrinsic value of partly paid share (Rs.14 paid per share) = Rs.34.775 - Rs.6 = Rs.28.775 Number of bonus shares = 60,000 x 3/5 = 36,000

Particulars	Rs.
Amount of bonus issue = 36,000 x Rs.20 Less: Amount to be adjusted against Capital reserve (amount realized in cash) Securities premium (Rs.1,00,000 - Rs.20,000) General reserve Amount to be utilized from Profit and Loss account	7.20.000 1.20.000 80,000 4,00,000
	1,20,000

The securities premium collected in cash can be utilized for the bonus issue. Hence the amount of Rs.20,00 on issue of shares to promoters cannot be utilized for issue of bonus shares.

Amount transferred to forfeited shares account in respect of shares reissued to Swathi

= 600 x 7 = Rs.4,200.

Therefore, Rs.4,200 can be transferred to capital reserve.

60.

Date	Particulars	Dr. (Rs.)	Cr. (Rs.)
July 1, 2008	Own Debentures a/c. Dr. Interest on Debentures A/c. Dr. To Bank A/c. (Being the purchase of 1,200 own debentures at the rate of Rs.102 cum interest. Interest for 3 months from April 1,2008 to June 30, 2008 is Rs.3,600)	1,18,800 3,600	1,22,400
Sept.01, 2008	12% Debentures A/c. Dr. To Own debentures A/c. To Capital reserve A/c. (Being the profit on redemption of debentures transferred to capital reserve A/c.)	1,20,000	1,18,800 1,200

Thus, the profit on cancellation of own debentures transferred to capital reserve is Rs.1,200.

61. D Provision for taxation of the previous year =    Rs. 7,60,000

Dividend on 10% 25,000 Preference Shares of Rs.100 =    Rs. 2,50,000

10% Dividend on 2,50,000 equity shares of Rs.15 each =

The total amount debited to Profit and Loss appropriation account =

Particulars	Rs.	Rs.
Net Profit as calculated Add: Revenue Profit on sale of plant Less: Directors remuneration Bonus paid to production executive Net Profit	1,50,000 75,000	45,00,000 60,000
		45,60,000 2,25,000
		43,35,000

Where the amount for which the fixed asset is sold exceeds the written-down value, credit shall be given fo so much of the excess as is not higher than the difference between the original cost of the fixed asset and it written down value. Hence only Rs.60,000 (Rs.3,00,000 - Rs.2,40,000) should be added.

The directors remuneration and the bonus paid to any member of companys staff should be deducte whereas Income tax and super tax should not be deducted.

Credit should not be given to profits by way of premium on shares

Managing Directors Commission = Rs.43,35,000 x 4 / 104 = Rs.1,66,731.

63. E

Particulars	Rs.
Loss as reported by the accountant	75,000
Less: Goods returned to supplier	(3,000)
Add: Rent not considered	4,000
Loss after considering all aspects	76,000

Non-recording of return of cheque does not affect the profit & Loss account. 64. A Balance Sheet of Pavani Ltd.

Liabilities Rs. Assets Rs. Share Capital 12,00,000 Goodwill 1,00,000 Securities Premium 1,10,000 Fixed Assets 8,80,000 Bank 3,30,000 Total 13,10,000 Total 13,10,000

Working Note: Assets are acquired against issue of shares at a premium of 10%. i.e.Rs.8,80,000 x 100 / 11 = Rs.8,00,000 = Share capital of Rs.8,00,000 and shares premium of Rs.80,000 Share issued to promoter

1,000 at par of Rs.100 = 1,00,000 and the account debited is goodwill with Rs.1,00,000; 3,000 shares ar issued to public at a premium of 10% i.e. the amount received 3,000 x Rs.110 = Rs.3,00,000 against shar capital and Rs.30,000 against securities premium.

65. A    Balance Sheet of Vaibhav Ltd., as on March 31, 2008

Alpha Ltd. Profit and Loss account for the year ended March 31, 2008 Cr.

Particulars Rs. Particulars Rs. To Establishment charges 15,40,000 By Gross profit 52,30,000

To Depreciation	4,30,000	By Commission	50,000
To M.D.s Remuneration (Note-1)	1,65,500
To Provision for Income Tax	18,86,700
(Note-2)
To Net profit c/d	12,57,800
	52,80,000		52,80,000

Working notes:

1.    Managing Directors remuneration has been calculated on the profit of Rs.33,10,000 {(Rs.52,30,000 Rs.50,000) - (Rs.15,40,000 + Rs.4,30,000)} because this profit is in conformity with the provisions c Section 349 and 350 of the Companies Act,1956. Therefore, Managing Directors remuneration will b 5% of Rs.33,10,000 = Rs.1,65,500.

2.    Provision for Income Tax:

Profit before remuneration and taxes    Rs.33,10,000

Less M.D.s remuneration    Rs. 1,65,500

Profit before tax    Rs.31,44,500

Income tax @60% on Rs.31,44,500 =    Rs.18,86,700

67.    E Calculation of Transfer to General Reserve:

Final dividend declared (Rs.12,35,000 - Rs.10,000) x 9% = Rs.1,10,250 Total of dividend declared and proposed during the year = Rs.(49,000 + 1,10,250) = Rs.1,59,250

Dividends as a percent of paid-up capital = (1,59,250 / 12,25,000) x 100 = 13%

Since this rate of dividend falls in the slab - greater than 12.5% but less than 15% - the transfer to reserve should be 5% of the current profits.

Transfer to reserves = (5 / 100) x Rs.3,75,000 = Rs.18,750.

68.    B Asset side of Consolidated Balance Sheet of Strong Ltd. and Weak Ltd. as at March 31, 2008

Assets	Rs.	Rs.
Goodwill		14,400
Fixed assets:
Strong Ltd.	7,80,000
Weak Ltd.	6,78,800	14,58,800
Stock:
Strong Ltd.	2,40,000
Weak Ltd.	72,000	3,12,000
Sundry debtors:
Strong Ltd.	88,000
Weak Ltd.	80,000
	1,68,000
Less: Mutual indebtedness	24,000	1,44,000
Bills receivable:
Strong Ltd.	31,600
Less: Mutual indebtedness	6,000	25,600
Cash at bank:
Strong Ltd.	29,200
Weak Ltd.	16,000	45,200
Total		20,00,000

Particulars	Rs.
Face value of shares to be redeemed (4,000 x Rs.100) Less: Proceeds from fresh issue (3,000 x Rs.100)	4.00.000 3.00.000
Balance to be utilized from profit & loss a/c. Hence, amount to be transferred to capital redemption reserve	1,00,000

The premium received on fresh issue of shares should not be used for redemption of preference shares However, the same can be used for the premium payable on redemption of preference shares.

960 (4

1"200 = I 5 I ^Holding ^Comp^any

Minority Interest = (12,000 x 1/5) = Rs.2,400.

71. C

Particulars	Rs.	Rs.
Cost of control on acquisition or cost of investments Less: share in share capital 75% of Rs.75,000 Less: share in pre-acquisition profit i.e.75% of Rs.38,000 Goodwill	56,250 28,500	1,05,000 84,750
		20,250

72. ^C

Shares applied (1)	Shares allotted (2)	Application money received (Rs.) (3) = (1) x Rs.20	Application money due (Rs.) (4) = (2) x Rs.20	Excess money (Rs.) (5) = (3) - (4)	Allotment money due (including premium) (Rs.) (6) = (2) x Rs.50	Surplus / (deficit) (Rs.) (7) = (5)-(6)
50.000 96.000 46.000	35,480 38,400 26,120	10,00,000 19,20,000 9,20,000	7,09,600 7,68,000 5,22,400	2,90,400 11,52,000 3,97,600	17.74.000 19.20.000 13.06.000	(14,83,600) (7,68,000) (9,08,400)
1,92,000	1,00,000	38,40,000	20,00,000	18,40,000

Hence the amount adjusted towards allotment is Rs.18,40,000.

The amount received on account of securities premium is 4,500 shares x Rs.20 = Rs.90,000. There is n impact of forfeiture of shares on securities premium account. The amount of premium received is to b utilized as per the provisions of the Companies Act.

Extract of consolidated balance sheet of Zolor Ltd., as on March 31,2008

Liabilities	Rs.	Assets	Rs.
		Closing stock Zolor 44,000 Zeft 72,000 1,16,000 Less: Unrealized 1,200 profit (Rs.3,600 x 50 / 150)	1,14,800

Consolidated financial statements should reflect the economic activities of a business enterprise measure without regard to the boundaries of the legal entity. A parent and subsidiary are legally separate but ar treated as a single business enterprise in consolidated statements, in recognition of Business entity concep

(b). The other concepts do not explain about consolidation of financial statements. The Going concer concept (a) assumes that the business entity will continue to operate in the absence of evidence to th contrary. Materiality (c) requires reporting the information that has a value significant enough to affec decisions of those using the financial statements. Cost concept (d) explains how the assets are to be recorde in the books of accounts. According to this, fixed assets are to be recorded at cost less accumulate depreciation. Periodicity (e) explains that the financial accounting process is meant to provide the informatio about the economic activities of the business enterprise at regular intervals. It does not speak abou consolidation of financial statements. Alternative (b) is the correct answer.

75. B

Model Question Paper Economics - I (MSF1A3)

Answer all 72 questions.

Marks are indicated against each question.

Total Marks

1.    Which of the following statements is/are not correct?

I.    The rationality on the part of a firm is to maximize utility.

II.    The rationality on the part of an investor is to maximize satisfaction.

III.    The rationality on the part of the consumer is to maximize revenue.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.

2.    Which of the following statements is not correct about command economy?

(a)    Command economy does not determine what type of goods and services to be produced using a hierarchical organizational structure

(b)    In a command economy, the state owns all the productive resources

(c)    In a command economy, authoritarian methods are used to determine the use of resources

(d)    Government enterprise and government ownership of resources are the rule rather than an exception in a command economy

(e)    Command economy is different from mixed economy.

3.    Veblen effect is one of the exceptions to the law of demand. According to this effect the consumers buy more amount of a commodity as the price increases because they feel that

(a)    The commodity is essential for them

(b)    The commodity is scarce

(c)    There is an improvement in the quality of the commodity

(d)    There will be a further increase in the price of the commodity in future

(e)    It is a pride to buy a commodity with higher price.

4.    Which of the following statements is not correct?

(a)    The demand for a good increases with the increase in the price of its substitute goods

(b)    If the demand for a good increases the demand for its complementary goods increases

(c)    Price elasticity of demand is the ratio of percentage change in quantity demanded to percentage change in price

(d)    If the demand is inelastic, a decrease in price of the commodity increases the quantity demanded for that commodity

(e)    Elasticity of demand increases as we move down along the demand curve.

5.    The demand for a commodity does not increase,

(a)    With the increase in income

(b)    With the increase in wealth

(c)    With an increase in the price of substitutes

(d)    With an increase in the price of complements

(e)    With the expectation of future increase in the price of the good.

6.    If price of a commodity is measured on the Y axis and the quantity demanded is measured on X axis, the middle point of a straight line demand curve represents

(a)    Perfectly elastic demand

(b)    Perfectly inelastic demand

(c)    Relatively elastic demand

(d)    Relatively inelastic demand

(e)    Unitary elastic demand.

7.    If the absolute value of price elasticity of demand for a commodity is one, then the marginal revenue for that commodity is

(a)    One

(b)    Zero

(c)    Infinity

(d)    Greater than one but less than infinity

(e)    Less than one but greater than zero.

8.    Which of the following statements is not true for the decrease in the supply of a commodity?

(a)    An increase in the price of the input required for producing a commodity

(b)    A deterioration in technology

(c)    A decrease in the number of producers

(d)    Contraction of supply is different from decrease in supply

(e)    It is represented by the outward shift of the supply curve.

9.    The demand for all producer goods is

(a)    Autonomous demand

(b)    Domestic demand

(c)    Induced demand

(d)    Replacement demand

(e)    Intermediate demand.

10.    A consumer who maximizes total utility will buy to that extent where

(a)    Marginal utility equals price

(b)    Marginal utility is greater than price

(c)    Marginal utility is less than price

(d)    Marginal utility of the good is zero

(e)    Price of the good is zero.

11.Indifference curve shows different combinations of two goods, each combination gives equal level of satisfaction to the consumer. A set of indifference curves is known as

(a)    Budget line

(b)    Preference map

(c)    Income consumption curve

(d)    Price consumption curve

(e)    Expansion path.

12.Which    of the following statements is/are not true about the indifference curve?

I.    For ordinary goods the indifference curve is L-shaped.

II.    For perfect complementary goods the indifference curve is a straight line sloping downward from left to right.

III.    For perfect substitute goods the indifference curve is downward sloping from left to right.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.

13.The    slope of an isoquant at any point is measured by the

(a)    Marginal rate of substitution

(b)    Marginal rate of technical substitution

(c)    Law of diminishing marginal utility

(d)    Law of demand

(e)    Law of negative returns to scale.

¹⁴.The    demand and supply functions for a product is as follows:

Qd = 12,000 - 6P Qs = 6,000 + 9P

The Government imposes a sales tax of Rs.40 per unit. The proportion of tax that is borne by the producer is

(a)    20%

(b)    40%

(c)    60%

(d)    80%

(e) 100%.

15.On a straight line demand curve, the current price is Rs.10 and quantity demanded is 20 units. If price elasticity of demand at the current price is 4, slope of the demand curve will be

(a)    0.125

(b)    0.250

(c)    0.325

(d)    0.224

(e)    8.000.

16.The demand schedule of products A and B are given below:

Product A		Product B
Price	Quantity Demanded	Price	Quantity Demanded
(Rs.)	(Units)	(Rs.)	(Units)
40	200	80	200
40	160	160	160

The absolute cross elasticity of demand for product A is

(a)    0.20

(b)    0.33

(c)    0.50

(d)    0.75

(2marks)

(e)    1.00.

¹⁷-A    firm supplied 4,000 pens at the rate of Rs.18 per pen to a store in a university in Mumbai. Next month due to a rise in the price of pen to Rs.24 per unit, the supply of the firm increases to 10,500 pens. The arc price elasticity of supply of pen is

(a)    0.25

(b)    3.14

(c)    5.68

(d)    6.98

(e)    4.88.

(2marks)

(2marks)

¹⁸-If    the demand function for a good is P = 50 - Q, over what range of price the demand is inelastic?

(a)    0 to 25

(b)    10 to 25

(c)    5 to 50

(d)    20 to 30

(e)    50 to 100.

¹⁹-A    consumer consumes two goods X and Y. The price of good X and Y are given as Rs.10 and Rs.40 respectively and the marginal utility for commodity X is given as 120 utils, marginal utility of commodity Y is

(a)    120 utils

(b)    240 utils

(c)    360 utils

(d)    480 utils

(e)    600 utils.

(2marks)

²⁰-The    total utility obtained from the consumption of ice cream for a consumer is given by the equation, TU = X¹⁵. How many units of ice cream the consumer consumes to maximize his utility if the price of ice cream is Rs.135 per unit?

(2marks)

(a)	8,100	units
(b)	4,500	units
(c)	6,585	units
(d)	1,230	units
(e)	5,000	units

²¹-A consumer consumes only two products, A and B. The utility function of the consumer is U = 20A^a5B'⁵

If the price of the good A is Rs.5 and the price of the good B is Rs.10 per unit, the optimum combination of the goods for the consumer is

(a)    2 units of good B for every unit of good A

(b)    2 units of good A for every unit of good B

(c)    4 units of good B for every unit of good A

(d)    4 units of good A for every unit of good B

(e)    8 units of good B for every unit of good A.

(2marks)

²²-A    consumer has a monthly budget of Rs.8,000. He spends all his income on two goods A and B. The prices of good A and B are Rs.4 and Rs.8 respectively. His marginal utility functions are given as follows:

6

mu_a= a 18

MU_b = B The consumer will consume

(a)    500 units of A and 750 units of B

(b)    250 units of A and 450 units of B

(c)    750 units of A and 600 units of B

(d)    600 units of A and 750 units of B

(e)    500 units of B and 750 units of A.

(2marks)

23-Which    of the following is defined as an activity that increases consumer usability of goods and services?

(a)    Demand

(b)    Supply

(c)    Consumption

(d)    Production

(e)    Cost.

(1 mark)

²⁴-Which    of the following is/are true about law of variable proportions?

I.    The state of technology is given.

II.    All factors are variable.

III.    This law is applicable when two factors of production are used in a fixed proportion.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.

(1 mark)

(1 mark)

(1 mark)

²⁵-If    the law of diminishing marginal product operates, the isoquant will be

(a)    A horizontal straight line

(b)    A vertical straight line

(c)    An upward rising curve

(d)    Convex to origin

(e)    Rectangular hyperbola.

²⁶-The    necessary condition for the maximization of output given the factor price is that

(a)    The isoquant must be a vertical straight line

(b)    The isoquant must be convex to origin

(c)    The isocost line must be tangent to one of the isoquant that is convex to origin

(d)    The isocost line must be tangent to one of the isoquant that is concave to origin

(e)    The isoquant must be a horizontal straight line.

27.Given the production function Q = 60K^a3L^a5 and input prices r = Rs.60 and w = Rs.40, the equation of the expansion path is

(a)    K =- L

2

2

(b)    K = -L

5

(c)    K =- L

5

(d)

(e)

K _ ⁴L 5

K _-L 5 .

28.The production function for a commodity is given as follows:

Q = 40K-⁵L-⁵

If the firm is currently using 36 units of capital and 100 units of labor, the level of output is

2,400 units

2,600 units

2.500    units 2,800 units

1.500    units.

(a)

(b)

(c)

(d) (e)

(1 mark)

29.When    a market is in equilibrium,

(a)    Marginal cost exceeds marginal utility for the good

(b)    Price tends to rise for the good

(c)    Price tends to fall for the good

(d)    Price neither tends to rise nor fall

(e)    Quantity demanded exceeds quantity supplied.

30.Refer    to the following diagram:

(1 mark)

In the short run, the firm will stop production when the price falls below

OA

OB

OC

OD

OE.

(a)

(b)

(c)

(d) (e)

(1 mark)

(2marks)

31.A    firm has the following short run function where the variable input is labor (L):

Q = 18L² - L³

A rational firm would employ labor between

(a)    9 < L < 12

(b)    8 < L < 10

(c)    4 < L < 19

(d)    15 < L < 20

(e)    19 < L < 25.

32.The    production function of Kalyan and co. is given as TP_L = 30L - 1.5L². The number of labor after which marginal production becomes negative is

8    units

9    units

10    units

11    units

12    units.

(a)

(b)

(c)

(d) (e)

33.The production function for a commodity is given as TP_L = 450L²- 30L³. The quantity of labor to be employed to maximize output is

(a)	10 units
(b)	20 units
(c)	30 units
(d)	40 units
(e)	45 units.
e Th. 34	shape of the average fixed cost curve is
(a)	A horizontal straight line
(b)	A vertical straight line
(c)	A downward sloping straight line from left to
(d)	Rectangular hyperbola
(e)	Concave to origin.

35.Technical    economies are considered as one of the important type of real economies. This technical economies are associated with

(1 mark)

I.    Specialization and indivisibility of capital.

II.    Set-up costs.

III.    Initial fixed costs.

IV.    Reserve capacity requirements.

(a)    Both (I) and (II) above

(b)    Both (II) and (III) above

(c)    Both (III) and (IV) above

(d)    Both (I) and (IV) above

(e)    All (I), (II), (III) and (IV) above.

(1 mark)

(1 mark)

36.When    marginal product is at its maximum, which of the following costs will be at its minimum?

(a)    Average cost

(b)    Average variable cost

(c)    Average fixed cost

(d)    Marginal cost

(e)    Total fixed cost.

³⁷-If the cost function for a commodity is given as TC = 150 + Q³ + 2Q² + 5Q, the marginal cost at 5 units of output is

(a)    Rs. 30

(b)    Rs. 50

(c)    Rs. 70

(d)    Rs. 80

(e)    Rs.100.

(1 mark)

38.The    total variable cost function for a commodity is given as follows:

TVC = 300Q - 40Q² + 4Q³

The level of output at which average variable cost will be minimum is

(a)    5 units

(b)    10 units

(c)    15 units

(d)    20 units

(e)    25 units.

(2marks)

39.The    cost function of firm is given as follows:

TC = 5,700 + 7Q

If the current market price of the good produced by the firm is Rs.10 per unit , the break even output of the firm is

(a)    1,700 units

(b)    1,900 units

(c)    2,100 units

(d)    2,300 units

(e)    2,500 units.

40.Cost    function of a firm is given as TC = 1,000 + 20Q - 0.5Q². If the current output is 100 units, average fixed cost is

(b)    Rs.40

(c)    Rs.60

(d)    Rs.20

(e)    Rs.80.    (1 mark)

41.The cost function of the firm is given as follows:

TC = 1,000 + 560Q + 32Q² - 4Q³

The level of output at which the firm will shut down its operation is

(a)    2 units

(b)    4 units

(c)    6 units

(d)    8 units

(e)    10 units.    (2marks)

⁴²    AC = + 20 + log + 50g²    , ,

If the average cost function of the firm is estimated to be    ^g     the fixed ^{cost of the firm is}

(a)    Rs. 250

(b)    Rs. 500

(c)    Rs.1,000

(d)    Rs.2,000

(e)    Rs.3,000.    (1 mark) 43.In a perfectly competitive market, the demand function of a firm is P = 60 - 6Q. If the average cost of

the firm is given as Rs. 12, at what level of output the firm will maximize profit?

(a)    4 units

(b)    6 units

(c)    8 units

(d)    10 units

(e)    12 units.    (2marks)

44.Which    of the following statements is not correct about Perfect Competition?

(a)    There is free flow of information

(b)    The individual buyer or seller is an insignificant player in the market

(c)    The technical characteristics of the products as well as services associated with the sales and delivery are identical

(d)    Free entry and exit of firms

(e)    The firm is a price maker.    (1 mark)

45.Which    of the following statements is/are true about perfect competition in the long run?

I.    A firm earns normal profit in the long run.

II.    The equilibrium level of output is the optimum level of output.

III.    There exists more than one equilibrium point.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.    (1 mark)

46.Which    of the following statements is/are true?

I.    If the industry is constant cost industry, the supply curve will be a horizontal straight line.

II.    If the industry is an increasing cost industry, the supply curve will be downward sloping curve.

III.    If the industry is a decreasing cost industry, the supply curve will be upward sloping curve.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.    (1 mark)

⁴⁷-Under perfect competition, the supply of an individual firm becomes zero, if the price is

(a)    Below the average variable cost

(b)    Above the average variable cost

(c)    Above the marginal cost

(d)    Equal to marginal cost

(e) Equal to average variable cost.

⁴⁸The total cost function of the firm is TC = 400 + 8Q + 4Q². The firm is a perfectly competitive firm and is selling its goods at Rs.24 per unit. At equilibrium the total cost of the firm is

(1 mark)

(a)    Rs.250

(b)    Rs.145

(c)    Rs.368

(d)    Rs.187

(e)    Rs.432.

(2marks)

⁴⁹.A firm functioning under monopolistic competition has the following total cost function TC = 250Q + 5Q². At 5 units of output, the marginal cost of the monopolistic competitive firm is

(a)    Rs.100

(b)    Rs.200

(c)    Rs.300

(d)    Rs.350

(e)    Rs.400.

(2marks)

50.In a perfectly competitive industry, the market demand and supply functions for a commodity are given as follows:

Qd = 27,000 - 20P Qs = 6,000 + 40P

An individual firm has the fixed cost of Rs.1,000. The average variable cost function is AVC = 350 -36Q + 2Q². The output at which the firm will maximize its profit is

(a)    10 units

(b)    12 units

(c)    14 units

(d)    16 units

(e)    18 units.

(2marks)

51.The    demand function for a commodity is estimated to be as

Q_d = 3,50,000 - 35P

The theoretical highest price that can prevail in the market is

(a)    Rs. 9,000

(b)    Rs. 10,000

(c)    Rs. 11,000

(d)    Rs. 12,000

(e)    Rs. 13,000.

(2marks)

52.Which    of the following statements is/are not true about monopoly?

I.    There is presence of close substitutes for the product.

II.    The monopolist can influence only the price of the product.

III.    The entry of other firms is allowed.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.

(1 mark)

53.Which    of the following reasons is not responsible for the creation of the monopoly market?

(a)    The existing firms do not have exclusive knowledge about the production techniques

(b)    Patent rights for a product or for a production process

(c)    Government licensing or the imposition of foreign trade barriers to exclude foreign competitors

(d)    The market cannot support more than one plant of optimal size

(e)    The existing firms adopt the limiting price policy.

⁵⁴.In which of the following situations price discrimination is possible?

I.    Discrimination owing to consumers peculiarities.

II.    Discrimination owing to the nature of the good.

III.    Discrimination owing to the distance and frontier barriers.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.    (1 mark)

55-which    of the following is true about monopoly?

(a)    Price = Marginal Revenue

(b)    Price > Marginal Revenue

(c)    Price < Marginal Revenue

(d)    Price > Marginal Revenue

(e)    Price < Marginal Revenue.    (1 mark)

⁵⁶-The    first order condition for profit maximization for a monopolist firm is

(a)    Marginal revenue > Marginal cost

(b)    Marginal revenue = Marginal cost

(c)    Marginal revenue < Marginal cost

(d)    Marginal revenue > Marginal cost

(e)    Marginal revenue < Marginal cost.    (1 mark)

⁵⁷-For    a monopoly firm, total revenue and total cost functions are given as follows:

q2

TR = 600Q - 2

TC = 1,000 + 120Q + 2Q² The profit maximizing price of the firm is

(a)    Rs.552

(b)    Rs.450

(c)    Rs.460

(d)    Rs.350

(e)    Rs.600.    (2marks)

⁵⁸-The    cost and demand functions of the monopolist are given as follows:

TC = 1,000 + 40Q² P = 800 - 40Q At profit maximizing output level, the total revenue of the firm is

(a)    Rs.3,000

(b)    Rs.4,000

(c)    Rs.5,000

(d)    Rs.6,000

(e)    Rs.7,000.    (2marks)

⁵⁹-The    cost and profit functions of XYZ Ltd., are given as follows:

TC = 400 + 20Q Profit = - 10Q² + 400Q - 400 If the firm is maximizing its profit, the level of output is

(a)    18 units

(b)    20 units

(c)    21 units

(d)    28 units

(e)    36 units.    (2marks)

60.The average cost function of a firm is given as follows:

AC = ⁸Q0+ 80 + 4Q

The total cost of the firm at 10 units of output is

(a) Rs.1,800

(b)    Rs.1,900

(c)    Rs.1,700

(d)    Rs.1,600

(e)    Rs.2,000.

61.Suppose at 9 units of output the price is Rs.25 per unit and at 10 units of output the price is Rs.24 per unit , the marginal revenue for the additional unit of the sale is

(a)    Rs.10

(b)    Rs.15

(c)    Rs.75

(d)    Rs.80

(e)    Rs.90.

(1 mark)

(1 mark)

(1 mark)

(1 mark)

62.Which    of the following features differentiates monopolistic competition from perfect competition?

(a)    Presence of large number of buyers and sellers

(b)    Free entry and free exit of the firms

(c)    The firms do not consider the reaction of the rival firm

(d)    They produce products which are close substitutes but not perfect substitutes

(e)    Perfect knowledge to the buyers about the market.

63.The    demand curve for a monopolistically competitive market is

(a)    A horizontal straight line

(b)    A vertical straight line

(c)    An upward rising curve

(d)    A downward sloping curve

(e)    Rectangular hyperbola.

64.In monopolistic competition, industry equilibrium is possible when for each firm

(a)    Average revenue equals average cost

(b)    Average revenue equals total cost

(c)    Average revenue equals average fixed cost

(d)    Average revenue equals average variable cost

(e)    Marginal revenue equals average cost.

^65.Which    of the following is/are true feature(s) of a cartel?

I.    It implies the direct agreement among competing oligopolist with aim of reducing uncertainty.

II.    The aim of cartel is to maximize the joint profit.

III.    Identical products are produced by the firms.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.

(1 mark)

_66.The    following is the sales data of various firms operating in an industry.

Firm	Sales (Rs. in crore)
I	3,000
II	2,200
III	1,570
IV	4,720
V	1,248
VI	1,008
VII	3,132
VIII	1,422

The 4-firm and 6-firm concentration ratios of the industry are respectively

(a)    0.66 and 0.74

(b)    0.71 and 0.88

(c)    0.78 and 0.83

(d)    0.64 and 0.81

(e)    0.59 and 0.74.

67.In the short run, a firm operating in a monopolistically competitive market has the following demand and cost functions:

P = 710 - 2.5Q TC = 710Q - 4Q² + 0.10Q³ At the profit maximizing level of output, the average cost of the firm is

(a)    Rs.220

(b)    Rs.440

(c)    Rs.680

(d)    Rs.740

(e)    Rs.880.

68. A monopolist is currently charging a price of Rs.12 for the product. If the Lerner index is 0.333, the marginal cost of the monopolist is

69.The following are the marginal productivity functions of labor and capital for a firm:

(a)	Rs.	2
(b)	Rs.	4
(c)	Rs.	6
(d)	Rs.	8
(e)	Rs.	10.
e Th. 9. 6	following

(2marks)

j 0.75    K⁰'⁷⁵

MP = 0.75- MR = 0.75-

^K K.²5 ^L L.²5

If the wage paid to the laborers is Rs.8 per unit and the cost of capital is Rs.5 per unit, the cost minimizing proportion of L to K is

⁽ 8 5 ⁽ 5 8

(a)

L =

K

(b)

L

(c)    L = (5 + 8) K

(d)    L = (5 - 8) K

(e)    L = (8 x 5) K.

70.If the concentration ratio of the four largest firms of an industry is 25%, 25%, 20%, 10%, the concentration ratio of the four-firm of the industry is

(a)    20%

(b)    40%

(c)    60%

(d)    80%

(e) 100%.

71.Rahul    Ltd., a monopolist, aims at profit maximization. The fixed cost of the firm is Rs.200 and its average variable cost is constant at Rs.30 per unit. Rahul Ltd., sells goods in Karnataka and Andhra Pradesh. The estimated demand functions for the goods in Karnataka and Andhra Pradesh are:

Pk = 40 - 2.5Qk P_A = 120 - 10Q_a where, P_K = Price charged by Rahul Ltd., in Karnataka

P_A = Price charged by Rahul Ltd., in Andhra Pradesh Q_K = Quantity of goods demanded in Karnataka

Q_A = Quantity of goods demanded in Andhra Pradesh

If price discrimination is not practiced, the output produced by the Rahul Ltd., to maximize sales revenue is

(a)    14 units

(b)    16 units

(c)    12 units

(d)    24 units

(e)    26 units.

72.A    survey by a market research firm estimated the supply schedule for toys as follows:

K

(2marks)

(2marks)

Price (Rs.)	Quantity supplied (Units)

100	25
200	50
300	75

The estimated supply function for toys is

(a)    Qs = 0.25P

(b)    Qs = 100 + 25P

(c)    Qs = 200 + 50P

(d)    Qs = 50 + 0.5P

(e)    Qs = 0.5 + 100P.

(1 mark)

END OF QUESTION PAPER

Suggested Answers Economics - I (MSF1A3)

Answer    Reason

1.    E Economics assume rationality on the part of its subjects like consumer, producer and

seller. Rationality implies acting objectively, keeping in view the ends and the means, the objectives and constraints. However following statements are correct regarding rationality on the part of consumer, seller and the investor.

I.    The rationality on the part of a firm is to maximize revenue.

II.    The rationality on the part of an investor is to maximize investment.

III.    The rationality on the part of the consumer is to maximize satisfaction.

Therefore option (e) is the correct answer.

2.    A A command economy is a method of determining what, how, when, where and for

whom goods and services are produced using a hierarchical organization.

Therefore option (a) is the correct answer.

3.    C According to this Veblen effect, the consumers buy more amount of a commodity

because they feel that there is an improvement in the quality of the commodity.

4.    E The elasticity of demand shows the degree of responsiveness of quantity demanded

due to change in price and if we measure the elasticity of demand for a commodity according to the point elasticity method then, the value elasticity decreases as we move along the demand curve. Therefore option (e) is the correct answer.

5.    D The demand for a commodity increases

a.    With the increase in income

b.    With the increase in wealth

c.    With an increase in the price of substitutes

d.    With a decrease in the price of complements

e.    Expectation of future increase in the price of the good.

Therefore option (d) is the correct answer.

6.    E Price of a commodity is measured in the Y axis and the quantity demanded is

measured on X axis, the middle point of a straight line demand curve represents unitary elastic demand. Therefore option (e) is the correct answer.

7.    B Elasticity of demand is the degree of responsiveness of quantity demanded due to

change in price and it is influenced by the marginal revenue of a commodity. If the elasticity of demand for a commodity is 1, then the marginal revenue for that commodity is zero. Therefore option (b) is the correct answer.

8.    E A decrease in the supply for a commodity is represented by the inward shift of the

supply curve. Therefore option (e) is the correct answer.

9.    C The demand for all producer goods is known as induced demand or derived demand.

Therefore option (c) is the correct answer.

10.    A A consumer who maximizes total utility will buy to that extent where marginal utility

equals price. Therefore option (a) is the correct answer.

11.    B An indifference map shows different combinations of two goods, each combination of

a particular curve giving same level of satisfaction to the consume. It is otherwise known as preference map. Therefore option (b) is the correct answer.

12.    D Following statements are true regarding indifference curve

I.    For ordinary goods the indifference curve is convex to origin

II.    For perfect complementary goods the indifference curve is L shaped

III.    For perfect substitute goods the indifference curve is a straight line sloping downward from left to right.

Therefore option (d) is the correct answer.

13.    B The slope of the isoquant is measured by the marginal rate of technical substitution.

Therefore option (b) is the correct answer.

Before the imposition of tax, the equilibrium price is determined at that point where Qd = Qs

12.000    - 6P = 6,000 + 9P

6.000    = 15P 6,000/15 = P

400 = P or P = Rs.400

When a sales tax of Rs.40 per unit is imposed = 6,000 + 9 (P - 40)

Qs

or

or

or

or

6,000 + 9 P - 360 = 5,640 + 9 P 5,640 + 9 P = 12,000 - 6P

15 P = 6,360 P = 424 Tax Imposed = Rs.40 Change in price = 424 - 400 = 24

x100 = 60%

Proportion of tax borne by customers = 40

Proportion of tax borne by producers = 40%.

Therefore option (b) is the correct answer.

dQ P dP I P

15.

A

e_p = dP Q ; dQ {Q

P = 10, Q = 20, e_p = 4

dP = (10

Slope of the demand curve, dQ [ 20 )/ = 0.125 Therefore option (a) is the correct answer.

% change in quantity demanded for Product A Cross elasticity of demand =    % change in price of Product B

16.

A

AQ_a P_b 160 - 200 80 -40 80 -3200

= x=-x-=-x-=-= - 0.20

AP_b Q_a 160 - 80 200 80 200 16000

So the absolute elasticity of demand is 0.20. Therefore option (a) is the correct answer.

The arc elasticity of supply is mathematically represented as follows

17.

B

Q, - Q, P, + P₂ Es = ² Q1 x-¹ 2

^Q1 ^+Q2 10,500 - 4,000

P -P ^P2 ^P1

44

10,500 + 4,000

24 -18

= 6500 x = 3.14

6 14,500

Therefore option (b) is t he correct answer.

For all straight line demand is elastic in the upper left portion than in the lower right portion. This is consequence of the arithmetic properties of the elasticity measure. The demand becomes inelastic once the elasticity is unitary elastic. The demand is unit elastic when MR = 0.

TR = 50Q - Q²

MR = 50 - 2Q

When MR = 0, 50-2Q = 0

Or, Q = 25

When Q = 25, P = 50 - 25 = Rs.25.

Thus, the range of prices where the demand is inelastic is zero to Rs.25. Therefore option (a) is the correct answer.

A consumer consumes two goods X and Y. If the price of good X and Y are given as Rs.10 and Rs.40 and the marginal utility for commodity X is given as 120 utils , the marginal utility of commodity Y can be determined as follows Px = Rs.10 Py =Rs.40 MUx =120 utils

As we know the consumer maximize his satisfaction at that point where

MU

P.

MU_y P_y

120 _10 MU_y 40

120 x 40 10

= 480 utils

Therefore the marginal utility of commodity Y is 480 utils. Therefore option (d) is the correct answer.

A rational consumer would consume up to the point where the Marginal utility = price Marginal utility is given by derivative of total utility i.e. X^1.5 Given 1.5X⁰⁵= 135 or X⁰⁵ = 90or X = 8,100 units

The rational consumer will consume 8,100 units of ice cream where he will maximize his satisfaction.

Therefore option (a) is the correct answer.

The utility function of the consumer is given as U

_: 20A'⁵B'⁵

= 10A-'⁵B'⁵

MU = 10A⁰⁵B^-05

PA = 5 P_B= Rs.10

The optimum combination of the commodity is purchased by the consumer at that point where

MU P

MU P

20.

A

A

21.

MU

10A^-a5B'⁵

10A'⁵B^-0'⁵

_5_

10

B5 _

A 10 2B = A

So the optimum combination purchased by the consumer is 2 units of good B for every unit of good A. Therefore option (a) is the correct answer.

22. A A consumer has a monthly budget of Rs.8, 000. He spends all his income on two goods A and B. The prices of good A and B are Rs.4 and Rs.8 respectively. His marginal utility functions are given as follows:

MU_a= 6/A

MU_b = 18/B

The consumer will consume at that point where

MU

A

B    B

6/A 4

MU

18/B 8

6 B 4 x = A 18 8

B

3A 2 2B = 3A

3A

2

P

A

Po

1

Since the consumer intends to spend Rs.8,000

8,000 = 4A + 8x= 4A + 12A =16A

2

8000

A =-= 500units

16

= 750units

3 x 500

2

So the consumer will consume 500 units of A and 750 units of B. Therefore optio0n

(a) is the correct answer.

23.    D Production is defined as an activity that increases consumer usability of goods and

services. Therefore option (d) is the correct answer.

24.    A Following assumptions are made about the law of variable proportion

I.    The state of technology is given.

II.    Only one or two factors are variable

III.    This law is not applicable when two factors of production are used in a fixed proportion.

Therefore option (a) is the correct answer.

25.    D Due to the operation of law of diminishing marginal productivity, the isoquant is

convex to origin. Therefore option (d) is the correct answer

26.    C The necessary condition for the maximization of output given the factor price is that

isocost line must be tangent to one of the isoquant that means the marginal productivities of the two commodities must be equal to their factor ratios. Therefore option (c) is the correct answer.

_ d60K⁰³L⁰⁵ " dK

d60K⁰'³L⁰'⁵

= 18K^-0'⁷L⁰'⁵

MPk =

= 30K⁰'³L^-0'⁵

MP,

w

r

The production function Q dQ dK

dQ ₌_

dL    dL

40

Factor Price ratio =

60

The expansion path of the equation MPl MP

30K⁰³L^-05

18K^-0'⁷L⁰'⁵

40

60

5 K

2

3 L 3 15K=6L

K= L

5

Therefore option (b) is the correct answer.

²⁸ A Q = 40K'⁵L'⁵ K = 36 units L = 100 units

Q = 40(36)⁰⁵ (100)⁰⁵ = 40 x 6 x 10 = 2,400 units

Therefore option (a) is the correct answer.

29.    D When a market is in equilibrium, price will neither tend to rise nor to fall because total

market demand is equal to total market supply for a good.

30.    D In the short run, the firm will stop production when the price falls below OD because

that is the short down point for the firm where price = AVC.

If the price falls below that the firm will shut down its production. Therefore option

(d) is the correct answer.

31.    A A rational firm will employ upto that point where

APl= MPl

AP_l = Q = 18L = 18L - L2

L

L

dQ

d18L² - L³

= 36L-3L²

MR =

dL dL By equating AP_Land MP_L , we will get

18L - L² = 36L-3L²

18L = 2L²

L = 9 units

Therefore the first stage will end at 9 units of output and at the end of the second stage of production

MP = 0

L=12units

Therefore the second stage of production function is over the range of labor input of

9 < L < 12

Therefore option (a) is the correct answer.

TP_l = 30L - 1.5L² MP_l = 30 - 3L

Marginal returns become negative, once MP_L equals zero. Thus,

30 - 3L = 0 Or, L = 10 units

As we know the total productivity of labor is maximum at that point where MP_l=0

A

33.

Now we can write that

TP_l = 450L² - 30L³

dTP, d(450L² - 30L³)    ₂

MP, =-- = -- = 900L - 90L²

^L dL    dL

Total productivity is maximum at that point where MP_L = 0

900L - 90L² = 0 L =10 units

Therefore option (a) is the correct answer.

The average fixed cost curve is rectangular hyperbola. Therefore option (d) is the correct answer.

34.

35.

D

E

The main technical economies are associated with

I.    Specialization and indivisibility of capital.

II.    Set-up costs.

III.    Initial fixed costs.

IV.    Reserve capacity requirements Therefore option (e) is the correct answer.

When MP is rising, MC is falling; when MP is diminishing, MC is rising. Marginal Cost (MC) will be minimum when Marginal Product (MP) is maximum. Therefore option (d) is the correct answer.

D

36.

37.

E

TC =150 + Q³ + 2Q² + 5Q

dTC _ d150 + Q³ + 2Q² + 5Q

, = 3Q²+ 4Q + 5

MC :

dQ

If Q = 5 units

MC = 3Q² + 4Q + 5 = 3(25) + 4x5 + 5 = 75 + 20 + 5 = Rs.100 Therefore option (e) is the correct answer.

TVC =300Q - 40Q² + 4Q³

dx

38.

A

300Q - 40Q² + 4Q³ Q

= 300 - 40Q + 4Q²

AVC =

dAVC _ d300 - 40Q+ 4Q²

= - 40 + 8Q = 0 dQ    dQ

- 40 + 8Q = 0

- 40 = -8Q

Q = 5 units

Therefore option (a) is the correct answer.

As we know at the break even point TR = TC

Here TC = 5,700 + 7Q

and the price is given as P = Rs.10

TR = 10Q

So at the break even point of the firm is TR - TC =0 10Q = 5,700 + 7Q or 3Q = 5,700 Q = 1,900 units

So the break even level of output is determined at 1,900 units of output .Therefore option (b) is the correct answer.

The total cost function of the firm is given as TC = 1,000 + 20Q - 0.5Q² Fixed cost =1,000

40.

A

Fixed cost 1,000

Average fixed cost =-=-= Rs. 10

Q 100

Therefore option (a) is the correct answer.

41.

B

TC = 1,000 + 560Q + 32Q² - 4Q³ = 560Q + 32Q² - 4Q³

AVC :

^Q

AVC = 560 + 32Q - 4Q²

In the short run the firm will shut down its production at the minimum level of average variable cost. Now we can write that

AVC is minimum at that point where

dAVC

= 0

dQ

d560 + 32Q - 4Q²

--- = 0

dQ

32 - 8Q = 0 32 = 8Q Q = 4 units

Therefore option (b) is the correct answer.

If the average cost function of the firm is estimated to be AC = 1,000/Q + 20 + 10Q + 50Q²

C

42.

TC = AC(Q) = Q(1,000/Q + 20 + 10Q + 50Q²) = 1,000 + 20Q + 10Q²+ 50Q³

Now the fixed cost of the firm will be Rs.1,000 which is independent of output. Therefore option (c) is the correct answer.

The firm will earn normal profit when MR = MC MR =P = 60 -6Q MC = dTC/dQ = Rs. 12

The firm will earn normal profit at the point where MR - MC = 0

60-6Q = 12 or 6Q = 48 or Q = 8units

Therefore option (C) is the correct answer.

44.    E Marginal revenue of the firm equals price as the firm is the price taker and the industry

is the price maker in case of perfect competition. Therefore option (e) is the correct answer.

45.    D Following statements are about the perfect competition in the long run

I.    A firm earns normal profit in the long run.

II.    The equilibrium output is known as optimum level of output.

III.    In the long run there is only one equilibrium point.

Therefore option (d) is the correct answer.

46.    A    Following statements are true.

I.    If the industry is a constant cost industry the supply curve will be a straight line.

II.    If the industry is an increasing cost industry, the supply curve will be an upward rising curve.

III.    If the industry is a decreasing cost industry, the supply curve will be a downward sloping curve.

Therefore option (a) is the correct answer.

47.    A In perfect competition the supply of an individual firm is equal to zero if the price is

below average variable cost. Therefore option (a) is the correct answer.

48.    E    The total cost function of the firm is TC = 400 + 8Q + 4Q². If the firm is a perfectly

competitive firm and is selling its goods at Rs.24. At equilibrium level in a perfectly competitive market, marginal revenue equals marginal cost.

MR = MC Here P = Rs.24 TR = PQ = 24Q TC = 400 + 8Q + 4Q² MR =Rs.24 MC = 8 + 8Q

So at the point of equilibrium 24 = 8+8Q 8Q =16 Q = 2 units

TC = 400 + 8Q + 4Q² = 400 + 8x2 + 4 (2)² = 400 +16 + 16= Rs.432 Therefore option (e) is the correct answer.

49.    C    TC = 250Q + 5Q²

MC = 250 + 10Q = 250 + 50

= Rs.300

Therefore the required the marginal cost is Rs.300.

50.    B The market demand function is given as

Qd = 27,000 - 20P Qs = 6,000 + 40P

Market will be in equilibrium at that point where Qd = Qs

27.000    - 20P = 6,000 + 40P

21.000    = 60P

P =21000/60 = Rs.350

Since the industry is operating under perfect competition all the firms are price takers Hence for each firm P = AR = MR Given the AVC function of the firm

AVC = 350 - 36Q + 2Q² VC = 350Q - 36Q² + 2Q³

MC = ^dVC

dQ

d(350Q - 36Q² + 2Q³) dQ

MC =

The firm will be in equilibrium at that point where 350 = 350 - 72Q + 6Q² 72 = 6Q Q = 12 units

Therefore at 12 units of output the firm will maximize his profit. Therefore option (b) is the correct answer.

51.    B The theoretical highest price that can prevail in the market is when the quantity

demanded is zero.

3.50.000    - 35 P = 0

3.50.000    = 35 P

3,50,000 P = 35 = Rs. 10,000.

52.    E Following statements are true about the monopoly market

I.    In monopoly there is no close substitute produced by the firm as single producer of the product

II.    The monopolist can influence both the price and quantity

III.    Since the firm is the single producer, the entry is totally restricted.

Therefore option (e) is the correct answer.

53.    A Following reasons are responsible for th creation of monopoly market

a.    Exclusive knowledge of the raw material.

b.    Patent rights for a product or for a production process.

c.    Government licensing or the imposition of foreign trade barriers to exclude foreign exchange.

d.    The market cannot support more than one plant of optimal size.

e.    The existing firms adopt the limiting price policy.

Therefore option (a) is the correct answer.

54.    E Price discrimination is possible under the following conditions

I.    Discriminating owing to consumers peculiarities.

II.    Discrimination owing to the nature of the good.

III.    Discrimination owing to the distance and frontier barriers.

Therefore option (e) is the correct answer.

55.    B In case of monopoly market price is greater than marginal revenue. Therefore option

(b) is the correct answer.

56.    B To maximize profit the first order condition requires that the MR should equal to MC.

A monopolist can maximize profits by equating MR with MC.

Therefore option (b) is the correct answer.

57.    A For a company total cost and total revenue functions are given as follows:

TR = 600Q - Q²/2 TC = 1,000 + 120Q + 2Q²

The profit maximizing price of the firm can be determined as follows Equilibrium price of the firm is determined at that point where

MR = MC MR = 600 - Q MC = 120 + 4Q

Equilibrium price of the firm is determined at that point where 600 - Q = 120 + 4Q or 480 = 5Q Q = 96 units

P = 600 - Q/2 = 600 - (96/2) = 600 - 48 = Rs.552.

Therefore the equilibrium price is Rs.552. So option (a) is the correct answer.

58.    A The cost and demand functions of the monopolist of the firm are given as follows:

TC = 1,000 + 40Q² P = 800 - 40Q

The profit maximizing output of the firm is determined at that point where MR = MC TC = 1,000 + 40Q² MC = 80Q P = 800 - 40Q

TR = P x Q = Q(800 - 40Q) = 800Q - 40Q² MR = 800 - 80Q

Now we can write that 80Q = 800 - 80Q 160Q = 800 Q = 5units P = 800 - 200 = 600 TR = PQ = Rs.3,000

Therefore option (a) is the correct answer.

59.    B Profit will be maximum when the first order derivative of profit function is equal to

zero.

3Q = -20Q + 400 = 0

Or, Q = 20 units.

60.    E AC = 800/Q + 80 + 4Q

TC = 800 + 80Q + 4Q² TVC = 80Q + 4Q² At output 10,

TC = 800 + 80(10) + 4(10)²

= 800 + 800 + 400 = Rs.2,000.

Therefore option (e) is the correct answer.

61.    B At 9 units of output the price is Rs.25 per unit. So the TR = PQ = 25 x 9 = 225

At 10 units of output the price is Rs.24 per units. So the TR = PQ = 24 x 10 = 240 The Marginal revenue of the additional unit of the sale, MR = TR_N -TR_N-1 = 240 -225 = Rs.15

Therefore option (b) is the correct answer.

62.    D In case of monopolistic competition, all the features are similar tot that of perfect

competition like presence of large number of buyers and sellers, free entry and free exit of firms, individual firm is the price taker but the industry is the price maker. A monopolist in case of a monopolistic competitive market produces the products which are close substitutes where as in case of [perfect competition, firms produce the

homogeneous products Therefore option (d) is the correct answer.

63.    D The demand curve for a monopolist firm is a downward sloping curve from left to

right.

Therefore option (d) is the correct answer.

64.    A In monopolistic competition, industry equilibrium is possible for each firm when

average revenue equals average cost. Therefore option (a) is the correct answer.

65.    E Cartel is a form of collusive oligopoly. Following are the true features of cartels.

I.    Cartels imply direct agreement among competing oligopolist with the aim of reducing uncertainty.

II.    The aim of cartel is the maximization of joint profit.

III.    Identical products are produced by the firms.

Therefore option (e) is the correct answer.

66.    B Total sales: 3,000 + 2,200 + 1,570 + 4,720 + 1,248 + 1,008 + 3,132 + 1,422 = 18,300

4-firm concentration ratio = (4,720 + 3,132 + 3,000 + 2,200) /18,300 = 13,052/18,300 =0.71

6-firm concentration ratio = (4,720 + 3,132 + 3,000 + 2,200 + 1,570 + 1,422)/18,300 = 16,044/18,300= 0.88.

67.    C A firm is operating in a monopolistically competitive market is followed by the

following demand and cost functions:

P = 710 - 2.5Q

TR = PQ = 710Q - 2.5Q²

TC =710Q - 4Q² + 0.10Q³

The profit maximizing level of output of the firm is determined at that point where MR = MC

710 - 5Q = 710 - 8Q + 0.30Q² 3Q = 0.3Q² 3Q = 0.3Q² Q = 10 units

AC = 710 - 4Q + 0.10Q² AC = 710 - 4(10) + 0.10 (10 )² AC = 710 - 40 +10 = Rs.680.

68.    D Learner Index of monopoly power is L = (P - MC) / P

0.33 = (12 - MC)/12

4 = 12 - MC MC = 12 - 4 = Rs.8.

69.    B Efficient allocation of L & K:

MP_L/w = MP_K/r

0.75K'⁷⁵/(L'²⁵ x 8) = 0.75L'⁷⁵/(K'²⁵ x 5)

5K = 8L Or, L = 5/8K.

Therefore option (b) is the correct answer.

70.    D The concentration ratio is the percentage of total industry sales made by the four

largest firms in the industry and the four firms concentration ratio = 25 + 25 + 20 +

10 = 80%.Therefore option (d) is the correct answer.

71.    A When price discrimination is not practiced by the monopolist, P_K = P_A.

Pk = 40 - 2.5Qk 2.5Qk = 40 - Pk

P_A = 120 - 10Q_a 10Q_a= 120 - P_A

Qa = ¹² - ⁰.^1PA

Total output sold by the monopolist = Q = Q_A + Q_K Thus, Q = 16 - 0.4P_k + 12 - 0.1P_A

Q = 28 - 0.5P

0.5P = 28 - Q P =56 -2Q TR = P x Q = Q(56- 2Q) = 56Q -2Q² Maximum TR: ^d TR/ ^d Q = 0

= ^d (56Q -2Q²)/ ^d Q = 56 - 4Q = 0 Or, Q =14 units

72. A The supply function can be represented by Q = a + bP : differentiating w.r.t P we get dQ/d P = b

When price changes from 100 -200,3P = 100 and dQ is 25 (from the question)

So b = 25/100= 0.25

When P is 100, Q is 25

So, we get 25 = a + (0.25 x 100)

Or a = 0

Therefore the supply function is Q = 0.25P.

Model Question Paper Economics - II (MSF1A4)

   Answer all 74 questions.

   Marks are indicated against each question.

Total Marks

1. Which of the following is true if the central bank of a country sells government securities in the open market?

(a)    LM curve shifts to left

(b)    LM curve shifts to right

(c)    IS curve shifts to left

(d)    IS curve shifts to right

(e)    Interest rates will fall.

(1 mark)

(1 mark)

(1 mark)

(1 mark)

² Which of the following is not an objective of macro economic policy?

(a)    Full utilization of human and non human resources

(b)    Maintenance of price stability

(c)    Maintenance of high living standard

(d)    Increasing economic inequality

(e)    Increasing the growth rate of the economy.

3.    Gross Domestic Saving is the difference between the

(a)    Net Domestic Product and Consumption

(b)    Gross Domestic Product and Aggregate consumption

(c)    Net National Product and Saving

(d)    Net National Product at factor cost and Saving

(e)    Gross National Product and Consumption.

4.    Which of the following is true with respect to Aggregate Supply (AS) curve in the classical model?

(a)    AS curve is positively sloped in the short run and it is vertical in the long run

(b)    AS curve is positively sloped both in the short run and in the long run

(c)    AS curve is positively sloped in the short run and negatively sloped in the long run

(d)    AS curve is vertical both in the short run and in the long run

(e)    AS curve is rectangular hyperbola in the long-run.

⁵    Which of the following constituents of Gross Domestic Capital Formation is/are known as the Gross Fixed Investment?

I.    Making good the depreciation on the existing fixed assets.

II.    Adding to the stock of fixed assets.

III.    Adding to the inventories.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.

(1 mark)

⁶    Income from domestic production accruing to the private sector is known as

(a)    GDP at factor cost

(b)    GNP at factor cost

(c)    NNP at factor cost

(d)    NDP at factor cost

(e)    NNP at market price.

⁷    Which of the following methods of the measurement of national income is/are used to estimate gross and net value added in the primary sectors like agriculture and allied activities?

I.    The output method.

II.    The income method.

III.    The expenditure method.

(a) Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.

⁸ Which of the following is/are the use(s) of National Income Statistics?

I.    As an instrument of economic planning and review.

II.    As a means of indicating changes in a countrys standard of living.

III.    As a means of comparing the economic performance of different countries.

(a)    Only (I) above

(b)    Only (II) above

(c)    Both (I) and (II) above

(d)    Both (II) and (III) above

(e)    All (I), (II) and (III) above.

(1 mark)

' In the consumption function, C = a + PY, a represents

(a)    Autonomous Consumption

(b)    Marginal Propensity to consume

(c)    Marginal Propensity to save

(d)    Average Propensity to consume

(e)    Average Propensity to save.

(1 mark)

(1 mark)

¹⁰'The    desired increase in government expenditure to attain full employment is

(a)    The output gap

(b)    The multiplier

(c)    The difference between the output gap and the multiplier

(d)    The sum of the output gap and the multiplier

(e)    The ratio of the output gap (at the equilibrium level) and the multiplier.

H'In an open economy, aggregate demand is the sum of consumption, investment, government expenditure and net export. An autonomous increase in the aggregate demand means

I.    Rise in the investment demand.

II.    An upward shift of the consumption function.

III.    A downward shift of the saving-supply function.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.

(1 mark)

(1 mark)

¹²'When the marginal propensity to consume increases, the marginal propensity to save

(a)    Decreases and multiplier will grow larger

(b)    Increases and multiplier will grow larger

(c)    Decreases and multiplier will become smaller

(d)    Increases and multiplier will become smaller

(e)    Decreases and multiplier will remain unchanged.

13'Which of the following is not one of the basic postulates of the Keynesian model?

(a)    Full employment occurs only by coincidence in an economy

(b)    Effective demand determines the level of employment and output

(c)    Since full employment is not always possible, Government intervention is essential

(d)    Budget deficit is a tool to fight recession

(e)    Monetary policy is more effective than fiscal policy.

¹⁴'A country may be able to correct its persistent balance of payments deficit by

(a)    Lowering the import barriers

(b)    Reducing its official reserves

(c)    Increasing the national income

(d)    Reducing the international value of its currency

(e) Reducing the money supply. lS-which of the following occurs during the phase of depression in the economy?

(1 mark)

(1 mark)

(1 mark)

(a) Output increases, employment decreases (b) Output decreases, employment increases (c) Output decreases, employment decreases (d) Output increases, employment increases (e) Output decreases, employment remain the constant. e th In 1 short run if all the available resources are fully utilized in the economy, aggregate supply curve (a) Is a horizontal straight line (b) Is vertical straight line (c) Is upward sloping from left to right (d) Is downward sloping from left to right (e) Is rectangular hyperbola.

17-Which of the following factor(s) influence the short run supply curve?

I. Changes in the cost of production. ii. Supply disturbances. III. Investment spending and technological changes (a) Only (I) above (b) Only (II) above (c) Both (I) and (II) above (d) Both (II) and (III) above (e) All (I), (II) and (III) above.

18-Which    of the following is a monetary liability for the Reserve Bank of India?

(a)    Paid-up capital

(b)    Statutory reserve

(c)    Contingency reserve

(d)    Government deposits

(e)    Notes in circulation.

(1 mark)

(1 mark)

¹⁹-The    RBI money together with government money constitutes the monetary base which is known as

(a)    Money supply

(b)    High powered money

(c)    Transactions demand for money

(d)    Speculative demand for money

(e)    Precautionary demand for money.

20-Which    of the following factors is/are responsible for an increase in the money supply?

I.    Increase in cash reserve ratio.

II.    Increase in currency deposit ratio.

III.    Increase in high powered money.

(a)    Only (I) above

(b)    Only (III) above

(c)    Both (I) and (II) above

(d)    Both (II) and (III) above

(e)    All (I), (II) and (III) above.

(1 mark)

²¹-Unemployment    in the Keynesian model is caused by the

(a)    Deficiency in aggregate demand

(b)    Deficiency in aggregate supply

(c)    Increase in the interest rate

(d)    Increase in the inflation rate

(e)    Increase in the money supply.

²²According to the Classical Model, a change in the money supply will affect

I.    The price level.

II.    The money wage.

(a)    Only (I) above

(b)    Only (III) above

(c)    Both (I) and (II) above

(d)    Both (II) and (III) above

(e)    All (I), (II) and (III) above.

23-Which    of the following statements is true about the Classical model of income determination?

(a)    The existence of the underemployment in the economy

(b)    The demand creates its own supply

(c)    The intervention of the Government is necessary in the economy

(d)    The model provided an adequate explanation of the cyclical phenomenon

(e)    Classical economists favored partial equilibrium analysis.

(1 mark)

²⁴-In    which of the following situation(s) money is neutral according to the Keynesian model of income determination?

I.    At the full employment level.

II.    Special case of liquidity trap.

III.    At some point of underemployment level.

(a)    Only (I) above

(b)    Only (III) above

(c)    Both (I) and (II) above

(d)    Both (II) and (III) above

(e)    All (I), (II) and (III) above.

(1 mark)

25-Which    of the following statements is not true?

(a)    According Keynes precautionary demand for money is directly related to income

(b)    Keynes explained the existence of the liquidity preference for money

(c)    Keynes formulated his theory of interest explicitly in flow terms

(d)    In Keynesian analysis both the accumulation of real capital and the accumulation of debt are excluded from the explicit consideration

(e)    Keynes rejection of neutrality of money is closely linked with his monetary theory of interest.

(1 mark)

26-Which    of the following statements is not true of the monetarist approach?

(a)    Monetary policy is more effective than the fiscal policy

(b)    Changes in money stock causes change in the output, employment and prices

(c)    Fiscal Policy unless supported by the changes in the money supply is ineffective

(d)    An increase in government spending must be financed by the tax decrease

(e)    If increase in government spending is financed by the increase in the high powered money, private spending is not crowded out and this results in high growth of output and employment.

(1 mark)

²⁷According to the Supply Side economists, which of the following is/are the positive measures to effect a lowering of cost?

(1 mark)

I. Reduction of the national insurance contribution II. Improving the supply and quality of labor. III. Providing advisory services. (a) Only (I) above (b) Only (III) above (c) Both (I) and (II) above (d) Both (II) and (III) above (e) All (I), (II) and (III) above.

28-Which    of the following statements is not true in the stage of boom of a business cycle?

(a)    Industrial production increases

(b)    Commodity prices increase

(c)    Cost of production increases rapidly but slower than the rise in prices of goods and services

(d)    The level of profit and investment is high

(e)    Inventory stock gradually increases.

²⁹-The    persistent rise in the general price level in an economy is referred as

(a)    Inflation

(b)    Deflation

(c)    Sterilization

(d)    Devaluation

(e)    Stagflation.

Which of the following real factors cause a shift in the aggregate demand curve?

I.    An increase in government expenditure with no change in the tax receipts.

II.    A decrease in the tax receipts with no change in government spending.

III.    A rightward shift in the consumption function.

IV.    A rightward shift of the investment or export function.

(a)    Both (I) and (III) above

(b)    Both (II) and (III) above

(c)    Both (II) and (IV) above

(d)    (I), (II) and (III) above

(e)    All (I), (II), (III) and (IV) above.

(1 mark)

31.

As there is no trade off between inflation and unemployment in the long run, the Philips curve is

(a)    A vertical straight line

(b)    A horizontal straight line

(c)    An upward rising curve

(d)    A downward sloping curve

(e)    Rectangular hyperbola.

(1 mark)

(1 mark)

(1 mark)

(1 mark)

³²-Which of the following is not a cause of international trade?

(a)    Unequal distribution of natural resources

(b)    Difference in technology

(c)    Different preferences

(d)    Cost advantages

(e)    Decrease in the rate of inflation.

^33.Terms of trade refers to

(a)    The difference between export price and import price

(b)    The sum of export price and import price

(c)    The multiplication of export price and import price

(d)    The ratio of export price to import price

(e)    The ratio of import price to export price.

³⁴-Which    of the following is primarily a macroeconomic issue?

(a)    The growth of aggregate output in the economy

(b)    A worker deciding how many hours to work at a given wage rate

(c)    The equilibrium price of apples

(d)    A firms decision as to whether to invest in new capital at a given interest rate

(e)    A consumers response to the change in price of a complimentary good.

³⁵-Which    of the following statements is/are correct?

I.    In case of progressive tax, greater the volume of income, larger will be the burden of tax.

II.    In case of regressive tax, the tax burden remains same irrespective of the level of income.

III.    In case of proportional tax, the greater the volume of income, lower will be the burden of tax.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.

³⁶-Which    of the following statements is not true?

(a)    Depreciation is the allowance given for using capital equipment

(b)    Net factor income from abroad refers to inflow of factor income from abroad minus the corresponding outflow

(c)    National product at factor cost is always higher than national product at market price

(d)    GDP at market price is the most comprehensive measure of aggregate income

(e)    Net exports are also known as balance of trade.    (1 mark)

³⁷-The nominal GDP grows faster than the real GDP because of

(a)    Indirect taxes

(b)    Subsidies

(c)    Depreciation

(d)    Inflation

(e)    Net exports.    (1 mark) ³⁸According to the Keynesian theory beyond full employment level of output,

(a)    The aggregate supply will increase with increase in aggregate demand and prices remain unchanged

(b)    The aggregate supply will decrease with increase in aggregate demand and prices remain unchanged

(c)    The aggregate supply will increase with increase in aggregate demand and prices also increase

(d)    The aggregate supply will decrease with increase in aggregate demand and prices increase

(e)    The aggregate supply will remain the same with increase in aggregate demand and prices

increase.    (1 mark)

³⁹-Which of the following is/are the assumption(s) of IS Curve?

I.    Investment equals savings at equilibrium.

II.    Investment increases with income.

III.    Saving is related to interest.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (III) above

(e)    All (I), (II) and (III) above.    (1 mark) ⁴⁰According to Keynesian theory, business investment will decline as a result of

(a)    A fall in the interest rate

(b)    A decrease in business taxes

(c)    A decline in business expectations

(d)    Decrease in depreciation

(e)    An increase in consumption expenditure.    (1 mark)

⁴¹-Which    of the following statements is true with regard to price indices?

(a)    GDP deflator measures the cost of buying a fixed basket of goods and services

(b)    Consumer Price Index (CPI) measures the prices of a larger basket of goods than the GDP deflator does

(c)    When automobile production in the economy is relatively large, automobiles receive a relatively larger weight in the computation of the GDP deflator

(d)    If prices of imports increase, the GDP deflator also increases

(e)    When automobile production in the economy is relatively large, automobiles receive a relatively

larger weight in the computation of the CPI.    (1 mark)

⁴²-The    quantity theory of money implies that a given percentage change in the money supply will cause

(a)    An equal percentage change in nominal GDP

(b)    A smaller percentage change in nominal GDP

(c)    A larger percentage change in nominal GDP

(d)    An equal percentage change in real GDP

(e)    A smaller percentage change in real GDP.    (1 mark)

⁴³-An    economy operating below full employment, a deficiency in demand will result in

(a)    Full employment

(b)    Fall in interest rates

(c)    Larger level of unemployment

(d)    Inflation

(e) Rise in real wages.

^44.If the marginal propensity to consume is zero, a decrease in investment would lead to

(1 mark)

(1 mark)

(a)    A decrease in the equilibrium level of income by the same amount

(b)    No change in the equilibrium level of income

(c)    An unending downward spiral in equilibrium level of income

(d)    An unending upward spiral in the equilibrium level of income

(e)    An increase in the equilibrium level of income by the same amount.

⁴⁵-Following information is given about a hypothetical economy for the year 2008:

Particulars	MUC
GNP at factor cost	7,500
NNP at market price	6,250
Indirect taxes	1,345
Subsidies	1,587

The depreciation value of the economy is

(a)    1,750 MUC

(b)    1,950 MUC

(c)    1,008 MUC

(d)    1,050 MUC

(e)    1,250 MUC.

(2marks)

^46.An economy consists of the three sectors: Primary, Secondary and Tertiary sectors. Transactions related to the three sectors are given below:

_(MUC)

Items Primary Sector Secondary Sector Tertiary Sector Sales 200 300 260 Closing stock 30 40 50 Intermediate consumption 30 50 30 Opening stock 20 20 30 Indirect taxes 24 26 34 Depreciation 20 24 30 Subsidies 14 16 14

The GDP at factor cost for the economy is

(a)    450 MUC

(b)    684 MUC

(c)    750 MUC

(d)    897 MUC

(e)    950 MUC.

(2marks)

^47.The following data is extracted from the National Income accounts of a country for the year 20072008:

Particulars	MUC
GNP at factor cost	3,545
Subsidies	1,242
NNP at market price	4,343
Depreciation	250
NDP at factor cost	150

The indirect taxes of the economy is

(a)    2,290 MUC

(b)    3,245 MUC

(c)    4,578 MUC

(d)    1,245 MUC

(e)    3,645 MUC.

⁴⁸-Following information is given about an economy:

Particulars	MUC
NNP at factor cost	5,445
Corporate tax	1,223
Retained Profit	1,145
Personal Income tax	1,321

The personal disposable income is

(a)    1,050 MUC

(b)    1,526 MUC

(c)    1,756 MUC

(d)    1,945 MUC

(e)    2,178 MUC.

(1 mark)

⁴⁹-The    net export function for the economy is estimated as E = 200 - 0.1Y. The marginal propensity to consume is 0.75 and the tax rate is 20%. Assuming that the investment is autonomous and increases by

1,462MUC during the year, the trade balance deteriorates by

(a)    146.2 MUC

(b)    292.4 MUC

(c)    300.0 MUC

(d)    450.0 MUC

(e)    525.0 MUC.

(2marks)

⁵⁰-The    consumption function for an economy is ascertained as follows:

C_t = 25 + 0.60 Yd + 0.20 C_t-1

Where C_t and C_t-1 denote consumption function in periods t and t-1 respectively and ^Yd is the disposable income in period t.

If ^Yd^t has been 250 MUC for a long time, compute the steady level of consumption in the economy

(a)    200.00 MUC

(b)    225.50 MUC

(c)    210.75 MUC

(d)    218.75 MUC

(e)    230.00 MUC.

(2marks)

⁵¹-The    following table shows the different level of consumption at different level of disposable income:

Disposable Income (Y)	Consumption (C)
800	320
1,200	420

The value of multiplier is

(a)    0.25

(b)    1.25

(c)    1.33

(d)    3.25

(e)    4.25.

(2marks)

⁵²-Given the saving function as S = -250 + 0.4Y, at what level of income, saving will be equal to investment if autonomous investment is 200 MUC.

(a)	1,125 MUC
(b)	1,250 MUC
(c)	1,345 MUC
(d)	1,457 MUC
(e)	1,546 MUC

"The consumption function for a is given as ^C = ¹⁸⁰ + P^Yd. If the level of disposable income is 1,000 MUC and consumption is 800 MUC, the marginal propensity to consume is

(b)	1.222
(c)	1.567
(d)	2.000
(e)	2.456.
54'The	following

Income elasticity of demand for real balances Acceptable inflation rate Money multiplier

3

6%

8

If the real GDP is desired to grow at 6%, what is the rate at which reserve money should grow?

(a)

(b)

(c)

(d) (e)

1%

2%

3%

4%

6%.

(2marks)

⁵⁵'In an economy, classical quantity theory of money holds and the velocity of money is constant at 5. Output is fixed at the full employment level of 10,000 MUC and the price level is 2. The real demand for money in the economy is

(a)

(b)

(c)

(d) (e)

2.000    MUC 1,250 MUC

1.500    MUC

2.500    MUC

3.000    MUC.

(1 mark)

In an economy, demand for money is L = 0.4Y - 100i and supply of money is 600 MUC. If the government intends to increase the equilibrium interest rate from the current level of 6% to 9%, what will be the change in the equilibrium level of income?

56.

(a)    750 MUC (increase)

(b)    750 MUC (decrease)

(c)    500 MUC (decrease)

(d)    500 MUC (increase)

(e)    No change in the equilibrium level of income.

(2marks)

57'

Following information is given about an economy:

Transaction and precautionary demand for money (Mt)	0.50Y
Speculative demand for money (Ms)	2,500 - 200i
Investment function (I)	400 - 20i
Supply of money (M)	1,000 MUC
Current equilibrium rate of interest	16%
Tax rate	40%

If the expansionary fiscal policy increase the equilibrium rate of interest to 32% and the IS function to

Y = 5,800 - 200i, what should be the money supply in the economy to avoid the crowding out?

(a)

(b)

(c)

(d) (e)

200 MUC 400 MUC 600 MUC 800 MUC 900 MUC.

⁵⁸'Consider an economy described by the following equations:

Government spending (G)

= 1,000 MUC = 1,000 MUC = 500 + 0.75Y

= 100 - 50i = 0.25Y

= 125 - 50i

= 500 MUC

Taxes (T)

Consumption (C)

d

Investment demand (I)

Transaction demand for money (M_t/P)

Speculative demand for money (M_a/P)

Money supply (M_s/P)

(a)	2,000 MUC
(b)	2,750 MUC
(c)	2,450 MUC
(d)	3,000 MUC
(e)	3,500 MUC

⁵⁹-Following information is given about an economy:

Goods market equilibrium	0.5Y = 2,925 - 37.5i
Money market equilibrium	0.25Y = 312.5 + 125i
Export	650 MUC
Import function	25 + 0.25Y

The trade balance at equilibrium in the economy is

(a)    452.25 MUC (deficit)

(b)    452.25 MUC (surplus)

(c)    687.50 MUC (deficit)

(d)    687.50 MUC (surplus)

(e)    900.45 MUC (deficit).

(2marks)

⁶⁰-Following information is given about an economy:

New issue ratio	0.128
Intermediation ratio	0.144
Financial Interrelation ratio	2.42
Net capital formation	10,000 MUC

The amount of secondary issues are

(2marks)

(a)	184.32 MUC
(b)	174.32 MUC
(c)	163.84 MUC
(d)	124.82 MUC
(e)	155.53 MUC

⁶¹-Following information is given about an economy:

Particulars	MUC
Consumption (C)	1,000
Investment (I)	300
Government Expenditure (G)	280
Export (X)	160
Import (M)	120
Money supply (Ms)	324

The velocity of money in the economy is

(a)    5

(b)    6

(c)    7

(d)    8

(2marks)

(e) 9.

⁶²-In    an economy the monetary liability of the Reserve Bank of India (RBI) is 20,000 MUC and the government money is 4,000 MUC. The currency deposit ratio is 0.66. The Central banks money supply target is 45,000 MUC. The reserve ratio that RBI must impose on banks to achieve the money supply is

(a)    0.015

(b)    0.225

(c)    0.325

(d)    0.457

(e)    0.625.

⁶³-The    monetary liabilities of the central bank of an economy are 20,000 MUC. The government money in

the economy is 200 MUC. Currency deposit ratio for the economy is estimated to be 0.2 and reserve ratio imposed by the central bank is 5 percent. If foreign exchange reserves of the country decline by

1,245 MUC, what would happen to the money supply?

(a)    Decline by 5,976 MUC

(b)    Increase by 5,976 MUC

(c)    Decline by 1,245 MUC

(d)    Increase by 1,245 MUC

(e)    Decline by 1,480 MUC.

(2marks)

⁶⁴-The following information is extracted from the Union budget for the year 2008-09:

Particulars	Rs. in crore
Tax revenue (Net) Non-tax revenue Recoveries of loans Borrowings and other liabilities Non-plan expenditure: On revenue account (which includes interest payments of Rs.3,36,900 crore) On capital account Plan expenditure: On revenue account On capital account	3,89,093 2,06,142 45,492 3,48,942 7,51,023 74,346 1,80,670 1,04,625

The revenue deficit of the government is

(a)    Rs.3,09,024 crore

(b)    Rs. 66,492 crore

(c)    Rs.3,87,397 crore

(d)    Rs.3,36,458 crore

(e)    Rs.4,15,429 crore.

(2marks)

⁶⁵-Following information is given about an economy:

Particulars	MUC
Credit to banks Government deposits Credit to government Other non monetary liabilities Foreign exchange assets Credit to the commercial sector Net worth Other assets Government Money	60,000 2,000 8,000 810 1,400 15.000 70.000 8,000 10

The currency deposit ratio is 0.4 and the Central bank has imposed a reserve ratio of 10%, the value of money supply in the economy is

(a)    24,580 MUC

(b)    34,680 MUC

(c)    44,780 MUC

(d)    54,880 MUC

(e)    54,980 MUC.

⁶⁶-Following information is given about an economy:

Particulars	MUC
External assistance to the country	72
External assistance by the country	164
Transfers (Credit)	340
Transfers (Debit)	496
Merchandise Exports	69,908
Merchandise Imports	73,968

The overall trade balance is

(a)    1,010 MUC (Deficit)

(b)    3,060 MUC (Surplus)

(c)    3,060 MUC (Deficit)

(d)    4,060 MUC (Surplus)

(e)    4,060 MUC (Deficit).

⁶⁷-Following information is given about an economy:

Particulars	MUC
Agricultural Exports	2,000
Aircraft Exports	900
Automobile Imports	2,100
Dividend paid to the foreign Investors	200
Donations received from abroad	550
Direct Investment abroad	244
Long-term loans and investment abroad	1,800
Foreign Direct Investment	200

The Current Account balance is

(a)    494 MUC

(b)    - 494 MUC

(c)    594 MUC

(d)    - 694 MUC

(e)    694 MUC.

(2marks)

⁶⁸-The    capital inflows and capital outflows in an economy during the year 2008 are

12,600 MUC and 9,000 MUC respectively. During the same period, Foreign Direct Investment is 1,000 MUC. Suppose there is no change in the official foreign exchange reserve assets held by the Central Bank , the current account balance for the economy is

(a)    3,600 MUC

(b)    4,600 MUC

(c)    5,600 MUC

(d)    6,600 MUC

(e)    7,600 MUC.

(1 mark)

⁶⁹-The    following data pertains to a hypothetical economy:

Year	Nominal GNP	GNP deflator
2006-07	1,250	62.5
2007-08	1,650	75.0

What is the rate of inflation in the economy for the year 2007-08?

(a)    10.0%

(b)    12.5%

(c)    20.0%

(d)    5.5%

(e)    16.7%.

(2marks)

⁷⁰-The following balances are taken from the balance sheet of the Central Bank of an economy:

Particulars	MUC
Loans given to the Government	1,200
Reserves maintained by the banks	300
Net worth	80
Loans to the commercial banks	800
Government deposits	200
Other assets	60
Other deposits with the central bank	10
Net foreign exchange assets	1,500
Loans to the commercial sector	20

If the government money is 300 MUC, high-powered money in the economy is

3,100 MUC 3,250 MUC 3,300 MUC 3,400 MUC 3,600 MUC.

(a)

(b)

(c)

(d) (e)

^71.The following data is given for an economy:

Total Reserves with the central Bank    Rs.10,000 Cr.

Volume of demand deposits    Rs.30,000 Cr.

If the volume of reserves is decreased by Rs.5,000 Cr. and the volume of demand deposits increased by Rs.6,000 Cr., the new reserve ratio will be

0.010

0.025

0.298

0.139

7.200.

(a)

(b)

(c)

(d) (e)

(2marks)

^72.In a hypothetical economy, population is expected to grow at 2.5% p.a. Planners fix a target of per capita GDP growth of 5.5% p.a. If the capital output ratio is 5:1 assuming no depreciation, what should be the rate of investment as a percentage of GDP?

10.0%

15.0%

20.0%

40.0%

100.0%.

(a)

(b)

(c)

(d) (e)

(2marks)

^73.The consumption schedule for a two sector economy is given below:

Consumption (C) (MUC)	Disposable Income (Yd) (MUC)
475.0	500
400.0	400

If savings in the economy is 100 MUC, the equilibrium income in the economy is

(a)	200 MUC
(b)	400 MUC
(c)	600 MUC
(d)	800 MUC
(e)	900 MUC.
Refer	to the graph below:

(2marks)

1,250 4,000 Disposable income, Yd

The level of autonomous consumption in the economy is

5.000    MUC

1.000    MUC

2.000    MUC

3.000    MUC

4.000    MUC.

(a)

(b)

(c)

(d) (e)

END OF QUESTION PAPER

Suggested Answers Economics - II (MSF1A4)

1' A If the central bank of a country sells government securities in the open market the money supply decreases and hence, the LM curve shift to left.

2' D Following are the goals of macro economic policy.

a.    Full utilization of human and non human resources

b.    Maintenance of price stability

c.    Maintenance of high living standard

d.    Reduction of economic inequality and removal of poverty

e.    Increasing the growth rate of the economy.

3' B Gross domestic saving is the difference between gross domestic product and aggregate consumption. Therefore option (b) is the correct answer.

4' A The aggregate supply explains the production behavior of an economy. If the actual price achieved is more than the expected price, firms will experience a higher than anticipated level of profits. This will lead to increase in production. Thats why the short run aggregate supply curve slopes upward. But in the long run, the difference between expected and actual price levels is negligible. In the long run, the output of an economy doesnt depend on the price level, but on factors such as labor import costs, capital stock, technological progress, etc. So aggregate supply curve of an economy in long run is vertical.

(a)    Is the answer because aggregate supply curve is positively sloped in the short run and vertical in the long run.

(b)    Is not the answer because aggregate supply curve is not positively sloped in the short run as well as in the long run.

(c)    Is not the answer because aggregate supply curve is not positively sloped in the short run as well as in the long run.

(d)    Is not the answer because aggregate supply curve is not vertical in the short run and it is vertical in the long run.

(e)    Is not the answer because in the long run, output of an economy doesnt depend on the price level, but on factors such as labor import costs, capital stock, technological progress, etc.

5' D Following are the constituents of the Gross Domestic Capital Formation

I.    Making good the depreciation on the existing fixed assets

II.    Adding to the stock of fixed assets

III.    Adding to the inventories.

First two of the above three are known as the Gross Fixed Investment.

Therefore option (d) is the correct answer.

6' D Income from domestic production accruing to the private sector is known as NDP at factor cost. Therefore option (d) is the correct answer.

7' A The output method for the measurement of national income used to estimate gross and net value added in the primary sectors like agriculture and allied activities. Therefore option (a) is the correct answer.

8' E Following are the uses of national income statistics

I.    As an instrument of economic planning and review.

II.    As a means of indicating changes in a countrys standard of living.

III.    As a means of comparing the economic performance of different countries. Therefore option (e) is the correct answer.

9' A Consumption function shows the functional relationship between income and consumption. C = a + PY

Here

a = Autonomous Consumption P = Marginal Propensity to consume Y = Level of income

Therefore option (a) is the correct answer.

10.    E The desired increase in government expenditure to attain full employment is the ratio

of the output gap and the multiplier. Therefore option (e) is the correct answer.

11.    E An autonomous increase in the aggregate demand means

I.    Rise in the investment demand

II.    An upward shift of the consumption function.

III.    A downward shift of the saving and supply function.

Therefore option (e) is the correct answer.

12.    A When the marginal propensity to consume increases, the marginal propensity to save

decreases and multiplier will grow larger

13.    E (a) Is not the answer because Keynes considered the existence of full employment as

a special case. The Keynesian underemployment equilibrium is reflecting real life situations.

(b)    Is not the answer because aggregate demand or effective demand indicates the total quantity of goods and services that people want to buy. According to Keynes, effective aggregate demand determines the level of employment and output.

(c)    Is not the answer because Keynes argues that State intervention is essential as full employment is not possible in an economy.

(d)    Is not the answer because Keynes argues that an economy facing recession, budget deficit is an important tool to overcome recession.

(e)    Is the answer because in the Keynesian model, monetary policy is not effective as compared to fiscal policy. Rather it is the fiscal policy, which is very effective and powerful. Keynes argues that government should maintain an active stance with a combination of tax and expenditure policies to maintain the desired levels of output and employment through manipulation of effective demand.

14.    D A country may be able to correct its persistent balance of payments deficit by reducing

the international value of its currency.

15.    C During the period of depression in the economy, output decreases and employment

decreases.

16.    B In the short run when all the available resources of the economy are fully utilized the

aggregate supply curve will be a vertical straight line. Therefore option b is the correct answer.

17.    E Following factors influence the aggregate supply in the short run

I.    Changes in the cost of production.

II.    Supply disturbances.

III.    Investment spending and technological changes.

Therefore option (e) is the correct answer.

18.    E Notes in circulation is a monetary liability whereas others are non monetary liabilities

Therefore option (e) is the correct answer.

19.    B The RBI money together with government constitutes the monetary base which is

known as high powered money. Therefore option (b) is the correct answer.

20.    B Money supply will increase when

I.    Decrease in cash reserve ratio

II.    Decrease in currency deposit ratio.

III.    Increase in high powered money

In the given cases the money supply will increase in case of the increase in the high powered money or decrease in the currency deposit ratio Therefore option c is the correct answer.

21.    A Unemployment in the Keynesian model is caused by the deficiency in the aggregate

demand. Therefore option (a) is the correct answer.

22.    C According tot the classical model, changes in the aggregate supply will affect only the

price level and the money wage. Therefore option (c) is the correct answer.

23.    E Following statements are true about the classical model

a.    The existence of the full employment in the economy

b.    The supply creates its own demand

c.    The intervention of the Government is not necessary for the existence of the economy

d.    The model does not provided an adequate explanation of the cyclical phenomenon

e.    Classical economists favored partial equilibrium analysis Therefore option (e) is the correct answer.

24.    C In the situation of full employment money is neutral in the following cases

I.    At the situation of full employment.

II.    Special case of liquidity trap.

Therefore option (c) is the correct answer.

25.    C Following statements are true about the Keynesian model

a.    Keynes separated the demand for money into transaction and precautionary demand for money

b.    Keynes explained the existence the liquidity preference for money

c.    Keynes formulated his theory of interest explicitly in stock terms

d.    In Keynesian analysis both the accumulation of real capital and the accumulation of debt are excluded from the explicit consideration

e.    Keynes rejection of neutrality of money is c loosely linked with his monetary theory of interest.

Therefore option (c) is the correct answer.

According to the monetarist approach the increase in the government spending must be accompanied by the increase in the tax rate. Therefore option (d) is the correct answer.

26.

D

According to the supply side economists, following are the the positive measures to effect a lowering of costs include

27.

E

I.    Reduction of the national insurance contribution

II.    Improving the supply and quality of labor

III.    Providing and advisory services.

Therefore option (e) is the correct answer.

28.    E In the stage of boom the inventory stock gradually decreases. Therefore option (e) is

the correct answer.

29.    A The inflation caused by the shift in the aggregate supply curve is Cost push inflation.

Therefore option (a) is the correct answer.

30.    E Following real factors cause a shift in the aggregate demand curve

I.    Increase in government expenditure with no change in the tax receipts.

II.    A decrease in the tax receipts with no change in government spending.

III.    A rightward shift in the consumption function.

IV.    A rightward shift of the investment or export function.

31.    A As there is no trade off between inflation and unemployment in the long run, therefore

the long run Philips curve is vertical. Therefore option (a) is the correct answer.

32.    E Decrease in the price level is not a cause of international trade. And all others are the

reasons responsible for international trade. Therefore option (e) is the correct answer.

33.    D Terms of trade refers to the ratio of export price to import price and it depends upon on

the price ratio at which the countries exchange products. Therefore option (d) is the correct answer.

34.    A The growth of total output in the economy is primarily a macroeconomic issue. Total

output is the aggregate output in the economy.

35.    A I. Progressive tax is that tax where the burden of tax increases with the increase in

income.

II.    Regressive tax is that tax where the burden of tax decreases with the increase in income

III.    Proportional tax is that tax where the burden of tax remains the same what ever the level of income

Therefore option (a) is the correct answer.

36.    C National product at market price is always higher than national product at factor cost

because the amount of indirect taxes which increases the prices is always greater than the subsidies which lower the price.

37.    D Real GDP is a measure of the value of all goods and services produced in a country

during a period of time, corrected for inflation. Thus the extent of difference between nominal GDP and real GDP shows the rate of inflation.

38.    C According to the Keynesian theory beyond full employment level of output, the

aggregate supply will increase with increase in aggregate demand and prices also increase.

39.    E IS curve is based on the assumptions that

   Investment equals savings at equilibrium

   Investment increases with income

   Saving is related to interest

40.    C According to Keynesian theory, business investment will decline as a result of a

decline in business expectations

41.    C It is Consumer Price Index (CPI) that measures the cost of buying a fixed basket of

goods and services, but not the GDP deflator. GDP deflator considers much wider group of goods, all final goods and services produced during the year, than WPI and CPI. The basket of goods included in the GDP deflator varies from year to year, depending on what is produced in the economy during the year.

a.    (a) is not correct. GDP deflator measures changes in the price levels of a basket of goods that varies from year to year depending on the goods and services produced during the year.

b.    The basket of goods of the GDP deflator includes all final goods and services produced during the year irrespective of their nature (i.e. consumer or producer goods), and hence is broader than WPI and CPI.

c.    The basket of goods included in the GDP deflator changes every year depending on what is produced in the economy in that year. Thus, when automobile production is large, it receives a relatively larger weight in the computation of GDP deflator.

d.    GDP deflator includes only prices of goods and services that are produced within the boundaries of a country. Hence prices of imports do not affect the GDP deflator.

e.    CPI measures only the cost of buying a fixed basket of goods and services, hence increase in automobile production does not affect computation of the CPI.

42.    A Quantity theory of money (QTM) says

MV = PY Where,

M = money supply

V    = velocity of money P = price level

Y    = real GDP

PY = nominal GDP

Assuming V is a constant, a change in M leads to an equal percentage change in PY.

Is the answer because the quantity theory of money implies that a given percentage change in the money supply will cause an equal percentage change in nominal GDP

Is not the answer because the quantity theory of money implies that a given percentage change in the money supply will not cause a smaller percentage change in nominal GDP

(b)

(c)

Is not the answer because the quantity theory of money implies that a given percentage change in the money supply will not cause a larger percentage change in nominal GDP

Is not the answer because the quantity theory of money implies that a given percentage change in the money supply will not cause an equal percentage change in real GDP

(d)

Is not the answer because the quantity theory of money implies that a given percentage change in the money supply will not cause a smaller percentage change in real GDP.

(e)

An economy with less than full employment level will lead to further unemployment, if the level of aggregate demand is not equal to aggregate supply. Hence the correct answer is C.

43.

C

Is not the answer because in an economy operating below full employment, a deficiency in demand will not result in full employment

(a)

(b)

(c)

(d) (e)

Is not the answer because in an economy operating below full employment, a deficiency in demand will not result in fall in interest rates

Is the answer because in an economy operating below full employment, a deficiency in demand will result in larger level of unemployment

Is not the answer because in an economy operating below full employment, a deficiency in demand will not result in inflation

Is not the answer because in an economy operating below full employment, a deficiency in demand will not result in rise in real wages

When MPC = 0

44.

A

1

= 1

Multiplier = 1 - 0 . Therefore, the equilibrium income would also decrease by the same amount as decrease in investment.

Depreciation = GNP at market price - NNP at market price

45.

C

GNP at market price = GNP at factor cost + Indirect taxes - Subsidies

GNP at market price = 7,500 + 1,345 - 1,587 = 7,258

Depreciation = GNP at market price - NNP at market price = 7,258 - 6,250 =1,008 MUC

Therefore option (c) is the correct answer.

Value added by the factors of production = Sales - Intermediate Consumption - Indirect taxes + Subsidies Value added by the primary sector = 200 - 30 -24 + 14 =160 Value added by the secondary sector = 300 - 50 - 26 +16 =240 Value added by the tertiary sector = 260 -30 -34+14 = 210

46.

B

NDP at factor cost = Sum of value added by the primary sector, secondary sector and the tertiary sector

= 160 + 240 + 210 = 610

Depreciation    = 20+24+30 = 74

GDP at factor cost = 610+74 = 684 MUC

The GDP at factor cost is 684 MUC. Therefore option (b) is the correct answer.

GNP at market price = GNP at factor cost + Indirect taxes - Subsidies GNP at market price = NNP at market price + Depreciation = 4,343 +250 = 4,593

4,593 = 3,545 + Indirect taxes - 1,242 Indirect taxes = 4,593+1,242-3,545 = 2,290 MUC Therefore option (a) is the correct answer.

Personal disposable income = NNP at factor cost - Corporate tax- Retained Profit -Personal Income tax = 5,445-1,223 -1,145 -1,321 =1,756 MUC

The personal disposable income is 1,756 MUC. Therefore option (c) is the correct answer.

49.

B

Multiplier = 1/(1 - MPC + MPC x t + MPI) = 1/(1 - 0.75+ 0.75 x 0.2+0.10) = 1/ 0.50=

2

Thus if investment increases by 1,462MUC, income increases by 2,924MUC. Thus, change in trade balance = - 0.1 x 2924= (292.4).

The consumption function for an economy is ascertained as:

50.

D

C_t = 25 + 0.60 Yd + 0.2 C_t-1

C_t = Consumption function in period t

: Consumption function in period t-1

C

t-1

^Yd^t = disposable income = 250 MUC At steady state level, C_t = C_t-1

.-.C_t = 25 + 0.60 Yd + 0.2C_t

C_t - 0.2C_t = 25 + 0.60 Yd

1

[25 + 0.6Yd]

C

0.80

1

[25 + (0.6 x 250)]

C

= 0.80 = 218.75 MUC MPC = AC/AY= 100/400= 0.25 Multiplier = 1/0.75 = 1.33

51.

52.

C

A

A

Saving is equal to investment at equilibrium. Therefore

S = -250 + 0.4Y = 200

0.4Y = 450

Y = 1,125 MUC.

Therefore option (a) is the correct answer.

53.

54.

C =180 + pY_d

800 = 180 + P1000 1000 p = 620

P = 620 / 1000 = 0.62

Rate of growth of money stock (gM) = a.gY + gP Where, a = income elasticity of demand for real balances gY = expected rate of growth in real GDP gP = acceptable rate of inflation Thus, gM = (3 x 6) + 6= 24%

C

Given money multiplier is 8,

Rate of growth of reserve money = 24 / 8 = 3.0%.

We have MV = PY or M = PY / V = 2x 10,000 / 5 = 4,000 MUC.

The real demand for money = Nominal demand / Price level = 4,000 / 2 = 2,000 MUC. 56' A L = 0.4Y - 100i

At equilibrium, demand for money = Supply of money

i.e. 0.4Y - 100i = 600

When, i = 6, 0.4Y - 100(6) = 600

Or, 0.4Y = 1200

Or, Y = 3000

When i = 9 , 0.4Y-100 (9) = 600 Or, 0.4Y = 1500 Or, Y = 3750

Change in the equilibrium level of income = 3750 - 3000= 750 MUC (increase).

57' C There will not be any crowding out if i = 16%

This can happen only when the IS function shifts to the left substituting i = 16% becomes

Y    = 5,800 - 200 (16) = 2,600

Total money demand f unction = (Mt/p) +(Ms/p) = 0.50Y+ 2,500 - 200i

Substituting Y =2600 and i =16%the total demand for money function becomes

0.50(2,600 ) + 2,500 - 200(16) =1,300 + 2,500 -3,200 = 600MUC

To avoid the crowding out the money supply is 600 MUC. Therefore option (c) is the correct answer.

58' C Goods market will be in equilibrium when Y = AD = C + I + G

Y    = 500 + 0.75(Y - T) + 100 - 50i + 1000

= 1600 + 0.75(Y - 1000) - 50i

Y    = 850 + 0.75Y - 50i

0.25Y = 850 - 50i    .....IS curve

Money market will be in equilibrium when:

Money supply (M_s) = Money demand (M_d)

500 = 0.25Y + 125 - 50i 375 = 0.25Y - 50i

0.25Y = 375 + 50i    .....LM curve

Thus, at simultaneous equilibrium,

850 - 50i = 375 + 50i 475 = 100i i = 4.75

When i = 4.75, 0.25Y = 375 + 50 (4.75) = 612.5 Or, Y = 612.5/0.25 = 2450 MUC.

59' C Goods market equilibrium 0.5Y = 2,925 - 37.5i

Y    = 5,850 - 75i

Money market equilibrium 0.25Y = 312.5 + 125i

Y    =1,250 + 500i

At simultaneous equilibrium of goods and money market 5,850 - 75i = 1,250 + 500i or 575i = 4,600 or, i =8%

Y    = 5850 -8(75) = 5,850 - 600 = 5,250

Trade balance equilibrium at equilibrium = E - M

= 650 - (25 + 0.25Y) = 650 - 25 - 0.25(5250)

= 650 - 25 - 1312.50 = - 687.5MUC

So there is deficit of 687.5 MUC. Therefore option (c) is the correct answer.

Primary issues = New issue ratio x Net capital formation = 0.128x 10,000 = 1,280 MUC

Secondary issues = Intermediation ratio x Primary issues = 0.144 x 1,280 = 184.32 MUC

Therefore option (a) is the correct answer.

The velocity of money supply = Y/Ms

61. A

62. B

Y    = C + I + G + X - M

Y    = 1,000 + 300 + 280 + 160 -120 = 1,620 Velocity of Money = 1,620/324 = 5 Therefore option (a) is the correct answer.

High powered money (H) = Monetary liability of the Central bank + Government money = 20,000 + 4,000 = 24,000 Currency deposit ratio = 0.66 Money supply (M) = 45,000

45,000(0.66+r)=24,000(1+0.66) 45,000r + 29,700=39,840 45,000r = 39,840 - 29,700 =10,140

Therefore the cash reserve ratio is 0.225.

Ms = High-powered money x {(1 + Cu)/(Cu + r)}; where High powered money = monetary liabilities of the central bank + government money.

63. A

AMs = AH. m

m= (1+Cu) /( Cu + r)

= (1+0.2)/ (0.2+0.05)

= 4.8

When foreign exchange reserves of the country decline by 1,245MUC, the monetary liabilities also fall by 1,245MUC Thus, money supply decline by 4.8 x 1,245MUC = 5,976 MUC

Revenue deficit = Revenue expenditure - Revenue receipts

64. D

Revenue expenditure = Non-plan revenue expenditure + Plan revenue expenditure

= 7,51,023 + 1,80,670= 9,31,693

Revenue receipts = Tax revenue + Non-tax revenue

= 3,89,093 + 2,06,142 = 5,95,235

Revenue deficit = 9,31,693 - 5,95,235 = Rs.3,36,458crore Money supply in the economy

M = H

H =High powered money

r = Reserve ratio

Cu = Currency deposit ratio

H = Monetary liabilities of the RBI + Government money

Monetary liabilities of the RBI = Financial assets of the RBI + Other assets of RBI -Non monetary liabilities of RBI

FA(RBI) = 60,000 + 8,000 + 1,400 + 15,000 = 84,400

OA (RBI) = 8,000

NML (RBI) = 2,000 + 810 + 70,000 = 72,810 Thus

ML(RBI) = 84,400 + 8,000 - 72,810 = 19590 Hence, H = 19,590 + 10 = 19,600

f1

Money multiplier = c+r)

(1 + 0.4) / (0.4 + 0.1) = 2.8 M = 19,600 x 2.8 = 54,880 MUC Therefore option (d) is the correct answer.

Trade balance = Merchandise Export - Merchandise Import = 69,908 - 73,968 = 4,060 (deficit)

66.    E

67.    E

68.    A

69.    C

70.    E

71.    D

72.    D

73.    D

Therefore option (e) is the correct answer.

	Particulars	Credit	Debit	Net
I.	Merchandise	2,900	2,100	800
II.	Invisibles	444	550	106
	a. Services	200	0	200
	b. Transfers	244	0	244
	c. Investment Income	0
	Total Current Account
		3,344	2,650	694

So the current account balance is 694 MUC

The current account balance = Capital Inflows - Capital Outflows

= 12,600 - 9,000 = 3,600MUC

Therefore option (a) is the correct answer.

Inflation rate = (GNP deflator of current period - GNP deflator of previous year)

divided by GNP deflator of previous year x 100 = 62.5 ^x1 = ²⁰%.

High - Powered money (H) = monetary liabilities of central bank + Government money.

Monetary liabilities = Financial assets + other assets - Non monetary liabilities Financial assets = Loans given to Government + Credit to banks + Loans given to commercial sector + foreign exchange assets

= 1,200 + 800 + 20 + 1,500 = 3,520 Non monetary liabilities = 200 + 80 = 280 Monetary liabilities = 3,520 + 60 - 280 = 3,300 M = 3,300 + 300 = 3,600 MUC

When reserves are decreased by 5000, the new reserves = 5000.When volume of demand deposits is increased by 5000, new demand deposits = 30000 + 6000 = 36,000 Reserve requirements = 5000 / 36000 = 0.1388=0.139.

Reason: Growth = 2.5 + 5.5 = 8%

Rate of investment = 5 x 8 = 40%

C = a + pYd

Where, a = autonomous consumption and p = marginal propensity to consume (MPC)

P = AC/AY_d = (475 - 400)/100 = 0.75 If MPC = 0.75, autonomous consumption:

475 = a + 0.75(500)

Or, a = 100.

Thus, C = 100 + 0.75Y_d

Or, S = - 100 + 0.25Y_d

When S = 100, 100 = -100 + 0.25Y_d

or, 200 = 0.25Y_d

or, Y_d = 800 MUC

Since the economy is a two sector economy, Y = Y_d (disposable income). 74. B MPC = Change in consumption / Change in disposable income = AC/AYd = (4,200 - 2,000) / (4,000 - 1250)

= 0.8 If MPC = b = 0.8, then 4200    a + 0.8(4,000)

4200    = a + 3,200

Or, a = 4,200 - 3,200 = 1,000 MUC.

Model Question Paper Quantitative Techniques - I (MSF1B1)

Answer all 78 questions.

Marks are indicated against each question.

Total Marks : 100

¹    A box contains 3 red balls and 7 green balls. If two balls are taken one after the other without replacement, the probability that both are red is

1

^(a) 2 3

^(b)    10

(c)

(d)

(e)

2

10

15

40

6

¹⁹    (1 mark)

²    Which of the following is/are true regarding probability?

I.    The probability of the entire sample space S is 1.

II.    The probability of an event contained in the sample space should be greater than or equal to 0 and less than or equal to 1.

III.    If A and B are dependent events, then the probability of (A and B) is equal to the product of probabilities of A and B.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.    (1 mark)

-b

3.

( 2 \ a³ x⁸

⁶a^4b x⁶ x

The simplified form of the expression

is

(a)	x1 - b
(b)	x1 - 6b
(c)	x1 - 8b
(d)	x6 - 8b
(e)	x2 - 8b. X + Y 1
log

(1 mark)

4.

i. ^X+^Y . , then Y X is equal to

(a)

(b)

(c)

(d) (e)

16

27

38

47

50.

The harmonic mean of two numbers is 4. The arithmetic mean and geometric mean of the same numbers are A and G respectively. The relationship between A and G is 2A + G² = 27. One of the two numbers is

(a)    3

(b)    4

(c)    5

(d)    7

(e)    8.

The product of three numbers in a Geometric Progression (G.P) is 216 and the sum of their products taken in pairs is 156. The highest of the three numbers is

(a)    8

(b)    10

(c)    18

(d)    38

(e)    48.

(2marks)

(2marks)

⁷ The number of combinations that can be made by taking 4 letters of the word COMBINATION is

(a)    80

(b)    136

(c)    230

(d)    330

(e)    430.

The mean and standard deviations of the following observations 3, 7, 12, 15, 18, 21 are 12.6667, 6.18 respectively, if each observation is increased by 2.5, then the mean and standard deviation are

8.

(a)    12.6667, 6.18

(b)    15.1667, 6.18

(c)    23.1667, 8.68

(d)    25.1667, 6.18

^(e)    32.1667, 8.68.

(1 mark)

9.

An organization has 30 members 5 of them are women in how many ways a committee of 4 members is selected so as to include at least 1 woman?

(a)    12,547

(b)    14,755

(c)    13,526

(d)    15,874

(e)    16,875.

(1 mark)

10.

The intercept for the line joining points (1, 2) and (3, 4) is <a> 4

5 3

(b)

(c) 1

8

3

(d)

r 1⁰

^{(e) y}

-Consider the following equations:

111-x + y z =5

2 2 6

111

   x+ y +z =10

3 4 2

111

   x + y +z =7.

643

The value of z in the above simultaneous equations is

10

11

12

13

14.

(a)

(b)

(c)

(d) (e)

'if

(a)

(b)

(c)

(d) (e)

12.

n - 3

ⁿC,

C₃ =33:4

. Then the value of n is

6

10

11

12

14

16.

(2marks)

The roots of the quadratic equation x² + 7x + 12 = 0 are

13.

-    1 and - 2

-    2 and - 3

-    1 and - 4

-    1 and - 3

-    3 and - 4.

(a)

(b)

(c)

(d) (e)

(1 mark)

14.

(1 mark)

(1 mark)

The factors of 16Q2 - 81 is
15.	(a) (2Q + 8)(2Q - 8) (b) (2Q + 9)(2Q - 9) (c) (2Q + 9)(4Q - 8) (d) (4Q + 8)(4Q - 8) (e) (4Q + 9)(4Q - 9). 8 What is the value of P6 ? (a) 20,160 (b) 30,420 (c) 41,256 (d) 45,217 (e) 48,217.
16    dy If xy = loge x, then dx at x = e is

1+y

(a)

(b)

(c)

(d) (e)

e

^{1 -} y

e

2+y e 1 0.

2x² - x - 3

The limit of the function x² - 2x - 3 at x = -1 is

5

4

5

2

(a)

(b) (c)

4

(d) 0

(e) 1.

18.    10² 2.25Q

The total costs of ordering and carrying costs are given as TC = Q 2 where Q is the quantity per order. The order quantity for which the total cost will be minimum is

(a)    6.4251

(b)    9.4281

(c)    8.2569

(d)    7.2564

(e)    5.2316.

(2marks)

19.Which    of the following is/are true regarding interpolation and extrapolation?

I.    Interpolation and extrapolation provide us with estimates of independent variable.

II.    There must exist a functional relationship between interpolation and extrapolation for them to work.

III.    Interpolation is a statistical technique, which through a study of time series of known figures of population, allows us to make insertions.

IV.    Interpolation allows us to forecast or anticipate a value for some future data.

V.    In interpolation or extrapolation problem, time can be taken as one of the dependent variables.

(a)    Only (I) above

(b)    Only (III) above

(c)    Both (I) and (III) above

(d)    Both (II) and (III) above

(e)    All (I), (II), (III), (IV) and (V) above.

(1 mark)

(1 mark)

20.Which    of the following is false with regard to histograms?

(a)    The class intervals are represented by the base of the rectangles

(b)    The frequencies are represented by the heights of the rectangles

(c)    If the class intervals are of equal width then the bases of the rectangles will be equal

(d)    The tallest rectangle represents the class interval with the lowest frequency

(e)    The tallest rectangle represents the class interval with highest frequency.

21.A    project requires an initial outlay of Rs.35 lakhs and has the following cost flow projections:

Year	Cash flows (in Rs. lakhs)
1	15
2	10
3	10
4	20

Internal Rate of Return (IRR) is

(a)    12.31%

(b)    14.31%

(c)    15.81%

(d)    18.85%

(e)    19.82%.

(2marks)

(1 mark)

22.    A graph of cumulative frequency distribution is called as

(a)    Histogram

(b)    Frequency polygon

(c)    Ogive

(d)    Skewed curve

(e)    Frequency curve.

23.A    relative frequency polygon indicates the_of the distribution.

(a)    Skewness

(b)    Mean

(c)    Median

(d)    Mode

(e)    Variance.

24-A    positively skewed distribution curve tails off towards the higher end, and for such a curve

(a)    Mean = Median = Mode

(b)    Mean < Median = Mode

(c)    Mean = Median > Mode

(d)    Mean < Median > Mode

(e)    Mean > Median > Mode.

²⁵-The    sum of deviations of the items from the arithmetic mean is always

(a)    One

(b)    Two

(c)    Three

(d)    Four

(e)    Zero.

(1 mark)

²⁶-A    problem in statistics is given to two students A and B. The probability of A solving the problem is 2/5 and the probability of B solving the problem is 5/11. If A and B attempt, what is the probability of the problem being solved?

(a)    0.253

(b)    0.453

(c)    0.673

(d)    0.783

(e)    0.853.

(2marks)

²⁷-Bag    A contains 2 white and 3 red balls and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. What is the probability that it was drawn from

(2marks)

bag B?
	15
(a)	52
	25
(b)	52
	35
(c)	52
	45
(d)	52
	50
(e)	52

²⁸-The probability that a boy will get a scholarship is 0.9 and that a girl will get is 0.8. What is the probability that at least one of them will get the scholarship?

(a)    0.45

(b)    0.65

(c)    0.75

(d)    0.85

(e)    0.98.

(2marks)

29.A    train runs 25 miles at a speed of 30 mph, another 50 miles at a speed of 40 mph, then due to repair of the tracks it travels for 6 minutes at a speed of 10 mph and finally covers the remaining distance of 24 miles at a speed of 24 mph. What is the average speed in miles per hour?

(a)    31.41

(b)    41.21

(c)    51.22

(d)    62.22

(e) 68.66.

30.The    value of the median of the following data would be

Income (Rs.) 1,000 1,500 800 2,000 2,500 1,800 No. of persons 24 26 16 20 6 30

(a)    Rs. 150

(b)    Rs. 800

(c)    Rs.1,000

(d)    Rs.1,500

(e)    Rs.1,900.

31.In a certain city two news papers A and B are published. It is known that 25% of the city population reads A and 20% reads B, while 8% reads both A and B. It is also known that 30% of those who read A but not B look into advertisement and 40% of those who read B but not A look advertisements while 50% of those who read both A and B look into advertisement. What is the percentage of the population who look into advertisement?

(a)    11.2%

(b)    12.3%

(c)    12.8%

(d)    13.9%

(e)    24.5%.

(2marks)

³².The function y =

x³ - 8x² + 21x - 18 has a minimum value at

(a)

(b)

(c)

(d) (e)

1

2

3

4 5.

(2marks)

33.

Which of the following is true when ^{f (x)} > ⁰ and ^f ' ^(x) > ⁰ ?

(a)    f(x) is increasing at an increasing rate

(b)    f(x) is decreasing at an increasing rate

(c)    f(x) is increasing at a decreasing rate

(d)    f(x) is decreasing at a decreasing rate

(e)    f(x) is decreasing at a constant rate.

(1 mark)

34.Which of the following is most affected by the presence of extreme values in the data set?

(a)

(b)

(c)

(d) (e)

Mean

Median

Mode

Quartiles

Deciles.

(1 mark)

35.

dU dU dU x--+ y--+ z-

dx dy dz

If U :

: log (x⁴ + y⁴ + z⁴ - x²y² - y²z² - z²x²), then

4

2U

3U

4U

5U.

(a)

(b)

(c)

(d) (e)

(1 mark)

Consider the frequency distribution

Wages in (Rs.) 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 No. of workers 60 140 110 150 120 100 90

The modal wage of the workers is
37.	(a) 15.8671 (b) 20.8671 (c) 27.8571 (d) 35.8571 (e) 45.8671. .The harmonic mean from the following data is 25 45 75 5

36.

(a)    14.5231

(b)    15.6287

(c)    16.2987

(d)    17.3085

(e)    19.6234.

³⁸-The    variance of a group values is 12.25. If every observation is increased by 3 the variance of the resulting values

(a)    Decreases by 3

(b)    Increases by 9

(c)    Decreases by 9

(d)    Remains 12.25

(e)    Increases by 3.

(1 mark)

³⁹-The    derivative of a function, y = f (x), at a point x = a is equal to

(a)    The limit of the function at x = a

(b)    The value of the function at x = a

f (x)

(c)    lim xa a

f (x)

(d)    lim -T--xaf (a)

f (x)-f (a)

^(e)    lim --

xa x - a .

(1 mark)

40.    _{v 2} _

If for a sample of 10 items, b^x _ ³⁸⁵ and x = 5.5, then the standard deviation of the sample is

(a)    1.0377

(b)    2.0377

(c)    3.0277

(d)    4.0377

(e)    5.0377.

(1 mark)

⁴¹-Consider the following distribution:

Percentage of dividend declared	Number of companies
10 - 20	6
20 - 30	15
30 - 40	10
40 - 50	14
50 - 60	11

What is the third quartile for the above data?

(a)    23.5645

(b)    28.5236

(c)    47.8571

(d)    33.5845

(e)    43.5954.

⁴²-Data on the readership of a certain magazine show that the proportion of male readers under 35 is 0.40 and over 35 is 0.20. If the proportion of readers under 35 is 0.70, what is the probability that a randomly selected male reader is under 35 years of age?

(a)    0.67

(b)    0.77

(c)    0.87

(d)    0.97

(e) 0.99.

⁴³.Consider the following 2 sets of observations.

Set 1 : 3, 10, 12 Set 2 : 6, 4, 1, 9

The combined standard deviation of the data is

(2marks)

(a)	1.736
(b)	2.736
(c)	3.736
(d)	4.736
(e)	5.736

⁴⁴.Which    of the following statements is false?

(a)    If the primal formulation of a linear programming problem is a minimizing problem then the dual formulation will be a maximizing problem

(b)    If the primal formulation of a linear programming problem is a maximizing problem then the dual formulation will be a minimizing problem

(c)    The dual formulation is a inverse of the primal formulation in every respect

(d)    The dual formulation cannot be solved for optimal solution

(e)    The dual formulation can be derived from the same data from which the primal is formulated.

(1 mark)

⁴⁵.The    feasible region for a profit maximizing linear programming is bounded by the vertices (1, 0), (6, 0), (4, 9) and (0, 15). The profit function is Z = 2x + 3y. The maximum value of Z is

(a)    2

(b)    12

(c)    35

(d)    45

(e)    65.

(1 mark)

⁴⁶.If the objective function in a graphical linear programming problem is parallel to an edge of the feasible region then

(a)    The optimal solution lies outside the feasible region

(b)    There cannot be any optimal solution

(c)    There will be a unique optimal solution

(d)    The optimal solution is always one of the corner points

(e)    There will be multiple number of optimal solutions.

(1 mark)

⁴⁷.Consider the following Linear Programming Problem(LPP):

Maximize z = 3x₁ + 2x₂ + 5x₃

Subject to constraints x₁ + 2x₂ + x₃ < 430

3x₁ + 2x₃ < 460

x₁ + 4x₃ < 420

And x₁, x₂, x₃ > 0.

The optimum value of z by using simplex method is

(a)    117

(b)    277

(c)    310

(d)    950

(e)    1,050.

⁴⁸-A company manufactures two types of printed circuits. The requirements of transistors, resistors and capacitors for each type of printed circuits along with the other data are given below:

Particulars	Circuit		Stock available (in units)
	A	B

Transistor	15	10	180
Resistor	10	20	200
Capacitor	15	30	210
Profit (Rs.)	5	8

What is the optimum value of the above problem by graphical method?

60

76

80

67

100.

(a)

(b)

(c)

(d) (e)

The reciprocals of the terms in a harmonic progression are

(a)    In geometric progression

(b)    In harmonic progression

(c)    In arithmetic progression

(d)    Always in decreasing order

(e)    Always in increasing order.

(1 mark)

⁵.The inverse of the function y = f(x) = 7x - 5 is

y+7

(a)

(b)

(c)

(d) (e)

4 y7 4

y + 7 7

y+5 7 y + 7 5    '

(1 mark)

⁵¹.Consider the following LPP : Minimize Z = 2x₁ + 3x₂ +4x₃ Subject to constraints: x1 + 2x₂ + 3x3 > 5 3x1 + 4x₂ + 5x3 > 6 6x₁ + 7x₂ + 8x₃ > 8 And x₁, x₂, x₃ > 0 The dual of the above LPP is

(a)    Maximize Z *= 5y₁ + 6y₂ + 8y₃ Subject to constraints:

y1 + ³y₂ + ⁶y3 < ²

²y1 + ⁴y2 + ⁷y3 < ^{3 3}y1 + ⁵y2 + ⁸y3 < ^{4 And} yl^, y2^, y3 > ⁰

(b)    Maximize Z* = 5y₁ + 6y₂ + 8y₃

Subject to constraints:

y1 + ³y₂ + ⁶y3 < 2

2y₁ + 4y₂ + 6y₃ < 3 ³y1 + ⁵y2 + ⁸y3 < ^{4 And} yl^, y2^, y3 > ⁰

(c)    Maximize Z* = 5y₁ + 8y₂ + 6y₃ Subject to constraints:

y1 + ³y₂ + ⁶y3 < ²

²y1 + ⁴y2 + ⁷y3 < ^{3 3}y1 + ⁵y2 + ⁸y3 < ^{4 And} y y2- y3 ^{- 0}

(d)    Maximize Z* = y₁ + 6y₂ + 3y₃

Subject to constraints:

y1 + ³y₂ + ⁶y3 < ²

2y₁ + 4y₂ + 7y₃ < 3 ³y1 + ⁵y2 + ⁸y3 < ^{4 And} y y2- y3 ^{- 0}

(e)    Maximize Z* = 5y₁ + 6y₂ + 8y₃

Subject to constraints:

y1 + ³y₂ + ⁶y3 < ²

2y₁ + 4y₂ + 7y₃ < 3 ³y1 + ⁵y2 + %3 ^{- 4}

^{And y}1, ^y2, ^y3 - ⁰.    (2marks)

⁵². = 9/81x7/49 _y= 3/625x3/3 _z= 9

^X 25 , and xT⁶ then the value of xyz is

5

(a)    

21

7

^{(b)    15}

15

^{(c)    7}

21

^{(d)    7}

3

^{(e)    35}

^{35 .}    (2marks)

⁵³Three terms are in geometric progression. The second term and the third term are 16 and 64 respectively, then the first term is

(a)    1

(b)    2

(c)    3

(d)    4

(e)    5.    (1 mark) ⁵⁴Tf mean = 29.51 and median = 39.69, then the value of empirical mode is

(a)    30.05

(b)    40.05

(c)    50.05

(d)    60.05

(e)    70.05.    (1 mark) What is the value of ^log3 ⁸¹?

(a)    4

(b)    5

(c)    6

(d)    8

(e)    9.

⁵⁶' n    \ 2! \,2/    \ . 2/    \ _tu d f d f d f

f(x,y,z) = x2(y - z) + y2(z - x) + z2(x - y) then     =

If    d x d y d z

(a)    0

(b)    1

(c)    f(x, y,z)

(d)    2f(x,y,z)

(e)    3f(x, y,z).

(2marks)

57    2 2

⁵ 'If the ratio of the sum of m terms and n terms of an Arithmetic Progression (A.P) is m² : n , then the

ratio of its m^th and n^th terms will be

(1 mark)

(a)	(2m + 1)	: (2n + 1)
(b)	(2m - 1)	: (2n + 1)
(c)	(2m - 1)	: (2n -	1)
(d)	(2m + 1)	: (2n -	1)
(e)	(m + 1) :	(n + 1)

⁵⁸-According to the Bienayme-Chebyshev rule, at least_percent of the observations in a

sample are contained within two standard deviations around the mean, regardless of the shape of the distribution.

(a)    88.89

(b)    93.75

(c)    68.26

(d)    75.00

(e)    50.00.

(1 mark)

^59.The data below represents the amount of carbohydrates in grams contained in breakfast cereal:

11, 15, 23, 29, 19, 22, 21, 20, 15, 25, 17.

The median carbohydrate amount in the cereal is

(a)    10 grams

(b)    20 grams

(c)    30 grams

(d)    40 grams

(e)    50 grams.

(1 mark)

⁶⁰-The    coefficient of variation of a data set is 20 and the variance of the data set is 16. What is the mean of the data set?

(a)    20

(b)    30

(c)    40

(d)    50

(e)    60.

(1 mark)

⁶¹-A    data set contains the following observations:

10, 12, 8, 14, 15, 7, 17, 20 What is the range of the data set?

(a)    10

(b)    11

(c)    12

(d)    13

(e)    15.

⁶²-The following distribution shows the ages of 100 persons in a group:

Age group (in years)	Number of persons
20 - 25	3
25 - 30	16
30 - 35	22
35 - 40	18
40 - 45	14
45 - 50	10
50 - 55	7
55 - 60	6
60 - 65	4

What is the average age of the persons in the group?

(a)    25.3

(b)    26.3

(c)    35.3

(d)    39.3

(e)    46.3.

(1 mark)

⁶³-The    mean annual salary paid to 100 employees of a company was Rs.5,000. The mean annual salaries paid to male and female employees were Rs.6,000 and Rs.4,000 respectively. The percentage of males employed by the company is

(a)    40

(b)    50

(c)    60

(d)    70

(e)    80.

(2marks)

⁶⁴-The    Arithmetic Mean (A.M) between two numbers exceeds their Geometric Mean (G.M) by 2 and the

G.M exceeds their Harmonic Mean (H.M) by 8/5. The highest of the two numbers is

(a)    12

(b)    16

(c)    20

(d)    32

(e)    54.

(1 mark)

⁶⁵-A    function, y = f (x), is said to have a relative maxima or minima at x = a, if

^(a)    f '(x) = 0 at x = a

(b)    f '(x) > 0 at x = a

^(c)    f '(x) < 0 at x = a

(d)    f(x) > 0 at x = a

^(e)    f(x) < 0 at x = a.

(1 mark)

66-Which    of the following is/are true with regard to High-level language?

I.    It is a English like language with a predefined format.

II.    In High-level language the instructions are not more powerful compared to machine language.

III.    It is a machine independent and can be used on various computer systems.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    Both (I) and (III) above.

⁶⁷-If    the slope and intercept of a line on Y-axis are 4 and 3 respectively, then the equation of a line can be written as

(a)    Y = 4X + 3

(b)    Y = 3X + 4

(c)    Y = 4X² + 3

(d)    Y = 3X² + 4

(e)    Y = 4X² + 7.

^68.The    limit of a function, y = f (x), at a point x = a, is the

(a)    Minimum value of the function for all values of x greater than a

(b)    Minimum value of the function for all values of x less than a

(c)    Maximum value of the function for all values of x greater than a

(d)    Maximum value of the function for all values of x less than a

(e)    Value which the function approaches if x approaches a.

(1 mark)

69.

For a real number, a, the interval [a, + ) indicates

(a)    Set of all real numbers less than a

(b)    Set of all real numbers less than or equal to a

(c)    Set of all even numbers greater than a

(d)    Set of all odd numbers greater than a

^(e)    Set of all real number greater than or equal to a.

(1 mark)

⁷.Which of the following symbols indicates the off-page connector in drawing flowchart?

(a) O

/U

(e) O.

⁷¹Which of the following statements is false?

(a)    Java can be downloaded straight from internet

(b)    Modem is a piece of equipment that connects a computer to a data transmission line

(c)    WWW is a big part of network of networks

(d)    Internet is a global network of computers linked by exclusive and regular phone lines and microwave and satellite signals

(e)    Baud is a bundle of data.

(1 mark)

(1 mark)

⁷²Generally, the word size in mini computers are

(a)    8 bits

(b)    16 bits

(c)    24 bits

(d)    28 bits

(e)    32 bits or more.

⁷³Tn which of the following classification of computers uses the properties of electronic circuits to represent exactly two states - on and off?

I.	Digital computer.
II.	Analog computer.
III.	Hybrid computer.
(a)	Only (I) above
(b)	Only (II) above
(c)	Only (III) above
(d)	Both (I) and (II) above
(e)	Both (II) and (III) above

⁷⁴.The Control Unit along with Main Memory and Arithmetic Logic Unit ( ALU) is called as

(a)    Input Unit

(b)    Central Processing Unit

(c)    Output Unit

(d)    Digital computer

(e)    Minicomputers.

⁷⁵.The    highest common factor of 64, 72 and 164 is

(a)    2

(b)    4

(c)    10

(d)    12

(1 mark)

(1 mark)

(1 mark)

(e) 14.

⁷⁶.The    Arithmetic Logic Unit (ALU) contains one or more storage locations are called as

(a)    Registers

(b)    Card readers

(c)    Magnetic disk drives

(d)    Card punching machines

(e)    Printers.

^77.The    appropriate average for a set of ratios, using the denominators of the ratio data as weights is

(a)    Simple arithmetic mean

(b)    Geometric mean

(c)    Simple harmonic mean

(d)    Weighted arithmetic mean

(e)    Weighted harmonic mean.

⁷⁸-A sum of Rs.1,800 deposited today in a bank gets tripled in a period of 6 years. Then, what is the

(2marks)

annual	rate of interest?
(a)	10.02%
(b)	15.26%
(c)	17.56%
(d)	18.26%
(e)	20.09%.

END OF QUESTION PAPER

Suggested Answers Quantitative Techniques (MSF1B1)

REASON

ANSWER

C

Let R₁ is the event of getting a red ball in the first attempt and R₂ is the event of getting a red ball in the second trial. As the two events are dependent,

P(R₁ n R₂) = P(R₁) . P(R₂/R₁)

3    2

P(R₁) = 10 , P(R₂/ R₁) = 9

A 2 -_1

P(R₁ n Rj) = 10 ^X 9 ^- 15 .

The probability of the entire sample space S is 1.

2

D

The probability of an event contained in the sample space should be greater than or equal to 0 and less than or equal to 1.

If A and B are independent events, then the probability of (A and B) is equal to the product of probabilities of A and B.

Hence option (d) is correct.

1 2

X(a3 x* )-b= 6PV X(a³ x')-^b = (a^4b x⁶ )⁶ X(a³ x')"^b

C

3

-2b

a ⁶ x a ³ x^-8b= a⁰x^1-8b - x^1-8b.

- - (logX + logY) log 7 2    ^;

4

D

_RHS = 2log (XY)- log (XY )^1/2

X + Y

- log (XY)

-(XY)

7

Squaring on both sides

(X + Y)² - 49XY

X² + Y² + 2XY - 49XY X² + Y² - 47XY

Dividing both sides by XY we get

X Y

+ = 47.

Y X

H.M = 4, A.M = A, G.M = G

G.M² G²

We know that H.M= 4 = A.M A = G² = 4A

The relationship is 2A + G² = 27.

2A + 4A = 27

6A = 27 A = 27/6 = 9/2.

So G² = 4(9/2) = 18 Let the numbers be a, b

a + b = 9    ........(1)

ab = 18

(a - b)² = (a + b)² - 4ab = 81-72 = 9.

(a - b)² = 9 a - b = 3

let us take a - b = 3    .......(2)

by solving (1) and (2) we get a = 6, b = 3 similarly if we take a - b = - 3 we get a =3 and b = 6. The numbers are 3 and 6.

m

C

6

Let the numbers be r , m and mr.

The product of the numbers is m¹ = 216 or m = 6

m

m

The sum of the products of the pairs is r . m + m.mr + mr. r = 156

1

36(7 + r + 1) =156 3r² + 3r + 3 = 13r 3r² - 10r + 3 = 0 = 3r - 9r - r + 3 = 0 (r - 3)(3r - 1) = 0 So r = 3 or 1/3.

If we take r =3 we get 2, 6, 18

If we take r =1/3 we get 18, 6, 2.

The highest number is 18.

B There are 11 letters of 8 different kind C, (O, O), M, B, (I, I), (N, N), A, T.

7

In all the required combination some may contain all dissimilar letters, some may not contain all different letters. Following cases arises.

All the 4 letters are different

2 letters are alike, 2 are different

2 letters are alike of one kind, 2 letters are alike of second kind There are 8 different letters. The required number of combination = ⁸C 4

There are 3 pairs of alike letters (O, O), (I, I), (N, N). One pair can be chosen in ³C1 ways. Remaining 2 different can be selected from the remaining 7 different letters in ⁷C2 ways. Hence the number of combinations of this type is ³C1 x ⁷C2

Two pairs of similar letters can be chosen in ³C 2 ways.

Hence the total number of required combinations is ⁸C4 + (³C1 x ⁷C2) + ³C2 = 136.

B If each observation in the data set increased by a constant 2.5 then the mean increased by that constant and standard deviation remains same.

Given mean = 12.6667, standard deviation = 6.18

If we increased a quantity 2.5 so the observations (5.5 + 9.5 + 14.5 + 17.5 + 20.5 + 23.5) / 6 =

15.1667.

Standard deviation =

(5.5 -15.1667)² + (9.5 -15.1667)² + (14.5 -15.1667)² + (17.5 -15.1667)² + (20.5 -15.1667)² + (23.5 -15.1667)²

6

: 6.18

So mean is increased by 2.5 and standard deviation remains same.

Here mean is 15.1667 and standard deviation is 6.18.

Total number of ways in which 4 can be selected out of 30 = ^30C4

Number of ways in which 4 can be selected so that no women is included = ^(30-5)C4 = ²⁵C4 The number of ways in which 4 members can be selected so that at least one women is included is ³⁰C4 ^{- 25}C4 = 27405 - 12650 = 14755.

The equation of line y = a + bx with a as intercept and b = slope It passes through (1, 2) and (3, 4)

C

10.

2 - 4

y ^- y

2 -

1 _ 2 -1 _ 1.

y

x

1-3

The intercept is a =

1 1 1 =5 x + y --z 2 2 6 1 1 1 = 10 x + y + z 3 4 2 1 1 1 = 7 x + y + z 6 4 3

x - x

11.

C

....(i)

.(ii)

..(iii)

By doing (ii) + (iii) - (i) we get

111,

+ + I z = (7 + 10 - 5)

Or, z _ 12.

12.

B

ⁿc₆ : ^{(n -3)}c₃ =33:4

n

Or,

33 ^: 4

(n - 3)

3

Or, 4xⁿc = 33x^{(n 3)}c

63

n!

Or, 4x-

3!(n - 6)!

= 33x ^{(n - 3)!} = 33x-^{(n - 3)!}

6!(n - 6)! 3 !(n - 3 - 3)!

Or, 4x^{(n - 2)(n - 1)n} =33 4x5x6

Or, (n - 2)(n - 1)n = 30x33 = 9x10x11 = (11 - 2)(11 - 1)(11)

So the value of n =11.

The quadratic equation is x² + 7x + 12 = 0

13.

14.

15.

E

E

(-7) V7² - 4(1)(12) -7 1 x =    ²⁽¹⁾    = 2 = - 3 and - 4.

16Q² - 81 = (4Q)² - (9)² = (4Q - 9)(4Q + 9) (Q a² - b² = (a + b)(a - b))

8p _

Given x^y = log_e x

Taking logarithms on both sides w.r.t to base e y log_e x = log_e(log_e x)

Differentiating both sides w.r.t x

y '^(loge ^x) + - =    ¹ .

x (log_e x)x

y = 1    ¹ - y

At x = e, ^y' + e e = ^y' = e .

2x² - x - 3

17.

A

lim

^x-1x - 2x - 3

2x - 3x + 2x - 3 lim --

^x-1 x - 3x + x - 3

x-1 x(x - 3) + 1(x - 3)

x(2x - 3) + 1(2x - 3)

lim

(2x - 3) (x +1)

lim

x-¹ (x - 3) (x +1)

lim(2xz3)

x-¹ (x - 3)

2(-1) - 3 = -5 = 5 -1 - 3 -4 ~ 4

10 2.25Q TC = Q 2

18.

B

-10² 2.25

d(TC)

dQ

+

Q

2

-10² 2.25

d(TC) Equating dQ

-2--+--

: 0 to we have ^Q 2 = 0

2 x 10²

Q² = 2.25 = 88.8889

Q = -\/88.8889 = 9.4281.

19.    B The following are true:

   Interpolation and Extrapolation provide us with only estimates of the dependent variable.

   For interpolation and extrapolation to work there must exist a functional relationship between an independent variable and a dependent variable and it must be required to estimate the value of the dependent variable corresponding to a certain value of independent variable.

   Interpolation is a statistical technique, which through a study of time series of known figures of population, allows us to make insertions.

   Extrapolation allows to forecast or anticipate a value for some future data.

In interpolation or extrapolation population is taken to be a function of time or years and while

time is the independent variable, population is the dependent variable.

Hence option (b) is correct.

20.    D The given option (d), The tallest rectangle represents the class interval with the lowest frequency

is false and the correct one is the tallest rectangle represents the class interval with highest

frequency.

So, option (d) is the correct answer.

Let the IRR of the project be r

15 10 10 20

35 =-r +--+--+-

... (1 + r)¹ (1 + r)² (1 + r)³ (1 + r)⁴ For, r = 20%,

RHS = ¹¹⁹ (1.19)² (1.19)³ (1.19)⁴ = 35.5742

The following pairs of r and values of RHS are obtained: r = 19% RHS = 35.5742 r = ? RHS = 35 r = 20% RHS = 34.8765

35 5742- 35

--⁵ => 19.822%

r = 19 + 35.5742 - 34.8765    .

A graph of cumulative frequency distribution is called as ogive.

A relative frequency polygon indicates the skewness of the distribution.

A positively skewed distribution curve tails off towards the higher end and for such a curve Mean > Median > Mode.

The sum of deviations of the items from the arithmetic mean is always zero.

P(As solving the problem) =

P(B s solving the problem) =

P(As not solving the problem) =

P(Bs not solving the problem) =

3x =

P(Both A and B are unable to solve the problem) =5 11 55

1 - H = ³⁷ = 0.673 P(The problem being solved) = 55 55    .

Let E₁ be the event that be the event the ball is drawn from bag A. E₂ the event that it is drawn from bag B and E that the ball is red.

We have to find P(E₂/E)

Since both the bags are equally likely to be selected, we have 1

P(E1) = P(E₂) = 2

35

p ( e|e, ) = - p ( e|e₂ ) = ⁵

Also,    ¹ 5 and    ² 9

RHS = ¹-²⁰ (1.20)² (1.20)³ (1.20)⁴ = 34.8765 For, r = 19%,

15 10 10 20

+- +-+-

10 20

-+-

Hence by Bays theorem, we have

15 10

+-

22.

23.

24.

25.

26.

C

A

E

E

C

2
5
5
11
2	3
1 =
5	5
5	6
1--=
11	11

P(E₂).P ( e|e₂ )

P (E₂ |e ) = P(E ).P (E |E1) + P(E₂) p ( e|e₂ )

1    5

X-

2    9

1    3 1 (1 5

-x- I + 1 -X-

2    5 J V 2 9

25 52 .

28.    E The probability that a boy will get a scholarship = 0.9

The probability that a girl will get a scholarship = 0.8 The probability at least one of them will get the scholarship is P(A or B) = P(A) + P(B) - P(A and B)

= 0.9 + 0.8 - (0.9 x 0.8) = 1.7 - 0.72 = 0.98.

29.    A Time taken in covering 25 miles at a speed of 30 mph = 50 minutes.

Time taken in covering 50 miles at a speed of 40 mph = 75 minutes Distance covered in 6 minutes at a speed of 10 mph = 1 mile Time taken in covering 24 miles at a speed of 24 mph = 60 minutes Therefore, taking the time taken as weights we have the weighted mean as

6000 Average speed = 191

Income arranged in ascending order No. of persons c.f Income arranged in ascending order No. of persons c.f 800 16 16 1800 30 96 1,000 24 40 2000 20 116 1,500 26 66 2500 6 122

N +11th    122 +1

Speed (in mph) [x] Time taken (in minutes) [W] Wx 30 50 1500 40 75 3000 10 6 60 24 60 1440 EW = 191 EWx = 6000

= 31.41mph.

30.

D

Median = Size of v 2 J item = 2 = 61.5^th item

Size of 61.5^th item = Rs.1500.

31. D Let P(A) and P(B) denote the percentage of city population who read newspapers A and B. Then from given data we have

1 1 2 P(A) = 25% = 4; P(B) = 20% = 5 ; P(A and B) = 8% = 25"

Percentage of those who read A but not B = 0.25 - 0.08 = 0.17

/    12 = 17 =

= ^P (A and ^B) = P(A) - P(A and B) = 4 25 = 100 =

Similarly P (A and B) = P(B) - P(A and B) = 0.20 - 0.08 = 0.12

1 2 3

¹ - = = 12%

= 5 25 25

If P(C) denote the percentage of those who look into advertisement then from the given data we obtain

P(C) = 30% of P (A and B )+ 40% of P (A and B ) + 50% of P(A and B)

3 17 2 3 1 2 51 + 48 + 40 139

x-+ x + x =-=-

= 10 100 5 25 2 25 1000 1000

Thus the percentage of population who read an advertisement is 13.9%. f(x) = x³ - 8x² + 21x - 18

dy

The function will be maximum or minimum where dx = 0

f '(x) = 4 = 3x ² - 1 6x + 21 = 0 dx

x = 3 and x =7/3

f"(x ) = 6x - 16

The condition for the minimum value is that second derivative f"(x ) > 0

At x =3 , f"(x ) = 6(3) - 16 = 2 > 0

At x =7/3 f"(x ) = 6(7/3) - 16 = -2< 0

So at x =3 f"(x ) > 0

The function f(x) is minimum at x =3.

A

A

A

33.

34.

35.

A derivative is a slope of a function if f '(x) > 0 and f ''(x) > 0 then function is increasing at increasing rate.

Mean is a mathematical average. So it is most affected by the presence of extreme values all other are positional measures, so they are not effected by the presence of extreme values.

Given that,

, , 4 4 4 2 2 22 2 2

u = log(x + y + z - xy - yz - zx), or, u = logf(x,y, z)

4x³ - 2xy² - 2z²x 4y³ - 2x²y - 2yz² Now,u =-,u =

^x    _N     y

f(x,y,z)

4z³ - 2y²z - 2zx²

f(x,y,z)

u=

z

f(x,y,z)

_Ar 4 4 4 22 22 2 2_n

4[x + y + z - xy - yz - z x ] f (x, y, z)

xu + yu + zu =

x *' y    z

4f(x,y, z)

= 4.

f(x,y,z)

Here highest frequency is 150 so mode lies in the class (25 - 30) f-f

C

36.

M = L +-¹ x W

o    mo

2f - f1 - f₂

f = 150, f₁ = frequency of preceding class =110, f₂ = frequency of succeeding class = 120

Where L_mo = 25; W =5

150 -110 _oc 40 _

M₀ = = 25 +-= 25 + x 5

2(150)-110 -120 70 = 25 + 2.8571 = 27.8571.

Calculation of harmonic mean

D

37.

X	1/X
25	0.04
45	0.02222
75	0.01333

5	0.2
10	0.1
20	0.05
50	0.02
60	0.01667
290	0.4622

= 17.3085.

1

0.4622

X

H.M :

The value of standard deviation remains the same if in series each of the observation is increased or decreased by a constant quantity. Thus, the value of variance remains the same if every observation is increased by 3.

38.

39.

40.

41.

D

E

C

C

f (x) f (a)

lim

The derivative of a function, y = f(x) at x = a is equal to ^xa x a which f(x) is changing with respect to the corresponding change in x.

. It indicates the rate at

n 1 n 1 iation = J --- =J 10(5'5) =V9.1667 = 3.0277. 10 1 10 1

Percentage of dividend declared Number of companies Cumulative frequency 10 - 20 6 6 20 - 30 15 21 30 - 40 10 31 40 - 50 14 45 50 - 60 11 56

S tan dard deviation =

Here N = 56, 3N/4 = 42

L_q = Lower limit of the quartile class = 40

F = Cumulative frequency up to quartile class = 31 f_q = Frequency of the quartile class = 14

W = Width of the class interval = 10.

3N

- F

x W

4

f

Q3

= ^Lq +

42 31

x10 =

47.8571.

Let the events be denoted as follows:

A: Reader of the magazine is a male and B: Reader of the magazine is more than 35 years of age Now, we are given that,

P(AandB) = 0.20, P(AandB)=0.40and P(B)=0.70 P(B)=0.30 P(A) = P(A and B) + P(A and B ) = 0.2 + 0.4 = 0.60.

The probability that a randomly selected male subscriber is under 35 years is given by:

- P(A andB) 0.40 2

P(B / A) = -- =- = - = 0.67

P(A) 0.60 3    .

40 +

14

A

42.

For set 1, Mi = 8.333 and ₁ = 3.859

(Consider these 2 sets of observations as populations).

N1 M1 + N2 M-2 Combined mean p. = N1 + N2

(3 x 8.333) + (4 x 5) 3 + 4    = 6.429

---

d₁ = M - M = 8.333 - 6.429 = 1.904 d₂ = M2 - M = 5 - 6.429 = -1.429

o [i.e. standard deviation for the combined set of 7 observations]

1(3 x 3.859²) + (4 x 2.915²) + (3 x 1.904²) + [4 x (-1.429)²]

= V    3 + 4    = 3.7360.

The dual formulation can be solved for optimal solution. All other statements are true.

44.    D

45.    D

The profit function Z = 2x+3y

The vertices are (1, 0), (6, 0), (4, 9) and (0, 15).

For (1, 0) Z = 2(1) + 3(0) = 2 + 0 = 2 For (6, 0) Z = 2(6) + 3(0) = 12 + 0 = 12 For (4, 9) Z = 2(4) + 3(9) = 8 + 27 = 35 For (0, 15) Z = 2(0) + 3(15) = 0 + 45 = 45.

So for (0, 15) the profit function is maximum

If a objective function in a graphical linear programming problem is parallel to an edge of the feasible region. It mean there is more than on multiple number of optimal solution.

46.    E

47.    D

Maximize z = 3x₁ + 2x₂ + 5x₃ Subject to constraints x₁ +2x₂ + x₃ < 430

3x₁+ 2x₃ < 460 x₁ + 4x₃ < 420

x x₂, x3 > 0.

For applying simplex method, we convert the inequalities into equalities by adding the slack variables S_p S₂ and S₃ for the constraints.

The problem now is: Maximize Z = 3x₁ + 2x₂ + 5x₃ + 0S₁ + 0S₂ + 0S₃

Subject to: x₁ + 2x₂ + x₃ + S₁ = 430

3x₁ + 2x₃ + S₂ = 460

x₁ + 4x₃ + S₃ = 420

x₁ x₂ x₃ > 0, S₁ > 0, S₂ > 0, S₃ > 0

The tableaus are constructed below to obtain the optimal solution. The pivots identified in each tableau are circled.

Profit 3 2 ? P lo |o Min M/zk Variable & kL iX-i iKj \ .5, Profit Variables Solution 0 S: 430 11 P ii jl 10 jo 430:1 = 430 0 S' 460 13 10 Q jo ii |o 460.-2 = 230 D Si 420 jl iii a id i 420:4 = 105 |0 _3 -2 -5 fl io io

Tableau 2

Profit			13 12 5 |0 |0	io
Variables			31 jjlj S S -i	Si	Min
Profit	Variables	Solution
0	:5.	325	Cjy Mi b	1 -4	= 325.>'2
0	5,	1250	5 io io io ii	1
			2 iii	2
5	k	105	1 io ii lo lo	1
			4 j :	4
			zl -2 io io io	' 5
			4 j 1	4

Tableau 3

Profit 3 2 5 0 0 0 Win Variables SL: X : J S: S' Si Ero fit Variables Solution 325:2 3 1 1 T X-. 1 0 0 = 433.333 2 s 0 S, 250 / 5 0 0 0 ii 1 100 "4.. 2 5 *i 105 1 0 1 0 0 1 420 4 4 -1 0 0 1 0 1

Tableau 4

Profit 3 2 5 0 0 0 Variables x1 x2 X 3 S1 S2 S3 Profit Variables Solution 2 x2 125 0 1 0 1 2 3 20 -1 20 3 x1 100 1 0 0 0 2 5 1 - 5 5 x3 80 0 0 1 0 1 10 3 10

The optimum solution is x₂ = 125 and x₃ = 80 and x₁ = 100 maximize Z = 950.

The given data can be formulated in appropriate mathematical form as follows Maximize Z = 5x₁+ 8x₂

Subject to constraints:

15x₁+10x₂ < 180

10x₁+ 20x₂ < 200 15x₁+ 30x₂ < 210 ^x1^{, x}2 > ⁰

Where x₁, x₂ are decision variables.

Considering the constraints as equations 15x1+10x2 = 180.................(I)

10x1+ 20x2 = 200.................(II)

15x1+ 30x2 = 210.................(III)

We get the points by putting x₁= 0 and x₂ = 0 in eq(I),(II) and (III) we get the ordered pairs as

(0, 18), (12, 0), (0, 10), (20, 0) and (0, 7), (14, 0)

The feasible region is shown in the graph below

The corner point of the solution space are

O = (0, 0)

A = (12, 0)

B = (11, 3/2)

C = (0, 7)

The value of the objective function at these corner points can be determined.

Corner points	Coordinates of corner points (x1, x2)	Objective function Z = 5x1 + 8x2	Value
O	(0, 0)	5(0) + 8(0)	0
A	(12, 0)	5(12) + 8(0)	60
B	(11, 3/2)	5(11) + 8(3/2)	67
C	(0, 7)	5(0) + 8(7)	56

The maximum value of Z is 67 found at corner point B i.e., x₁ = 11, x₂ = 3/2 At B(11, 3/2) the optimum solution is reached.

The reciprocal of the terms in a harmonic progression are in arithmetic progression. And vice versa. Therefore the reciprocals of a H.P. cannot be in H.P. There is no such connection between the H.P. and the G.P. If the terms in the corresponding A.P. are in the increasing order then the terms of the H.P. will be in the decreasing order and vice versa. Hence there is no reason why

terms of a H.P. will always be in increasing or decreasing order. y = f(x) = 7x - 5 Solving x in terms of y

f-1(y)=¹¹⁵ ,

x =    7 is the inverse.

The dual of lpp is Maximize Z* = 5y₁ + 6y₂ + 8y₃

51.

A

Subject to constraints:

y1 + ³y₂ + ⁶y3 < ²

²y1 + ⁴y2 + ⁷y3 < ^{3 3}y1 + ⁵y2 + ⁸y3 < ^{4 And} y1, y2^, y3 > ⁰

52.

E

99

325

78! x 749 625 x 33 xyz = 7-;=x-x

V5⁷ x

4 2 4 1    2

3⁹ x 7⁷ 5⁹ x 3³ 3⁹

2

5³

3    7 6

7⁷ 5⁹ x7⁷

4 + 3 + 2

9 9 9

3

(2- 4 +Z1 ( 3 + 6-2

513 9 9 J _x 77 7 7

9

3⁹

3

3

9 7

5⁹ x 7⁷

5 x7 35

Three terms are in geometric progression and the second and the third terms are 16 and 64 respectively

a, ar , ar² = a , 16, 64

ar² = 64 = 4 ar 16 ar = 16 a(4) = 16 a = 4

So first term = 4.

If mean = 29.51 and median = 39.69, then

Mode =3median - 2mean =3(39.69) - 2(29.51) = 60.05.

log₃ 81 = log₃ 3⁴ = 4log₃ 3 = 4.1 = 4(Q log₃ 3 = 1) .

Given that,

f (x, y, z) = x²(y - z) + y²(z - x) + z²(x - y)

df ₂ 2

   = f_x = 2x(y - z) - y + z dx

df ₂ 2

   = f = x + 2y(z - x) - z 9y ^y

df 2 2

   = f_z = -x + y + 2z(x - y) dz

fx + fy + fz = 0.

D

53.

54.

55.

56.

D

A

A

Given that ^Sn n

(m/2)[2a + (m - 1)d] = m² . (n/2)[2a + (n -1)d] = n² 2a + (m - 1)d = m 2a + (n - 1)d n 2an + mnd - nd = 2am + mnd - md 2a(n - m) = (n - m)d = d = 2a.

a + (m- 1)d a + (m-1)2a 2m -1

Now T_n a + (n 1)d a + (n 1)2a 2n 1

According to the Bienayme-Chebyshev rule, at least 75 percent of the observations in a sample are contained within two standard deviations around the mean, regardless of the shape of the distribution.

Arranging the data in the ascending order

11, 15, 15, 17, 19, 20, 21, 22, 23, 25, 29. Here N is odd (N+1)/2 term is the median Median = (N+1)/2 = 12/2 = 6 ^th item = 20.

Standard deviation

Mean

-v/Variance

Coefficient of variation

-x100

x100

T

58.

D

59.

B

60.

A

Mean

yj\6

x100

or 20

Mean

4

x100 = 20. 20

61.

62.

D

D

Elm = 3930 Mean = Ef = 100 = 39.3 years.

63. B N₁ = number of males N₂ = number of females So that N₁ + N₂ = 100

We are given X₁₂ = 5000; ^X1 = 6000 ; X₂ = 4000 Substituting the value in the formula

or Mean Range = Highest value - Lowest value = 20 - 7 13.

Class Mid-value (m) Frequency (f) f x m 20 - 25 22.5 3 67.5 25 - 30 27.5 16 440 30 - 35 32.5 22 715 35 - 40 37.5 18 675 40 - 45 42.5 14 595 45 - 50 47.5 10 475 50 - 55 52.5 7 367.5 55 - 60 57.5 6 345 60 - 65 62.5 4 250 Total 100 3,930

NjXj + N₂X₂ Nj + N₂

N_t (6,000) + N₂ (4000) 100

5000    =

5,00,000 = 6000N₁ + [(100 - N₁) 4000]

[Since N₁ + N₂ = 100; N₂ = 100 - N₁)]

5,00,000 = 6000N₁ + 4,00,000 - 4000N₁ 2000 N₁ = 1,00,000 N₁ = 50 and N₂ = 50.

Let the numbers be a, b. Let the A.M be A, G.M be G and H.M be H

64.

B

As A.M. exceeds G.M by 2. So, A - G = 2; Or, (A -2)² = G²........(i)

As G.M exceeds H.M by 8/5. So, G - H = 8/5 Or, A - 2 - H = 8/5 18

Or, A - H = 5

18

G² = AH = A(A - 5 ) Putting this value of G² in equation (i) we get

18

18

(A -2)² = A(A - 5 ) Or, - 4A + 4 = - 5 A Or, 2A = 20    Or, A = 10. Or, (a+b) =

20

So, G = 8 Or, yjab = 8 i.e. ab = 64

64

So, a + a = 20 Or, a² -20a + 64 = 0.

Or, a² -16a - 4a+ 64 = 0 Or, a(a - 16) - 4(a - 16) = 0 Or, (a - 4)(a - 16) = 0

So the vale of the numbers would be (4, 16) or (16, 4)

So the highest number is 16.

A

E

A

E

E

D

E

E

65.

66.

67.

68.

69.

70.

71.

72.

For any function y = f(x), if ^{f (x)} = 0 at x = a, the function is said to have a relative maxima or minima.

High-level languages are English like languages with a predefined format and machine independent and can be used on various computer systems. Option (e) is correct.

In a linear equation Y = a + bX , a and b represent Y- intercept and slope of the curve respectively where X and Y represent independent and dependent variables respectively. Thus if the slope and intercept of a line on Y-axis 4 and 3 respectively, then the equation of the line is

Y = 3 + 4X.

The limiting value of a function, y = f(x) at x = a is defined as the value to which y approaches, as x approaches a; it is neither the minimum value, nor the maximum value.

For any real number, a, the interval [a, + ) indicates the set of all real numbers greater than or equal to a, it includes all the even and odd numbers greater than or equal to a.

Tib; symbol jj mdkatss otf-pas; connKtor m flow chart.

Packet is a bundle of data. Baud is the rate at which the medium can transfer groups of data. All other statements are true.

The word size in mini computers is 32 bits or more.

In digital computers uses the properties of electronic circuits to represent exactly two states - on and off.

The Control Unit along with Main Memory and Arithmetic Logic Unit is called as Central Processing Unit

A

B

B

73.

74.

75.

First we consider 64 and 72. The HCF for these two quantities is calculated as follows:

64) 72 (1 64

8)64(8

64

0

The HCF is 8, now consider 8 and 164 and obtain the HCF for these two quantities. 8) 164 (20 160

4)8(2

8

0

The highest common factor is 4 for the three quantities.

The Arithmetic Logic Unit (ALU) contains one or more storage locations are called as registers.

A

D

E

76.

77.

78.

The appropriate average for a set of ratios using the denominators of the ratio data as weights is weighted arithmetic mean.

Let r be the rate of interest

P_n = The value at the end of period n, P₀ = The value at the beginning of period n

^Pn = ^P0(¹⁺ r )ⁿ 5400 =1800(1+ r)⁶ (1+ r)⁶ = 5400/1800 = 3 (1+ r) = 3^1/6 = 1.20098

r = 1.20098 - 1 = 0.20098 = 20.098% = 20.09%.

1

2 6,

Model Question Paper Quantitative Methods - II (MSF1B2)

   Answer all 76 questions.

   Marks are indicated against each question.

Total Marks : 100

1. A random variable, Y, has the following probability distribution:

Y 20 40 60 80 100 Probability 0.15 0.20 0.30 0.25 0.10

15 values of Y have been observed. What is the probability that less than 12 observations are such that

(2marks)

(1 mark)

40 < Y < 80?
(a)	0.8441
(b)	0.1559
(c)	0.0668
(d)	0.4613
(e)	0.5387

2.    The t distribution is

(a)    Not a symmetrical distribution

(b)    A discrete probability distribution

(c)    A multimodal distribution

(d)    Different for different number of degrees of freedom

(e)    Positively skewed.

3.    Modern Books and Magazines sells a variety of books, magazines and newspapers. The manager of the shop is concerned about one particular newspaper, The City Times. This newspaper costs Rs.1.20 each to the shop and can be sold for Rs.1.50 each. Any copy of the newspaper not sold by the end of the day can be disposed off for Re.0.20 each to the paper packet manufacturers. The manager of the shop has recorded the daily sales of The City Times over the past 200 days and his observations are given below:

Number of copies sold in a day	Number of days sold
200	40
300	60
400	80
500	20
Total	200

It is assumed that the number of copies of the newspaper sold in a day is a discrete random variable which will assume only the numbers listed above, and the shop will stock only the same number of copies.

What is the optimal number of copies of the newspaper that should be stocked?

(a)    200

(b)    300

(c)    400

(d)    500

(2marks)

(e)    1,400.

⁴ Consider the following joint probability distribution.

X	-2	-1	0	-1	0
Y	1	0	1	2	0
P(X,Y)	0.1	0.2	0.1	0.3	0.3

If Z = (X + Y), then the value of V(Z) is

(a)    0.79

(b)    0.69

(c)    0.59

(d)    0.49

(e)    0.39.

⁵ Which of the following statements is/are true regarding assumptions of decision theory?

I.    The decision maker can define all decision alternatives or strategies which are being considered.

II.    The decision maker can define the various states of nature for the decision setting which are not under control.

III.    The decision maker can estimate quantitatively the consequences (benefits or costs) of selecting

any decision alternative and having any state of nature occurrence.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (II) and (III) above

(e)    All (I), (II) and (III) above.

⁶    Which of the following statements is/are true regarding normal distribution?

I.    It is a unimodal distribution.

II.    The mean of a normally distributed population lies at the center of its normal curve.

III.    The mean, median and mode of the distribution are never coincide.

IV.    The two tails of the distribution touches the horizontal axis.

(a)    Only (I) above

(b)    Only (III) above

(c)    Both (I) and (II) above

(d)    Both (III) and (IV) above

(e)    All (I), (II), (III) and (IV) above.

(1 mark)

⁷    A taxi cab company has 6 Ambassadors and 4 Fiats. If 3 of these taxi cabs are in the shop for repairs and ambassador is as likely to be in for repairs as a Fiat. Then the probability that two of them are Ambassadors is

(1 mark)

(a)	1
	8
(b)	1
	6
(c)	1
	4
(d)	1
	2
(e)	1
	10

⁸    The mean lifetime of a sample of 100 light bulbs produced by a company is found to be 1,580 hours with a standard deviation of 90 hours. We want to test the hypothesis that the mean lifetime of the bulbs produced by the company is 1,600 hours.

Which of the following conclusions can be drawn on the basis of the above test at a significance level of 5%?

(a)    The mean lifetime of the light bulbs is equal to 1,600 hours

(b)    The mean lifetime of the light bulbs is not equal to 1,600 hours

(c)    The mean lifetime of the light bulbs is significantly more than 1,580 hours

(d)    The mean lifetime of the light bulbs is equal to 1,580 hours.

(e)    The mean life time of the light bulbs is significantly less than 1,580 hours.

⁹    The following details are available with regard to a hypothesis test on population mean:

H0: ⁹ H₁: l< 9 n = 25 s² = 256

Significance level = 0.05

The population is normally distributed. It is later known that the true population mean is 5.

Which of the following is true with regard to the test?

(a)    There is insufficient information for doing the test

(b)    The normal distribution should be used

(c)    The test does not lead to either type I or type II error

(d)    The test leads to a type I error

(e)    The test leads to a type II error.

¹⁰-A    local credit card agency reported to the government that the unpaid balance for their customers is normally distributed with an average of Rs. 5,500 with a standard deviation of Rs. 500. If an auditor randomly sampled 10 of the credit card company's customers, what is the probability that the mean of the sample would be between Rs. 5,300 and Rs. 5,400?

(a)    0.1608

(b)    0.6608

(c)    0.3971

(d)    0.2363

(e)    0.6334.

(2marks)

^11-If    we accept H₀ : ^H = 20 against H : H- 20 at a given level of significance with a positive value of the test statistic, then a test with H₀ : ^H = 20 versus H : ^H > 20 using the same sample and the same level of significance

(a)    Will always accept H₀

(b)    Will always reject H₀

(c)    May or may not accept H₀

(d)    Will certainly lead to a Type I error

(e)    Will certainly lead to a Type II error.

(1 mark)

¹²-The    following details are available with regard to a hypothesis test on a population mean:

H₀: h = 20 H₁: h 20

o² = 81 n = 36

The null hypothesis is rejected if X < 17.06 or X > 22.94 . What is the probability of committing a type I error?

(a)    0.5

(b)    0.05

(c)    0.025

(d)    0.005

(e)    1.00.

(1 mark)

¹³-The    following details are available with regard to a hypothesis test on means of two populations:

H₀: ^H2 =^-1 H₁: H-H₂ *-1

n₁ = 64 x;² = 1852 xj = 320 n₂ = 36 x² = 891 X2 = 144

The samples collected from the two populations are independent.

What is the value of the test statistic?

(a)    -3.578

(b)    3.578

(c)    0

(d)    -0.354

(e)    1.789.

¹⁴-A    researcher is interested in determining the average urban household income for the state Uttar Pradesh (U.P) of the country. He divides U.P. into homogeneous sectors and then randomly chooses 3 cities from each sector to sample. From each city, he randomly chooses 1000 families to survey. This type of sampling is referred to as

(a)    Systematic sampling

(b)    Cluster sampling

(c)    Simple random sampling

(d)    Stratified random sampling

(e)    Judgment sampling.

(1 mark)

15-A    Ketchup manufacturer is in the process of deciding whether to produce a new extra-spicy brand. The companys marketing-research department used a national telephone survey of 6,000 households and found that the extra-spicy ketchup would be purchased by 335 of them. A much more extensive study made 2 years ago showed that 5 percent of the house holds would purchase the brand then. We want to test at a 2 percent significance level, should the company conclude that there is an increased interest in the extra-spicy flavor?

Which of the following is an appropriate null hypothesis for the above test?

(1 mark)

(a)	H0 :	: p = 0.5
(b)	H0 :	: p > 0.5
(c)	H1 :	: p > 0.05
(d)	H0	: p = 0.05
(e)	H1	: p < 0.05

¹⁶-As    the sample size increases, the interval estimate for the population mean at a given confidence level will

(a)    Increase in width

(b)    Remain the same

(c)    Increase initially and then decrease in width

(d)    Decrease in width

(e)    Double in width for increase in sample size by one observation.

(1 mark)

¹⁷-Which    of the following errors can occur at the time of observation, approximation and processing of data?

(a)    Sampling errors

(b)    Non-sampling errors

(c)    Random occurrence errors

(d)    Systematic errors

(e)    Estimation errors.

(1 mark)

18-which    of the following statements is true according to the Central Limit Theorem?

(a)    The distribution of the sample is always symmetric

(b)    The distribution of the sample is symmetric only for small sample sizes

(c)    The sampling distribution of the mean approaches normality as the sample size increases

(d)    The sampling distribution of the mean approaches normality as the sample size decreases

(e)    The sampling distribution of the mean never approaches normality.

¹⁹-Which    of the following statements is/are true?

I.    If a right tailed test is rejected at 1% significance level, then it is always accepted at 5% significance level.

II.    If a left tailed test is rejected at 5% significance level, then it is always rejected at 1% significance level.

III.    If a two tailed test is accepted at 10% significance level, then it is always accepted at 5% significance level.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.

²⁰'The manager of Pioneer Enterprises wants to formulate a relationship between total cost and sales revenue, which may be used to estimate the total cost for a given level of sales. He collects the following information from the past records.

Sales (Rs. in lakhs)	20	23	38	28	45	40
Total cost (Rs. in lakhs)	17	22	35	22	39	36

Formulate a relationship between sales and total cost with sales as the independent variable using simple regression technique.

What is the standard error of estimate for the regression relationship?

(a)    1.858

(b)    2.747

(c)    3.636

(d)    4.525

(e)    5.414.

(2marks)

²¹'The following table represents the heights of a sample of 12 fathers and their eldest sons:

Father (inches)	65	63	67	64	68	62	70	66	68	67	69	71
Son (inches)	68	66	68	65	69	66	68	65	71	67	68	70

The correlation coefficient between the heights of the fathers and sons is

(a)    0.7026

(b)    0.4946

(c)    0.5486

(d)    0.7856

(e)    0.8956.

(2marks)

²²'Mr. Ganapati Mendali, a second year MBA student, is doing a study on companies going public for the first time. He is curious to see whether there is a significant relationship between the sizes of the offering ( Rs. in crores ) and the price per share after the issue. The data are given below:

(2marks)

Size (Rs. in crores ) 108.00 39.00 68.40 51.00 10.40 4.40 Price ( Rs.) 12.00 13.00 19.00 12.00 6.50 4.00

The coefficient of determination for the above data set is

(a)	0.4523
(b)	0.5842
(c)	0.6753
(d)	0.7664
(e)	0.8575.
23'Which of the following statements is/are true?
I.	F = 0 o RSS = 0 o R2 = 0.
II.	F = 1 o RSS = 0oR2 = 0.
III.	F = 0 o RSS = 0 o R2 = 1.
(a)	Only (I) above
(b)	Only (II) above
(c)	Only (III) above
(d)	Both (I) and (II) above
(e)	All (I), (II) and (III) above.

'The following details are available with regard to an estimated regression relationship Y = a + bX

Error sum of squares = 56 n = 8

What is the 90 percent prediction interval for the value of Y at X = 2?

(a)    (17.56, 29.988)

(b)    (17.56, 30.125)

(c)    (18.064, 29.936)

(d)    (18.064, 30.125)

(e)    (18.064, 30.756).

²⁵-The coefficient of correlation between variables X and Y is 0.80.

(1 mark)

Cov	(X, Y)
X =	5
What is the
(a)	5
(b)	20
(c)	25
(d)	50
(e)	100.

²⁶-In    a University, correlation coefficient between college entrance exam grades and scholastic achievement was found to be -1.08. On the basis of this you would tell the university that:

(a)    The entrance exam is a good predictor of success

(b)    They correlation coefficient is incorrect

(c)    The exam is a poor predictor of success

(d)    Students who do best on this exam will make the worst students.

(e)    Students of this university are underachievers.

(1 mark)

²⁷-Which    of the following statements is/are true regarding Scatter Diagram?

I.    One of the easiest ways of studying the correlation between the two variables is with the help of a scatter diagram.

II.    It gives an indication of the nature of the potential relationship between the variables.

III.    Using scatter diagram if the variables are related, we cannot see what kind of line, or estimating equation, describes this relationship.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.

(1 mark)

8'For a data ^2X = ^{725, Y} = ⁷50^{, n} = 1.0. In the construction of a simple linear regression line,

Y = a + bX , the coefficient b is 0.81, then the value of coefficient a is

(a)    133.725

(b)    162.750

(c)    6.561

(d)    16.275

(e)    Data is insufficient.

(1 mark)

²⁹-The simple correlation coefficients between temperature (X₁), corn yield (X₂) and rainfall (X₃) are r₁₂ (Between X₁ and X₂) = 0.59, r₁₃ (Between X₁ and X₃) = 0.46 and r₂₃ (Between X₂ and X₃) = 0.77.

The multiple correlation coefficient R₁₂₃ for the three variables is

(a)    0.5561

(b)    0.5671

(c)    0.5781

(d)    0.5901

(e)    0.6021.

30-A    multiple regression relationship contains two independent variables. The standard error of estimate is 4.8. Error sum of squares = 576.

What is the number of data points?

(a)    24

(b)    25

(c)    26

(d)    27

(e)    28.

³¹-For    a regression relationship the ratio of regression sum of squares to error sum of squares is 3 : 2. The total sum of squares is 90. What is the regression sum of squares?

(a)    54

(b)    45

(c)    36

(d)    18

(1 mark)

(e) 27.

³²-The    following regression relationship between two variables, X and Y, has been obtained:

Y = 1,236 - 104X

Where X is the independent variable and Y is the dependent variable.

The following details are also available:

Y² = 19,00,400

Y = 612

EXY = 18,100 Number of observations = 5 What is the approximate 90 percent prediction interval for Y if X = 7.50?

(a)    (412.26, 409.38)

(b)    (421.62, 490.38)

(c)    (121.26, 499.38)

(d)    (222.26, 444,38)

(e)    (123.45, 543.21).

(2marks)

33-Which    of the following will be true, if in a regression relationship error sum of squares is equal to total sum of squares?

(a)    Coefficient of determination = 1

(b)    0 < Coefficient of determination < 1

(c)    Coefficient of determination = 0

(d)    Coefficient of determination < 0

(e)    Coefficient of determination > 1.

(1 mark)

³⁴-If    the coefficient of correlation between two variables X and Y is zero, then which of the following is true?

^(a)    c²x = 0

(b)    c²y = 0

^(c)    X = 0

(^d)    Y = 0

(e)    Cov (X, Y) = 0.

³⁵-Which    of the following is true with regard to multicollinearity in multiple regression analysis?

(a)    It increases the influence of the individual variables in the model

(b)    It reduces the accuracy of the model

(c)    It increases the reliability of the regression coefficients

(d)    It reduces the effectiveness of sensitivity analysis of the model

(e) It arises, if there is a low correlation among the independent variables.

³⁶-If    Error sum of Squares is 83.88 and Total sum of Squares is 1134.66, then the value of Coefficient of Determination is

(1 mark)

(a)    0.926

(b)    0.074

(c)    0.740

(d)    0.092

(1 mark)

(e) 0.0854.

³⁷-Which    of the following statements is/are true regarding Coefficient of Determination?

I.    It is the square of the correlation coefficient.

II.    It explains to what extent the variation of a dependent variable is expressed by the independent variable.

III.    A low value of it shows a good linear relationship between the two variables.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.

(1 mark)

38-which    of the following is/are advantage(s) of chain base method in index numbers?

I.    The link relatives calculated by using the chain base method, enable comparisons over successive years.

II.    It enables the introduction of new items and the deletion of old items without altering the original series.

III.    Whenever found necessary, weights can be adjusted in chain base method.

IV.    Seasonal variations have minimal impact on chain index numbers.

(a)    Only (I) above

(b)    Only (II) above

(c)    Both (III) and (IV) above

(d)    (II), (III) and (IV) above

(e)    All (I), (II), (III) and (IV) above.

(1 mark)

³⁹-A    food grains merchant wants to know the overall change in prices of the commodities he deals in. He provides the following information:

Commodity	Year
	2006		2008
	Price (Rs./kg.)	ty ak u (k a	Price (Rs./kg.)	ty ak u (k a
Wheat	7	5000	10	4800
Rice	10	6000	14	5500
Pulses	25	3000	28	3500
Sugar	10	3000	14	2400
Salt	2	500	4	600

What is the Fishers ideal price index for the year 2008 using 2006 as the base year?

(a)    115.5032

(b)    121.5032

(c)    129.5032

(d)    135.5032

(e)    139.5032.

⁴⁰-Estimate unweighted aggregate price index number from the following data.

Commodities (in Units)	Price in Base year (2006)	Price in Current Year (2008)
Rice (kg)	16.00	36.00
Wheat (kg)	12.25	22.10
Milk (lit.)	15.75	23.75

Egg (doz.)	15.30	28.50
Cheese (kg)	25.10	38.50

(a)    75.4826

(b)    99.8726

(c)    103.7626

(d)    125.8626

(e)    176.3626.

⁴¹-If the ratio between Laspeyres price index number and Paasches price index number is 28 : 27.

Commodity	Base Year		Current Year
	Price	Quantity	Price	Quantity
X	1	10	2	5
Y	1	5	?	2

What is the price of the commodity Y in current year?

(a)    1

(b)    2

(c)    3

(d)    4

(e)    5.

(1 mark)

⁴²-Mr. Neelam Singh a dealer of grocery-items requires an overall comparison of the prices of the commodities, between the years 2006 and 2008. The following information is provided by him:

Commodities	Sugar	Salt	Wheat	Rice	Pulses
P0(Q0 + Q1)	13750	9436	15000	14256	28700
P1(Q0 + Q1)	18750	13500	25000	28435	38700

The Marshall-Edgeworth price index for the year 2008, using the year 2006 as the base year, is

(a)    123.2530

(b)    138.6530

(c)    153.2930

(d)    165.4530

(e)    175.6430.

(1 mark)

⁴³-Consider the following data.

Commodities	Base Year (2006)		Current Year (2008)
	Price	Quantity	Price	Quantity
A	3	18	9	15
B	5	6	5	9
C	4	20	12	26
D	2	14	4	15

What is the weighted average of relatives price index that is to be calculated with the base values?

(a)    125.1667

(b)    175.1667

(c)    200.1667

(d)    225.1667

(e)    254.1667.

(1 mark)

⁴⁴-Which    of the following statements is false regarding index numbers?

(a)    Using index numbers we can establish trends

(b)    Index numbers guide policy making

(c)    Index numbers are not used to determine the purchasing power of a rupee

(d)    Index numbers play a vital role in adjusting the original data to reflect reality

(e)    Index number is calculated as a ratio of the current value to a base value and expressed as a percentage.

⁴⁵-An    aggregates price index, where the price for each item is weighted by its base period quantity is

(a)    Paasches price index

(b)    Unweighted aggregates price index

(c)    Fishers ideal price index

(d)    Laspeyres price index

(e)    Unweighted average of relatives price index.

⁴⁶'If Z P₀Q₀ = 218, Z P₁Q₀ = 391, Z P₁Q₁ = 371 and Z P₀Q₁ = 271, then the value index is

(a)    130.4435

(b)    151.7735

(c)    160.5835

(d)    170.1835

(e)    195.9435.

(1 mark)

(1 mark)

⁴⁷'Index number for the base year is always

(a)    1

(b)    10

(c)    100

(d)    1000

(e) 10000.

⁴⁸'A time series for the years 1997-2008 had the following Relative Cyclical Residuals (RCR), in chronological order as follows:

Year	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008
RCR	-1%	-2%	1%	2%	-1%	-2%	1%	2%	-1%	-2%	1%	2%

What will be the RCR for 2009?

(a)    +3%

(b)    -1%

(c)    -2%

(d)    +2%

(e) Cannot be determined on the basis of the given information.

(2marks)

⁴⁹'In general, if the actual value of the dependent variable in an year in a time series is more than the value estimated by the trend equation then the Relative Cyclical Residual (RCR) is

(a)    More than 0%

(b)    Less than 0%

(c)    Equal to 0%

(d)    Always equal to 100%

(e)    Always equal to 10%.

(1 mark)

⁵⁰'If the Relative Cyclical Residual (RCR) for an year is zero, then the percent of trend for that year is

(a)    100

(b)    50

(c)    10

(d)    5

(e)    1.

⁵¹'The linear trend estimating equation for a time series is given below:

Y = 139 + 7.5x, where x = Year - 2006 The observed value of Y for the year 2008 is 160.

What is the Relative Cyclical Residual (RCR) for the year 2008?

(a)    -2.1698

(b)    10.8961

(c)    3.8961

(d)    96.2561

⁵²-The    seasonal index sales of a company for four quarters of a year are 200, 180, 160 and 260 respectively. If the total sales in the first quarter are worth Rs.50,000, estimate the worth of sales expected during the2^nd quarter of the year.

(a)    Rs. 45,000

(b)    Rs. 55,000

(c)    Rs. 35,000

(d)    Rs. 55,500

(e)    Rs. 65,000.

(2marks)

⁵³-SE    company has recorded the following numbers (in Rs. millions) of total sales of its line of washing machines over 5 years:

Year	2004	2005	2006	2007	2008
Sales	3.5	3.8	4.0	3.7	3.9

Based on the above information, sales in which of the following year was closest to the trend line?

(a)    2004

(b)    2005

(c)    2006

(d)    2007

(e)    2008.

(3marks)

⁵⁴-The following information pertains to the actual and estimated sales on the basis of trend line, of wallets from the year 2001 to 2008.

Year	2001	2002	2003	2004	2005	2006	2007	2008
Actual Sales (Rs. in lakhs)	7.5	7.8	8.2	8.2	8.4	8.5	8.7	9.1
Estimated Sales (Rs. in lakhs)	7.6	7.8	8.0	8.2	8.4	8.6	8.8	9.0

Under Relative cyclical Residual (RCR) measure, in which year does the largest fluctuation from trend occur?

(a)    2001

(b)    2003

(c)    2005

(d)    2006

(1 mark)

(e) 2008.

⁵⁵-A business school is studying the number of enrolments to its various programs during six years. The following data are collected from past records:

Year 2003 2004 2005 2006 2007 2008 Number of enrolments in 000 185 175 190 180 185 200

What is the expected number of enrolments in the year 2009?

(a)    155.332

(b)    165.332

(c)    175.332

(d)    185.332

(e)    195.332.

⁵⁶-Consider the following data.

4

5

8

6

2

7

3

1

9

What is the moving average of order three associated with 7 of the following data?

(a)    5.667

(b)    6.333

(c)    5.333

(d)    5.000

(e) 4.000.

⁵⁷-If deseasonalized value in time series is 2.00 and actual data is 1.58, the seasonal index is

(1 mark)

(a)	79
(b)	61
(c)	19
(d)	12
(e)	2.

^58.Consider the following data.

n = 16,X = 125.85, R = 6.4 and d₂ = 3.532

The Center Line ( CL) and the Lower Control Limit ( LCL) are

(a)    7.866 and 124.073

(b)    7.866 and 127.627

(c)    125.85 and 124.491

(d)    125.85 and 127.627

(e)    0.40 and 124.073.

(2marks)

59.

For a data p = 0.45 and Upper Control Limit (UCL) = 0.737. What is the value of n (number of samples)? (Round off your answer to the nearest integer)

(1 mark)

(a)	27
(b)	31
(c)	34
(d)	38
(e)	42.
60-Each	of 20

these lots are as follows:

405	418	324	332	292	340	282	300	320	296
397	434	294	324	220	460	258	226	460	190

Calculate the value of Center Line (CL) for the p chart for the fraction of defectives.

0.1321

0.1432

0.1643

0.1552

0.1762.

(a)

(b)

(c)

(d) (e)

(1 mark)

The following data provides the values of sample mean (^x) , and range (R), for samples of size 5 each:

61.

(a)	16.20
(b)	15.33
(c)	14.64
(d)	12.65
(e)	10.66.
62.The	following

Sample No. 1 2 3 4 5 6 7 8 9 10 Mean (x) 11.2 11.8 10.8 11.6 11.0 9.6 10.4 9.6 10.6 10.0 Range (R) 7 4 8 5 7 4 8 4 7 9

The value for the Center Line (CL) of the x chart is

The following data provides the values of sample range (R), for samples of size 6 each.

Sample No. 1 2 3 4 5 6 7 8 9 10 Range(R) 7 4 8 5 7 4 8 4 7 9

The value of Upper Control Limit (UCL) for the R chart is (Use the relevant D3 or D4 factor)

(a)    13.3182

(b)    12.6252

(c)    12.4365

(d)    11.5648

(e)    11.6428.

⁶³-The    manager of a warehouse wants to construct a control chart for proportion of defectives obtained in repeated random samples of size 150 from a process, which is considered to be under control when the proportion of defectives, p, is equal to 0.15.

Calculate the Lower Control Limit (LCL) for the p chart.

(a)    0.1625

(b)    0.1425

(c)    0.1225

(d)    0.0825

(e)    0.0625.

(1 mark)

⁶⁴-The    manager of a food chain outlet wants to ensure that the variability in the service time by their bearers is in control. He does a sampling of the average time taken by the bearers in serving the customers in the outlet. He finds that the mean of the sample range to be 1.5 minutes. If he has collected five samples each of ten observations to conduct the test then what is the Upper Control Limit (UCL) of the R chart? (Given that d₂ = 3.078 and d₃ = 0.797 for sample size of 10)

(a)    0.3352

(b)    1.0052

(c)    1.5002

(d)    2.0052

(e)    2.6652.

(1 mark)

65-Which    of the following charts deal(s) with qualitative factor(s) possessed by the data?

(1 mark)

I.	R charts.
II.	p charts.
III.	x charts.
(a)	Only (I) above
(b)	Only (II) above
(c)	Only (III) above
(d)	Both (I) and (III) above
(e)	Both (II) and (III) above.

⁶⁶-For    generating X chart 40 samples are taken. The sum of all the observations is 560 and the value to be used for the centre line is 2.8. The size of each sample is

(a)    5

(b)    10

(c)    18

(d)    20

(1 mark)

(e) 36.

⁶⁷-The    demand for a particular spare part in a factory was found to vary from day to day. In a sample study the following information was obtained:

Days	Mon	Tue	Wed	Thurs	Fri	Sat
No. of parts demanded	1124	1125	1110	1120	1126	1115

We need to test the hypothesis that the number of parts demanded does not depend on the day of the week. What is the value of the test statistic for the above test?

(a)    0.159

(b)    0.179

(c)    0.279

(d)    0.259

(e)    0.079.

A study compared the effects of four 1-month point-of-purchase promotions on sales. The unit sales for five stores using all four promotions in different months follow:

Free samples	78	87	81	89	85
One-pack gift	94	91	87	90	88
Rupees off	74	78	70	82	76
Refund by mail	79	83	78	69	81

A test of ANOVA has to be performed.

What is the estimated population variance using the variance between the sample means?

(a)    194

(b)    196

(c)    198

(d)    200

(1 mark)

(e) 202.

⁶⁹'The fitness levels of the soldiers of two battalions of the Indian Army are believed to have same variance. The senior officers of the Indian Army want to compare the actual variances in the fitness levels of the two battalions. A sample of 16 soldiers from the first battalion had a variance of 3.75 in their fitness levels. A sample of 10 soldiers from the second battalion had a variance of 5.38 in their fitness levels. The officer wants to test the belief at a significance level of 10%.

What conclusion can be drawn on the basis of the above test?

(3marks)

(a)	There is no significant difference in the variances of the fitness levels of the two battalions
(b)	The two sample variances are incorrect
(c)	The variance in the fitness levels of first battalion is less than the variance in the second
	battalion
(d)	The variance in the fitness levels of first battalion is more than the variance in the second
	battalion
(e)	No conclusion can be drawn because the population means are not known.
70'The following details are available with regard to a multiple regression analysis:

Regression sum of squares    = 21.6

Error sum of squares    = 2.296

Number of observations    = 10

Number of independent variables = 2

What is the value of the F statistic for the multiple regression model?

(a)    3.293

(b)    32.9268

(c)    10.8268

(d)    2.2968

(e)    21.668.

(1 mark)

⁷¹'The following data shows the number of claims processed per day by four employees of an insurance company, observed for a number of days. It has to be tested whether the average number of claims processed per day by all the four employees is same.

Employee 1:	15	17	14	12
Employee 2:	12	10	13	17
Employee 3:	11	14	13	15	12
Employee 4:	13	12	13	15	10	9

What is the critical value for the appropriate statistical test at 5% level of significance?

(a)    2.87

(b)    3.29

(c)    4.43

(d)    4.77

(e)    5.29.

⁷²'In a chi-square test, the contingency table has 4 rows and 4 columns. The number of degrees of freedom is

3

4 8 9

16.

(a)

(b)

(c)

(d) (e)

⁷³-In    a test involving analysis of variance the following are found:

Estimate of the population variance based on the variance among sample means = 32.5 Estimate of the population variance based on the variance within the samples = 14.4

The F-ratio is equal to

(a)    0.44

(b)    0.0694

(c)    0.64

(d)    1.2569

(e)    2.2569.

(1 mark)

⁷⁴-If    X follows continuous uniform distribution. Its probability density function is given by

1 < X < 5 otherwise What is the variance of the distribution?

f(x) =

1

^w 2

2

<^b> 3

4 3

5 3 4.

(c)

(d)

(e)

(2marks)

75-which    of the following statements is/are true regarding simulation?

I.    If the mathematical model set up could always be optimized by the analytical approach, then, there would be no need for simulation.

II.    Only when interrelationships are too complex or there is uncertainty regarding the values that could be assumed by the variables or both, we would have to resort to simulation.

III.    Simulations cannot be used to break down complex systems into sub-systems and study the

behavior of each of these subsystems.

(a)    Only (I) above

(b)    Only (II) above

(c)    Only (III) above

(d)    Both (I) and (II) above

(e)    All (I), (II) and (III) above.

⁷⁶-Consider    the following probability distribution of a variable X :

X	5.0	10.0	15.0	20.0	25.0	30.0	35.0
p	0.1	0.05	0.05	0.1	0.3	0.2	0.2

In a Monte Carlo simulation process the number 49 was generated in a particular run from a uniform distribution of 0 - 99. The value of X in this run will be

(a)    35

(b)    20

(c)    25

(d)    15

END OF QUESTION PAPER

Suggested Answers Quantitative Methods - II (MSF1B2)

ANSWER    REASON

1.    E The event 40 < Y < 80 occurs when

Y = 40 or 60 or 80

P(40 < Y < 80 ) = 0.20 + 0.30 + 0.25 = 0.75 Let Z denote the number of observations of Y which satisfy the condition 40 < Y < 80.

Z follows a binomial distribution with number of trials = 15 and Probability of success = 0.75.

P (Z <12) = P (Z <11) = 1-P(Z > 12)

= 1- [P(Z = 12)+ P(Z = 13) + P(Z = 14) + P(Z = 15)]

= 1- [0.2252 + 0. 1559 + 0.0668 + 0.0134]

= 1 - 0.4613 = 0.5387.

2.    D The t distribution is different for different degrees of freedom.

3.    B Profit per newspaper sold = 1.50 - 1.20 = Re.0.30

Loss per unsold newspaper = 1.20 - 0.20 = Re.1.00 Deriving the probabilities:

Daily sales	200	300	400	500
Number of days sold (f)	40	60	80	20	Ef = 200
Probability
f f \	40	60	80	20
L f i	-	-	-	-	Ep = 1.00
I EfJ	200 = 0.20	200 = 0.30	200 = 0.40	200 = 0.10
Conditional profit table
	Daily demand		(Probability)		Expected
Stock level	200	300	400	500	daily profit
	(0.20)	(0.30)	(0.40)	(0.10)	(Rs.)
200	60	60	60	60	60
300	-40	90	90	90	64
400	-140	-10	120	120	29
500	-240	-110	20	150	-58

From the above table we can see that the maximum expected daily profit (Rs.64) is associated with the stock level of 300 newspapers. Hence the optimal number of the newspaper, The City Times, that should be stocked is 300.

Working notes:

Conditional profit for any stock level = Number of newspapers demanded and sold x 0.30 -Number of unsold newspapers x 1.00.

Given that Z = X+Y.

Notice that Z takes on the values -1, 1 and 0 with

)robabilities 0.3, 0.4 and 0.3 respectively.

Z	-1	0	1
P(Z)	0.3	0.3	0.4

E(Z)= 1x 0.3 + 0 x 0.3 + 1x 0.4 =0.1

V(Z)= (-1 - 0.1)² (0.3) + (0 -0.1)² (0.3) + (1 - 0.1)² (0.4) =0.69 Or

(X-(-0.7))² P Y

X

P(X)

XP(X)

P(Y)

YP(Y) (Y-0.8)² P

			(X)				(Y)
-2	0.1	-0.2	0.169	0	0.5	0	0.32
-1	0.5	-0.5	0.045	1	0.2	0.2	0.008
0	0.4	0	0.196	2	0.3	0.6	0.432
Total		-0.7	0.41	Total		0.8	0.76

To compute Cov(X,Y), we must examine the joint distribution COV(X, Y) = (-2 + 0.7 )(1 - 0.8)( 0.1) + (-1 + 0.7)(-0.8) (0.2) + (0.7 )(1 - 0.8)( 0.1) + (-1+0.7)(2 - 0.8)(0.3) + ( 0.7 )(-0.8)( 0.3)

= (-0.24)

V(Z) = V (X+Y)=V (X)+V (Y)+2Cov(X,Y) = 0.41+0.76+2x(-0.24) = 0.69.

The following statements are true regarding assumptions of decision theory.

5. E

I.

The decision maker can define all decision alternatives or strategies which are being considered.

The decision maker can define the various states of nature for the decision setting which are not under control.

II.

The decision maker can estimate quantitatively the consequences (benefits or costs) of selecting any decision alternative and having any state of nature occurrence.

So option (e) is correct.

The following statements are true regarding normal distribution.

I.    It is a unimodal distribution.

II.    The mean of a normally distributed population lies at the center of its normal curve.

Given statements (III) and (IV) are false. Since correct statements are

The mean, median and mode of the distribution are coincide.

The two tails of the distribution extend indefinitely and never touches the horizontal axis.

Hence Option (c) is correct.

Given that N (total number of taxi cabs) = 10,

M( number of Ambassador cars) = 6, n (sample size) = 3, x (number of Ambassadors ) = 2

III.

6. C

7. D

C

(n-x)

N

M_C (N-M)

^CY

P(X = x) =

^Cn

6 c (10-6)c

^C2 ^C(3-2) 15 X 4 1

10

C

3

120 2

The appropriate null hypothesis for the given test of hypothesis is given by, H0 : |J, = 1,600.

8. B

The appropriate alternative hypothesis for the given test of hypothesis is given by, H1 : |J, 1,600. Given that |J, = 1,600, ^x = 1,580, s = 90, n = 100.

-- = -- = ₉.

The standard error of mean = 4n VTCG

= -2.22

z = -

9

o-

The test statistic for this test is,

The critical value of z = 1.96 for a two tailed test at a 5% level of significance.

Since the test statistic z = - 2.22 falls in the rejection region, we reject the null hypothesis and conclude at 5% level of significance that the mean lifetime of the light bulbs is not equal to 1,600 hours.

J

J

H,

<

The sample is small and the population variance is not known. The sample variance is specified.

The population is normally distributed. Hence we should use the t distribution with 25 - 1 = 24 d.o.f.

t = O = 3.20 = -1.688 At a = 0.05, the critical value is -1.711.

The test statistic is more than the left tail critical value. So it falls in the acceptance region.

We accept H₀. The true mean is 5. So H₀ is false. Hence the test leads to a type II error.

A Because the sample size is small we cannot apply the CLT. However, since the population is normally distributed the sampling distribution of mean will also be normally distributed with mean

_ o

= population mean and standard deviation >/n E (x) =

256

I 25 = 3.20 3.60 - 9

5500

500

158.11

,P (5300 < x < 5400) = ₁₅₈₁₁

P(-1.265 < z < -0.632)

P(-1.265 < z < 0) - P(-0.632 < z < 0) P(0 < z < 1.265) - P(0 < z < 0.632)

,5300 - 5500 5400 - 5500

P |-< z <-

158.11

s

= ~Jn =

x-J

= Ox

10.

J =

o

yfn

VIq

0.3962 + (0-3980 - -3962) (1.265 -1.26) (1.27 -1.26) 0.2357 + (-2389 - -2357) (.632 - .63) (.64 - 0.63)

---

= 0.3971 - 0.2363 = 0.1608.

11.

12.

C If we accept H₀:j, = 20 against of Hj, * 20 at a given level of significance with a positive value of the test statistic, then a test with H: j = 20 versus > 20 using the same sample and the same level of significance may or may not accept H because in a one tailed test the critical region on the relevant tail is larger than a two tailed test for the same level of significance.

B Probability of committing a type I error = Probability of rejecting the null hypothesis when it is true

2

o

By the central limit theorem _x is normally distributed with mean = J and variance = n Hence Probability of rejecting the null hypothesis when it is true =

P(x < 17.06 or x > 22.94) = P(x < 17.06) + P(x > 22.94)

17.06 - 20    22.94- 20 .

= P(- < z) + P(-= > z)

n

n

-2.94    2.94

P(j=- < z) + P== > z)

= P(z < -1.96) + P(z > 1.96) = 0.025 + 0.025 = 0.05

13. B Estimated standard error of difference between means:

2 s² s² 4 9 a__ = + ii = + JL = 0.3125

^x1-x2 n₁ n₂ 64 36

2

1

s2 =-

n1 -1 1

s? =

ⁿ2 ^-1

2

2 1 1852 - 64 ( 320 n1x1 -1 = 63 V "64 2 1 144 j n2x2 = 35 1 OC 1 - 3 J

= 4 = 9 2 2

a - - =V0.3125 = 0.559

x1-x2

Value of the test statistic =

320

64

144

36

- (-1)

( ^x1 - ^x2 )-(1 -2 )

2

= 3.578

0.559

0.559

- a

14.    D This type of sampling is referred to as stratified random sampling because the entire population is

divided in to classes (sectors) or strata which are homogeneous in nature and samples a fixed number of observations from each stratum.

15.    D The appropriate null hypothesis for the given test of hypothesis is given by, H₀: p= 0.05.

The appropriate alternative hypothesis for the given test of hypothesis is given by, H₁: p > 0.05.

As the sample size increases, the interval estimate for the population mean at a given confidence level will decrease in width

16. D

17.

18.

19. C

Non sampling errors occur at the time of observation, approximation and processing of data. According to the CLT the sampling distribution of mean approaches Normality as the sample size increases.

Given statement (III) is true.

If a two tailed test is accepted at 10% significance level, then it is always accepted at 5% significance level.

Given statements (I) and (II) are false. Since correct statements are

If a right tailed test is rejected at 1% significance level, then it is always rejected at 5% significance level.

If a left tailed test is rejected at 5% significance level, then it may or may not rejected at 1% significance level.

Hence Option (c) is correct.

20. A

The equation of the regression line is ^Y = a + bX where, X = Sales (Rs. in lakhs)

Y = Total costs (Rs. in lakhs)

n2 XY - 2 XY

b = ⁿ2 ^x2-(2 ^x) ; a = Y - bX.

2 ^X = 194; 2 ^Y= 171;    n = 6;

2^XY = 5987 ; 2 ^x2 = 6782; Y = 28.5.

6 (5987)-(194) (171) 2748

b = 6 (6782)-(194) (194) = 3 -(0.899) 161 j = -0.568

Standard error of estimate (S_e) = V    n - 2

XY² = 5299

5299 (-0.568) (171) (0.899 )(5987) Se = V    62

= 1.858.

21. A

X (X - ^X)(Y - Y)

r =

a/X (X - X) X (Y - Y )²

	X	Y	(1 - X)	(Y - Y)	(X - X )x( Y - Y)	(X -X )2	(Y - Y )2
	65	68	-1.67	0.42	-0.7014	2.7889	0.1764
	63	66	-3.67	-1.58	5.7986	13.4689	2.4964
	67	68	0.33	0.42	0.1386	0.1089	0.1764
	64	65	-2.67	-2.58	6.8886	7.1289	6.6564
	68	69	1.33	1.42	1.8886	1.7689	2.0164
	62	66	-4.67	-1.58	7.3786	21.8089	2.4964
	70	68	3.33	0.42	1.3986	11.0889	0.1764
	66	65	-0.67	-2.58	1.7286	0.4489	6.6564
	68	71	1.33	3.42	4.5486	1.7689	11.6964
	67	67	0.33	-0.58	-0.1914	0.1089	0.3364
	69	68	2.33	0.42	0.9786	5.4289	0.1764
	71	70	4.33	2.42	10.4786	18.7489	5.8564
Total	800	811			40.3332	84.6668	38.9168

40.3332    _nn r = ,    = = 0.7026. V84.6668 x 38.9168

22. A To compute the coefficient of correlation between the two variables we tabulate them as below:

Size (X) Price (Y) x = X - X y = Y - Y x2 y2 xy 108 12 61.13 0.92 3736.8769 0.8464 56.2396 39 13 -7.87 1.92 61.9369 3.6864 -15.1104 68.4 19 21.53 7.92 463.5409 62.7264 170.5176 51.0 12 4.13 0.92 17.0569 0.8464 3.7996 10.4 6.5 -36.47 -4.58 1330.0609 20.9764 167.0326 4.40 4.0 -42.47 -7.08 1803.7009 50.1264 300.6876 Total 7413.1734 139.2084 683.1666

We know that the coefficient of correlation Z xy

r =

Z x Z y

683.1666

r=

V7413.1734 X139.2084 0.6725 The coefficient of determination = r² = (0.6725)² = 0.4523.

23. A Given statement (I) is correct. F = 0 o RSS = 0 o R² = 0 Hence option (a) is correct.

24.

C Se =m = J-* = 3.055 ^e \n-2 V 8-2

90% prediction interval = ^{t X S}e = ^{24 t}6,0.10^Se

24 ( 1.943 X 3.055) = (18.064, 29.936).

25. C Given that, r_Xy = 0.80

0.80=

^OX ^Oy

20

o_y =-

^y

5 X 0.80

Oy =5 Oy² = 25.

26.    B As correlation coefficient should always fall between +1 to -1 the value calculated by the

statistician is not correct.

27.    D The following statements are true regarding Scatter Diagram.

I.    One of the easiest ways of studying the correlation between the two variables is with the help of a scatter diagram.

II.    It gives an indication of the nature of the potential relationship between the variables.

Given Statement (III) is false. Since correct statement is

Using scatter diagram if the variables are related, we can see what kind of line, or estimating equation, describes this relationship.

So option (d) is correct.

²⁸.    ^D Given that Z ^X = ^725, Z ^Y=^{750, n}=¹⁰.

- 725    - 750

X =-= 72.5 Y =-= 75.

10    and 10

In the construction of a simple linear regression line, Y = a + bX, the coefficient b is 0.81 then the coefficient a is given by a = Y - bX a = 75-( 0.81)x 72.5 = 16.275.

29.    D We have to calculate the multiple correlation coefficient treating X₁ as dependent and X₂ and X₃ as

independent variables, i.e., we have to find

R = ^r 12 +^r 13 ^{2 r}12 ^r13 ^r23

¹²³ V 1 - r²23

Substituting the given values

⁽.5⁹⁾² + ⁽.^{46)2 - 2(0}.5_z⁹x⁰.²x .⁷⁷⁾ = 0.₅901.

¹    1 - (0.77)²

30. E In multiple regression relationship:

Z (Y - ^Y)

V n - k-1