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CA CPT : Volume 2 - Model Test Paper 8 (with Answers & Explanations)

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BOARD OF STUDIES THE INSTITUTE OF CHARTERED ACCOUNTANTS OF INDIA COMMON PROFICIENCY TEST Model Test Paper BOS/CPT 8 Time : 4 hours Maximum Marks : 200 The test is divided into four sections. Questions 1 to 200 have only one correct answer and carry + 1 mark for each correct answer and 0.25 mark for each wrong answer. SECTION A : FUNDAMENTALS OF ACCOUNTING (60 MARKS) 1. Golden rules of accounting are a) b) c) d) 2. The following error affect the trial balance (a) (c) 3. (b) (d) Error of principal All of the above Valuation of inventories Depreciation (b) (d) Valuation of investment All of the above Furniture purchased for Rs. 5,000. In this transaction accounts affected are a) c) 5. Error of partial omission Error of complete omission In which area different accounting policies are adopted (a) (c) 4. Debit the receiver credit the giver Debit what comes in and credit what goes out Debit all expenses and losses, credit all income and gains All of the above. Furniture Both (a) and (b) b) d) Cash Creditors. (b) (d) Real A/c None of the above Cash Account is .. (a) (c) Personal A/c Nominal A/c Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 191 MODEL TEST PAPER - 8 6. Sales during the year Rs. 22,45,500 Closing Inventory Rs. 2,35,000 Purchases Rs. 17,84,395 Gross Profit margin will be a) 31% c) 39% 7. (b) (d) Capital expenditure None of the above Cash A/c Salary A/c (b) (d) Labour A/c None of the above Revenue expenditure Capital expenditure (b) (d) Deducted from value of sales Either (a) or (c) Repairs A/c General expenses A/c (b) (d) Cash A/c Machinery A/c Cost of goods sold can be calculated from (a) (c) 14. Deferred revenue expenditure Revenue expenditure Rs. 40,000 spent on repairs of newly purchased old machinery is debited to (a) (c) 13. Purchase A/c None of the above Amount spent for the advertisement of company s products is (a) (c) 12. (b) (d) Wages Rs. 1,000 payable to labour will be credited (a) (c) 11. Motor A/c General expenses General Manager attended a meeting held abroad to develop market; meeting was successful. This expense is in the nature of (a) (c) 10. Under periodic inventory system, inventory control is possible Periodic inventory system is simple and less expensive Periodic system requires closure of business for counting of Inventory All of the above. Ram Motors will debit purchases of Motor in (a) (c) 9. 30% 28.06%. Which of the following statement is false? a) b) c) d) 8. b) d) Balance Sheet Trading A/c (b) (d) Profit & Loss A/c P & L Appropriation A/c X draws a bill on Y for Rs. 20,000 for 3 months. The maturity date of the bill is 04.04.2011. Find the date when the bill was drawn. a) c) 01.01.2011 02.01.2011 192 The Institute of Chartered Accountants of India b) d) 31.12.2010 03.01.2011. Common Proficiency Test (CPT) Volume - II 15. Interest on debentures is calculated on (a) (c) 16. A will draw a bill on B A will make a promissory note b) d) B will draw a bill on A A will draw the bill on third party. Paid up capital Authorized share capital (b) (d) Called up capital Net Profit Goods sent on approval, goods returned, date and particulars Goods sent on approval, goods returned, goods approved and date Goods sent on approval, goods returned, goods approved and balance None of the above. Rs. 15,000 Rs. 20,000 b) d) Rs. 26,667 None of the above. Mohan purchased a Motor Car costing Rs. 60,000 on 1st January 2009 transportation and repairing charge were incurred amounting Rs. 5,000 and 200 respectively. Dismentaling charge of old motor car in place of which new motor car was purchased amounted to Rs. 20,000. Marked value of motor car was estimated at Rs. 70,000 on 31st Dec., 2009 while finalizing the annual accounts. Mohan values the motor car at Rs. 70,000 in his book. Which of the following concepts was violated by the Mohan? (a) (c) 22. 11% 14% Sent goods to customers on sale or return basis (at cost plus 33-1/3) Rs. 1,00,000. Out of which, at the end of the year, goods with customers awaiting approval is Rs. 20,000; Goods returned by customers is Rs. 40,000; and received letter of approval from customers for Rs. 40,000. a) c) 21. (b) (d) While preparing Sales on approval or return journal , 4 main columns are a) b) c) d) 20. 12% 10% Dividend is usually paid as a percentage of (a) (c) 19. Market value of debentures All of the above If Mr. A sold goods to Mr. B, then in such a case who will draw the bill and on whom? a) c) 18. (b) (d) On 01.01.2011, X draws a bill on Y for Rs. 30,000. At maturity, bill was dishonoured and X paid noting charges of Rs. 100 on it. Y requested X to draw a fresh bill for 2 months together with interest of Rs. 602. The rate of interest applied is (a) (c) 17. Purchase value of debentures Face value of debentures Matching concept Cost Concept (b) (d) Realisation concept Periodicity concept AB Ltd. issued 50,000 equity shares of Rs. 100 each at a premium of Rs. 10 payable at Rs. 30 on application, Rs. 30 on allotment and balance in the first call. Application received for 1,00,000 equity shares but the company issued to them only 50,000 shares. Excess Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 193 MODEL TEST PAPER - 8 money was refunded to them after adjustment for further calls. Last call on 1,000 shares were not received and were forfeited after due notice. The above is the case of (a) (c) 23. Rs. 5,000 Rs. 5,555 (b) (d) Rs. 6,111 Rs. 4,500 Rs. 74,000 Rs. 54,000 (b) (d) Rs. 64,000 Rs. 52,000 Not required to be adjusted Deducted (b) (d) Added None of the above Rs. 72,000 Rs. 70,000 (b) (d) Rs. 40,000 Rs. 75,000 Ram paid Rs. 1,000 towards a debit of Rs. 3,000 which was written off as bad debt in the previous year. Ram s account will be credited with (a) (c) 29. Rs. 30,000 Rs. 45,000 If Goods purchased for Rs. 2,00,000; Sales Rs. 1,60,000; Margin 20% on sales, then closing Inventory is (a) (c) 28. (b) (d) When preparing a Bank Reconciliation Statement if you start with balance as per pass book then payments made by bank Rs. 4,000 recorded twice in pass book Rs. 4,000 will be (a) (c) 27. Rs. 25,000 Rs. 35,000 Rent Rs. 10,000; Provision for bad debts (old) Rs. 10,000 Salaries Rs. 8,000 Apprentice Premium (credit) Rs. 12,000 Gross profit Rs. 70,000 Net profit of the firm will be (a) (c) 26. Pro-rata allotment All of the above Total actual cost of machinery Rs. 50,000; salvage value Rs. 5,000; Useful life 9 years; then annual depreciation under Straight line Method will be (a) (c) 25. (b) (d) If purchases Rs. 30,000; Closing Inventory Rs. 5,000; Opening Inventory Rs. 10,000; then cost of goods sold will be (a) (c) 24. Over subscription Forfeiture of shares Rs. 1,000 Rs. 2,500 (b) (d) Rs. 3,000 NIL Income tax liability of the owner Rs. 2,000 was paid out of petty cash. Journal entry will be (a) (b) (c) (d) Dr. Income tax A/c Rs.2,000 and Cr. Cash A/c Rs. 2,000 Dr. Drawings Rs.2,000 and Cr. Cash A/c Rs. 2,000 Dr. Drawings Rs.2,000 and Cr. Petty Cash A/c Rs. 2,000 None of the above 194 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 30. An old motor car was purchased for Rs. 1,00,000. It was repaired for Rs. 10,000 and Rs. 15,000 spent on its painting. Machinery repairs A/c will be debited by (a) (c) 31. Rs. 12,500 & Rs. 7,500 Rs. 7,500 & Rs. 12,500 (b) (d) Rs. 8,000 & Rs. 12,000 Rs. 12,000 & Rs. 8,000 Rs. 22,000 Rs. 21,600 (b) (d) Rs. 24,000 Rs. 22,600 Rs. 1,000 Rs. 500 (b) (d) Rs. 1,500 Rs. 2,000 2:2:1 2:1:1 (b) (d) 3:1:1 None of the above On 1st Jan., 2010 goods costing Rs. 40,000 were consigned by A to his agent B at a proforma price which was cost plus one fifth of profit on invoice price. Invoice price of goods will be (a) (c) 37. Rs. 2,50,000 Rs. 3,80,000 X & Y are partners in a business sharing profits and losses in the ratio of 7:3. They admit Z as a partner. X sacrificed 1/7th of his share and Y sacrifice 1/3rd of his share in favour of Z. New profit sharing ratio will be (a) (c) 36. (b) (d) Z & Co. issued Rs. 10,000 10% Debentures at 5% discount redeemable at 5% premium after 10 years. Loss on issue of debentures will be (a) (c) 35. Rs. 2,80,000 Rs. 3,00,000 Goods costing Rs. 20,000 was sold to Mohan at the invoice price of 20% above cost with a trade discount of 10%. The amount of sales will be (a) (c) 34. Rs. 10,000 NIL X & Y purchased a building of Rs. 1,00,000 and sold it for Rs. 1,20,000. X had contributed for Rs.60,000 and Rs. 40,000. They decided to share profits in the ratio of their capital contribution. The profit on venture will be (a) (c) 33. (b) (d) Shyam started business on 1.4.09 with a capital of Rs. 2,00,000 for which he borrowed Rs. 30,000 from a friend. He earned a profit of Rs. 1,00,000 during the year and withdrew cash Rs. 50,000 for private use. What is his capital at the end of the year? (a) (c) 32. Rs. 25,000 Rs. 15,000 Rs. 48,000 Rs. 50,000 (b) (d) Rs. 35,000 Rs. 45,000 Ram of Mumbai sends out certain goods at cost plus 25%. Invoice value of goods sends out Rs. 20,000. 4/5th of the goods were sold by consignee at Rs. 17,600. Commission 2% upto invoice value and 10% on any surplus above invoice value commission amount will be (a) (c) Rs. 320 Rs. 520 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Rs. 400 Rs. 480 195 MODEL TEST PAPER - 8 38. Opening Inventory Rs.40,000 Purchase Rs.1,00,000 Closing Inventory Rs.30,000 Carriage inwards Rs.5,000 Carriage outwards Rs.3,000 Office rent Rs.4,000 Sales Rs.2,00,000 Gross profit will be (a) (c) 39. (b) (d) Rs. 56,250 Rs. 55,000 (b) (d) Rs. 13,500 Rs. 13,350 Cost of goods sold Opening Inventory Closing Inventory Purchases amount will be (a) (c) 43. Rs. 1,22,222 Rs. 1,33,333 Opening balance of capital Income tax Net profit Drawings Interest on capital Interest on drawings Capital at the end will be (a) (c) 42. Rs. 75,000 Rs. 65,000 Rs. 1,11,111 Rs. 1,44,444 A seller sells goods at a profit of 25% on sales. In a particular month, he sold goods costing Rs. 45,000. Sales price of goods will be (a) (c) 41. (b) (d) Mohan sells goods at cost plus 50%; total sales were 2,00,000. Cost price of the goods will be (a) (c) 40. Rs. 85,000 Rs. 95,000 Rs.15,000 Rs. 2,500 Rs.1,500 Rs.1,000 Rs.750 Rs.300 (b) (d) Rs. 1,80,000 Rs. 1,70,000 Rs. 65,000 Rs. 60,000 Rs. 13,450 Rs. 13,300 Rs.1,50,000 Rs.20,000 Rs.40,000 (b) (d) Rs. 1,30,000 Rs. 1,75,000 Mohan and Sohan are partners sharing profits and losses in the ratio of 5:3. They admit Shyam with 1/5th share in profit which he acquires equally from both 1/10 from Mohan and 1/10 from Sohan. New profit sharing ratio will be (a) (c) 15:10:5 21:11:8 196 The Institute of Chartered Accountants of India (b) (d) 20:10:4 None of those Common Proficiency Test (CPT) Volume - II 44. Share capital 50,000 shares of Rs. 15 each Rs. 10 called up - Rs. 5,00,000 Calls in arrears Rs. 20,000 Call in advance Rs. 30,000 Board of directors decide to provide 15% for dividend on share capital. Amount of proposed dividend will be (a) (c) 45. Sales book Cash book (b) (d) Purchases Account Journal Specific identification method LIFO (b) (d) Weighted average method FIFO Rs. 13,000 Rs. 12,000 (b) (d) Rs. 15,000 Rs. 17,000 Capital expenditure Revenue expenditure (b) (d) Deferred expenditure Both (a) and (c) No journal entry is required to be passed when there is (a) (c) 51. Increases every year None of the above Legal expenses incurred on a suit for breach of contract to supply goods is a (a) (c) 50. (b) (d) Actual total cost of plant - Rs 1,50,000 Salvage value - Rs. 20,000 Useful Life - 10 years Annual depreciation under Straight line method will be (a) (c) 49. Is constant every year Decreases every year Which stock valuation method best matches the cost of goods sold with current replacement cost (a) (c) 48. Rs. 70,000 Rs. 72,000 The total of the purchases day book is posted periodically to the debit of (a) (c) 47. (b) (d) Under diminishing balance method, depreciation (a) (c) 46. Rs. 65,000 Rs. 75,000 Loss by theft Loss of bad debts (b) (d) Normal loss Abnormal loss A plant & machinery worth Rs. 1,00,000 is insured for Rs. 60,000. It is completely destroyed by fire. The loss to be admitted by the insurance company will be (a) (c) Rs. 1,00,000 Rs. 40,000 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Rs. 1,60,000 Rs. 60,000 197 MODEL TEST PAPER - 8 52. There must be a gap of atleast _______ month between two calls. (a) (c) 53. (b) (d) Rs. 1,10,000 Rs. 1,20,000 Rs. 80,000 Rs. 1,60,000 Rs. 30,000 Rs. 1,00,000 Rs. 80,000 Credited to discount received A/c by Rs. 3,000 Credited to rebate account by Rs. 3,000 Credited to discount allowed A/c Rs. 3,000 Not shown in the books of B at all Rs. 12,000 Rs. 24,000 (b) (d) Rs. 20,000 Rs. 20,400 3:2:1 5:2:1 (b) (d) 4:2:1 2:2:1 Narain Ltd. invited application for 50,000 shares of Rs. 100 each at a discount of 8%. Discount per share will be (a) (c) 59. Rs. 7,500 Rs. 9,500 Ram and Rahim have been sharing profit and losses in the ratio of 4:3 Rahman is admitted as a partner. He acquires his 1/7 share only from Rahim. New ratio will be (a) (c) 58. (b) (d) Depreciation on plant and machinery whose cost is Rs. 80,000 with an accumulated depreciation reserve of Rs. 12,000 at 30% p.a. on written down value will be (a) (c) 57. 6 2 Bill of Rs. 15,000 accepted by A was endorsed by B to C on account of final settlement of Rs. 18,000. The benefit of Rs. 3,000 earn by B was (a) (b) (c) (d) 56. Rs. 8,500 Rs. 6,500 Cost of goods sold Sales Closing Inventory Gross profit will be (a) (c) 55. (b) (d) Cost of goods sold Rs. 8,000. Closing Inventory Rs. 3,000 opening Inventory Rs. 2,500. Wages Rs. 1,000 purchases will be (a) (c) 54. 3 1 Rs. 8.00 0.80 paise (b) (d) Rs. 0.08 paise Rs. 80.00 Debit means: (a) (c) An increase in asset A decrease in asset 198 The Institute of Chartered Accountants of India (b) (d) An increase in liability An increase in proprietor s equity. Common Proficiency Test (CPT) Volume - II 60. Forfeited shares may be re-issued at discount (a) (b) (c) (d) If the market value of the forfeited share is less than is nominal value If the forfeited shares were originally issued at discount If the loss on forfeited shares can be covered by the forfeited amount on those shares Any of the above SECTION B : MERCANTILE LAWS (40 MARKS) 61. The sources of Mercantile law include (a) (c) 62. Offer Contract (b) (d) Promise Obligation An executed contract An executory contract (b) (d) A tacit contract An implied contract Offer Lawful promise (b) (d) Acceptance Contract By the person to whom offer is made Without a Condition In clear terms either oral or written All of the above Under the Sale of Goods Act, 1930 the subject matter of goods (a) (c) 68. Correct subject to certain exception Wrong Consent should be given (a) (b) (c) (d) 67. (b) (d) A proposal when accepted becomes a (a) (c) 66. Correct Partially correct Auction sale is an example of (a) (c) 65. Mercantile Usages All of the above An agreement enforceable by law amounts to (a) (c) 64. (b) (d) Every contract is an agreement but every agreement is not contract. This statement is (a) (c) 63. English common law Principles of Equity & justice Is existing goods only May be existing or future goods (b) (d) Is future goods only None of the above Which one of the following statements is not correct? (a) (b) (c) (d) Oral acceptance is a valid acceptance Acceptance must be in writing Acceptance must be communicated Acceptance must be in prescribed manner Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 199 MODEL TEST PAPER - 8 69. Which one of the following falls into the category of offer? (a) (b) (c) (d) 70. A counter offer is (a) (c) 71. Standing offer Invitation to offer Proposal A promise (b) (d) An invitation to proposal An invitation for negotiation Shop public Customer (b) (d) Shop owner Officer Valid Void (b) (d) Invalid Voidable Valid Unenforceable (b) (d) Void None of the above (b) (d) Void Unlawful Agreement by competent parties is (a) (c) 77. (b) (d) An agreement without consideration is (a) (c) 76. Counter offer Offer Acceptance in ignorance of the offer is (a) (c) 75. An acceptance of the offer An invitation to treat When goods are displayed in a shop window with price tags attached to them, the offer comes from (a) (c) 74. (b) (d) A notice in the newspapers inviting tenders is (a) (c) 73. A rejection of the original offer A bargain When a person without expressing his final willingness, proposes certain terms on which he is willing to negotiate, he makes (a) (c) 72. Newspaper advertisement regarding sale Display of goods by a shopkeeper in his window with prices marked on them An advertisement for a concert Announcement of reward to the public Valid Illegal The consideration may move from (a) (b) (c) (d) The promisor or any other person The promisee or any other person The promisee only The promisor only 200 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 78. Inadequacy of consideration does not make a contract (a) (c) 79. (b) (d) Unlawful Valid Invalid agreements Contingent contract (b) (d) Voidable contracts Wagering agreements Illegal Void & punishable (b) (d) Punishable Voidable Valid Voidable (b) (d) Void None of the above The renewal of original contract Cancellation of contract Substitution of new contract Alteration of contract Novation means _______________. (a) (b) (c) (d) 86. Illegal Void Recession of a contract means_________. (a) (b) (c) (d) 85. Immoral or opposed to public policy All of the above An agreement to share the benefits of a public offer is ____________. (a) (c) 84. (b) (d) Illegality renders a contract________. (a) (c) 83. It is fraudulent It is forbidden by law Agreement which are in the nature of bets and gambling are called__________. (a) (c) 82. Voidable None of the above Due to change in law, if the performance of a promise becomes impossible, then the contract become (a) (c) 81. (b) (d) Consideration is unlawful when (a) (c) 80. Void Unenforceable Frustration due to change of circumstances Impossibility of contract sending it void No frustration of executed contracts Substitution of an existing contract with a new one Injuction may be ___________. (a) (c) Temporary (a) or (b) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Perpetual None of the above 201 MODEL TEST PAPER - 8 87. Caveat emptor means _________. (a) (c) 88. Who sells or agrees to sell goods Who only sells goods Who only agrees to sell the goods None of these Buys or agrees to buy goods Agrees to buy goods (b) (d) Buys goods None of the above Movable property Goods (b) (d) Immovable property Crops, Gross and other things Shares Old coins (b) (d) Growing crops All the above In a contract of sale, price of goods may be paid __________. (a) (b) (c) (d) 95. Void Illegal The term goods includes ________. (a) (c) 94. (b) (d) Things attached to land, which are agreed to be severed before sale constitute ________. (a) (c) 93. Voidable Valid According to the Sale of Goods Act, 1930, Buyer is a person who ________. (a) (c) 92. As operative and wait till the time for performance arrives As discharged and bring an immediate action for damages Exercise option either (a) or (b) Only option (a) is available According to Sale of Goods Act, 1930, seller means a person ____________. (a) (b) (c) (d) 91. A jus in personam None of the above Misrepresentation as to fact renders a contract (a) (c) 90. (b) (d) In case of anticipatory breach the agreed party may treat the contract __________. (a) (b) (c) (d) 89. Let the buyer aware A jus in rem In cash Other than cash Partly in cash and partly in goods valued in terms of money (a) and (c) The general rule of law is that the risk follows _________ of goods. (a) (c) Possession Ownership 202 The Institute of Chartered Accountants of India (b) (d) Delivery Contract of sale Common Proficiency Test (CPT) Volume - II 96. Where the goods are perishable in nature, unpaid seller can ___________. (a) (b) (c) (d) 97. When there is no reserve price, the auctioneer is ____________. (a) (b) (c) (d) 98. Firm Partner of the firm Continuing partner of the firm Retiring partners of the firm A borrows Rs. 500 from B to pay to C , to whom B has lost a bet. Contract between A and B is (a) (c) 100. not bound to accept the highest bid bound to accept the highest bid Can accept any price None of the above Partnership property vest in the ____________. (a) (b) (c) (d) 99. Resale the goods Not resale the goods Ask again the buyer Take possession and mark goods as bad Valid Void (b) (d) Voidable None of these A purchase a refrigerator on hire purchase from B and pledged with C. D purchased the refrigerator from C in good faith, on knowing the facts B wants to recover the refrigerator from D. Which of the following statements is/are correct? (a) (b) (c) (d) B can recover the refrigerator from D B can recover the refrigerator from A only B cannot recover the refrigerator from D D will get good title for the refrigerator as he bought it in good faith SECTION C : GENERAL ECONOMICS (50 MARKS) 101. When we are studying how a producer fixes the prices of his products we are studying. (a) (b) (c) (d) 102. Macro Economics Micro Economics Both Micro and Macro Economics None of the above Macro economics doesn t include one example from the following: (a) (c) National Income and output General Price Level Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Study of firms Saving and Investment 203 MODEL TEST PAPER - 8 103. If distribution of income is more equal, then the propensity to consumer of the country is (a) (c) 104. Positive Infinite Increase Remain the same (b) (d) Decrease None of the above .777 1 (b) (d) 1.4 .8 (b) (d) Commercial banks Both (a) and (b) Central bank Ministry of Finance Public Revenue Public Expenditure Both Public Revenue and Public Expenditure Public welfare Which of the following is not the objective of Monetary Policy? (a) (b) (c) (d) 111. (b) (d) Fiscal policy is the policy of the Government related to: (a) (b) (c) (d) 110. Negative Zero Monetary policy is given by: (a) (c) 109. Negative income elasticity Zero income elasticity If a good is priced at Rs 180 p.u. and its price is increased to Rs. 240 p.u. Now suppose quantity demanded previously was 100 units and as a result of price increase, the quantity demanded fell to 80 units. What is the price elasticity? (use Mid Point method) (a) (c) 108. (b) (d) Positive income elasticity Fluctuating income elasticity If demand for a good is elastic, an increase in its price will cause total expenditure of the consumers of the good to: (a) (c) 107. Relatively Low None of the above If the goods are complementary like car and petrol, their cross elasticity is: (a) (c) 106. (b) (d) Normal goods have: (a) (c) 105. Relatively High Unaffected To regulate monetary growth To ensure adequate expansion in credit to assist economic growth To introduce measures for strengthening the banking system To increase Public Revenue FEMA stands for (a) (b) (c) (d) Fiscal Exchange Management Act Foreign Exchange Monetary Act Foreign Exchange Management Act Foreign Exchange Money Act 204 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 112. __________________ refers to that portion of total deposits which a commercial bank has to keep with the RBI (a) (c) 113. (b) (d) Citi Bank All of the above 31 91 (b) (d) 51 101 Inflation Growth (b) (d) Unemployment All of the above NDP at market price Net Indirect Taxes NNP at factor cost NDP at factor cost NDPFC (+) Deprecation None of the above Difference between current and capital Account Difference between export and import of goods Difference between export and import of goods and services Balance of current account Which of the following is not included in the computation of GDP? (a) (b) (c) (d) 120. SBI ABN Amro Bank Balance of Trade is: (a) (b) (c) (d) 119. Indian Bank RBI Net Factor Income from abroad is equal to: (a) (b) (c) (d) 118. (b) (d) Macro economics is the study of: (a) (c) 117. SBI NABARD The initial membership of IMF in the year 1947 was________. (a) (c) 116. SLR Margin Requirement Which of the following is a commercial bank in India? (a) (c) 115. (b) (d) Which is the central bank of India? (a) (c) 114. CRR Bank Rate Spending on guns and tanks Purchase of Limca by a family Services of a teacher Price paid for a stolen car In terms of capacity of power generation, the highest capacity is of: (a) (c) Thermal Nuclear Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Hydel Others 205 MODEL TEST PAPER - 8 121. The highest user of commercial energy is (a) (c) 122. (b) (c) (d) 9 th 7 th 17,50,000 20,00,000 (b) (d) 8,00,000 50,00,000 Balance of current account and capital account Only Capital account Only Current Account Only trade account. Total Receipts and total expenditure Revenue receipts and revenue expenditure Fiscal deficit Interest Total Budgetary receipts revenue expenditure The aim of FRBM bill is to reduce gross fiscal deficit by_____________ % of GDP. (a) (c) 128. (b) (d) Budget Deficit means: (a) (b) (c) (d) 127. 10th 4 th Balance of payment consists of: (a) (b) (c) (d) 126. Unemployment rates on the basis of current daily status were same as those on the basis of usual status Unemployment rates on the basis of current daily status were higher than those of the basis of usual status Unemployment rates of the basis of current daily status were lower than those on the basis of usual status None of the above India s external debt stood at more than __________crore March, 2012. (a) (c) 125. Industry Agriculture Indian ranked _______ among top 15 debtor countries of the world according to the World Bank. (2011) (a) (c) 124. (b) (d) According to National Sample Survey Organisation (NSSO) during 2009-10. (a) 123. Railways Households 2.5% 1% (b) (d) .5% .25% Non-plan revenue expenditure consists of : (a) (c) Defence Food and Fertilizer subsidy 206 The Institute of Chartered Accountants of India (b) (d) Interest Payment All of the above Common Proficiency Test (CPT) Volume - II 129. The Government now taps 91 days treasury bills from the market and shows them as part of: (a) (c) 130. Usual Status Current Yearly Status Rice revolution Bajra revolution (b) (d) Wheat revolution All of the above Tax on agriculture is a state subject Under zamindari system, farmers directly paid land revenue to the state Cooperative banks are giving loans to agricultural sector at zero interest rates India has been a big importer of food grain especially since 1995 Slow and unplanned growth Inadequate reforms (b) (d) Inadequate finance All of the above Increasing returns imply: (a) (b) (c) (d) 136. (b) (d) Agriculture sector faces the problem of: (a) (c) 135. Current Weekly Status Current Daily Status Which of the following statements is correct? (a) (b) (c) (d) 134. In India, we mainly use the concept of relative poverty for measuring poverty Gini coefficients are used to measure absolute poverty Gini coefficients are often used for measuring poverty in relative sense When poverty is related to the distribution of income or consumption expenditure, it is absolute poverty The green revolution is also known as: (a) (c) 133. Loan Receipt None of the above According to ______________measure, a person is said to be employed for the week even if he is employed only for a day during that week (a) (c) 132. (b) (d) Which of the following statements is correct? (a) (b) (c) (d) 131. Revenue Receipt Capital Receipt Constant average cost Diminishing cost per unit of output Optimum use of capital and labour None of the above _____________ is an implicit cost of production (a) (b) (c) (d) Wages of the labour Charges for electricity Interest on owned money capital Payment for raw material Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 207 MODEL TEST PAPER - 8 137. All of the following are U-shaped curves except the: (a) (c) 138. AVC curve AC curve (b) (d) AFC curve MC curve Suppose that a sole proprietor is earning total revenue of Rs. 1,20,000 and is incurring explicit cost of Rs. 90,000. If the owner could work for another company for Rs. 50,000 a year, we would conclude that: (a) The firm is incurring an economic profit (b) The firm is incurring an economic loss (c) Total economic cost is Rs 2,10,000 (d) The firm is earning economic profit of Rs. 30,000 Use following table to answers questions 139-140 Hour of labour Total output Marginal product 0 300 720 0 300 240 - 0 1 2 3 139. What is the total output when 2 hours of labour are employed? (a) (c) 140. 160 360 (b) (d) 200 540 What is the marginal product of the third hour of labour? (a) (c) 120 200 (b) (d) 160 180 Use the following data to answer questions 141-143 Output Total Cost 0 240 1 330 2 410 3 480 4 540 5 610 6 690 208 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 141. The Average fixed cost of 2 units of output is: (a) (c) 142. (b) (d) 3 and 4 5 and 6 Average cost Fixed cost (b) (d) Marginal cost Variable cost Administered interest rate structure Quantitative restriction on credit flow High revenue requirements Keeping very less lendable resources Doesn t apply to rich, developed countries Applies only to the less developed countries Implies that consumer wants will be satisfied in a mixed economy Implies that consumer wants will never be completely satisfied Currencies and demand deposits Bonds, Government securities Equity shares All of the above A horizontal supply curve parallel to the quantity axis implies that the elasticity of supply is: (a) (c) 149. 2 and 3 4 and 5 Money includes (a) (b) (c) (d) 148. Rs. 75 Rs. 450 The law of scarcity: (a) (b) (c) (d) 147. (b) (d) Before financial reforms, the banking system was characterized by all of the following except: (a) (b) (c) (d) 146. Rs. 133 Rs. 80 Which cost increases continuously with the increase in production? (a) (c) 145. Rs. 85 Rs. 205 Diminishing marginal returns start to occur between units: (a) (c) 144. (b) (d) The marginal cost of the sixth unit of output is: (a) (c) 143. Rs. 80 Rs 120 Infinite Equal to one (b) (d) Zero Greater than zero but less than one Which of the following statements is correct? (a) (b) (c) (d) External debts constitute about 18% of GDP India is categorised as a high indebted country by the Word Bank India is self sufficient after the onset of economic reforms None of these Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 209 MODEL TEST PAPER - 8 150. Lesser production of ______would lead to lesser production in future (a) (c) Public goods Agricultural goods (b) (d) Consumer goods Capital goods SECTION D : QUANTITATIVE APTITUDE (50 MARKS) 151. How many numbers between 100 and 200 are divisible by 2 & 8? (a) (c) 152. n2 (n+1)2 (b) (d) (2n 1)2 None of these 40 50 (b) (d) 30 None of these Find the value of 13 + 23 + 33 + . + 123 (a) (c) 155. 13 16 Find the number which when multiplied by 36 is increased by 1050. (a) (c) 154. (b) (d) The sum of first n odd numbers is (a) (c) 153. 12 9 6804 6084 (b) (d) 6048 None of these Find the sum of n terms of the series 1 + 9 + 24 + 46 + 75 + ................. (a) (b) n(2n + 1) (4n 3) 6 (c) 156. n(n + 1) (7n 4) 6 n(2n + 1) (2n 3) 6 (d) None of these What must be added to each term of 83:263 to make it equal to 1:3? (a) (c) 157. (b) (d) 10 None of these An employer reduces the number of employees in the ratio of 9:8 and increases their wages in the ratio of 14:15. In what ratio is the wages bill decreased? (a) (c) 158. 13 7 20:22 21:20 (b) (d) Divide Rs. 680 among A, B and C such that A gets 20:33 None of these 2 1 of what B gets and B gets th of what 3 4 C gets. What is C s share (a) (c) Rs. 180 Rs. 480 210 The Institute of Chartered Accountants of India (b) (d) Rs. 280 None of these Common Proficiency Test (CPT) Volume - II 159. What must be added to each of the four numbers 10, 18, 22, 38. So that they become in proportion? (a) (c) 160. (b) (d) 5 None of these Find two numbers, such that the mean proportion between them is 24 and the third proportion to them is 192. (a) (c) 161. 2 7 48, 10 10, 33 (b) (d) 12, 48 None of these (b) (d) 0 None of these (b) (d) 1 None of these (b) (d) 1 None of these (b) (d) ab None of these (b) (d) 1 None of these ex + e x 2 x 0 x Evaluate lim (a) (c) 1 logx 1 162. Evaluate lim x 0 (a) (c) 163. 164. 165. x 0 eax e bx x a b 0 Evaluate lim x 0 (a) (c) 3x | x | 7x 5 | x | 2 does not exist Evaluate lim (a) (c) 1 ex + 1 1 does not exist Evaluate lim x 0 (a) (c) ex 1 ex 1 log (1 + x) 0 1 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 211 MODEL TEST PAPER - 8 If y = 1 x dy then is dx 1+ x (a) 2/3 (1 + x)(1 x) (b) (1 + x)3/2 (1 x) (c) 166. 3 / 2 (1 + x) 2 (1 x) (d) None of these (b) (d) y None of these x 167. If y = (a) (c) 168. 1+ x 2 1 3 , then x . dy is dx y2 y3 If xy = ex y; then dy is dx (a) (b) log x (1 log x) 2 (c) 169. log x (1 + log x) 2 1 (1 + log x) 2 (d) None of these if y3 . x5 = (x+y)8, then dy is dx (a) (b) y x (c) y5 x3 (d) None of these (a) y2 1 + y log x (b) y2 1 y log x (c) 170. y x y2 1 y log x (d) None of these dy is If y = x xx...... ; then x. dx 212 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 1 171. (e Evaluate x 1 (a) (c) e x ) dx 1 1 (b) (c) 0 None of these 1 + log x dx x 1 e 172. Evaluate: (a) 3 2 (b) (c) 0 (d) None of these (b) (d) log 2 None of these ) (b) 2 2 +1 3 ) (d) None of these (b) log (d) None of these log3 173. Evaluate: 0 (a) (c) 174. ex dx 1 + ex log 3 1 1 Evaluate: 1+ 0 x 1 + x2 (a) 2 3 ( (c) 2 3 ( 175. dx 2 +1 2 1 1 Evaluate: 3 2 ( ) dx (1 + x)(2 + x) 0 (a) (c) 176. log 4 3 0 3 4 The sum of the first two terms of an infinite geometric series is 15 and each term is equal to the sum of all the terms following it; then the sum of the series is (a) (c) 20 25 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) 15 None of these 213 MODEL TEST PAPER - 8 177. If x and y are positive intigers such that x + y = 1 and a = 1 + x + x2 + .. to , b = 1 + y + y2 + .. to then the value of (a) (c) 178. 1 1 + is a b 2 None of these (b) (d) 8 months None of these 6% 10% (b) (d) 5% None of these 0 1 (b) (d) 2 None of these 15 10 (b) (d) 5 None of these Find the coefficient of variation if the sum of squared deviations taken from mean 40 of 10 observations is 360. (a) (c) 184. 7 months 10 months The Standard Deviation of a set of 50 items is 10. Find the Standard Deviation if every item is increased by 5. (a) (c) 183. 6% None of these If the values of all observations are equal then the Standard Deviation of the given observations is (a) (c) 182. (b) (d) A person deposited a sum of Rs. 10,000 in a bank. After 2 years, he withdrew Rs. 4,000 and at the end of 5 years, he received an amount of Rs. 7,900; then the rate of simple interest is: (a) (c) 181. 5% 10% The time required for Rs. 5,400 to yield Rs. 216 at 6% simple interest. (a) (c) 180. (b) (d) At what rate, will a person who invests Rs. 2,000 will receive Rs.2, 090 as simple interest in 9 months? (a) (c) 179. 0 1 15 40 (b) (d) 20 None of these If the coefficient of mean deviation is 0.44 and the mean deviation from mean is 5.77; then the mean is (a) (c) 14 16 214 The Institute of Chartered Accountants of India (b) (4) 13.11 None of these Common Proficiency Test (CPT) Volume - II 185. The Standard Deviation of two values is equal to half their difference. This statement is (a) (c) 186. True cannot say (b) (d) Find the correlation coefficient between the following set of observation. x: (a) (c) 50 50 y: 187. false None of these 40 40 1 0 (b) (d) 1 None of these The value of Spearman s rank correlation coefficient of a certain number of observations was to be 2 . The sum of the squares of differences between the corresponding ranks was 55. 3 Find the number of Pairs. (a) (c) 188. 1.25 0.75 (b) (d) 0.25 None of these always positive always negative always 0 Either positive or negative or Zero The coefficient of regression of Y on X is byx = 1.2. If U = (a) (c) 191. 12 None of these The co variance between the two variables is (a) (b) (c) (d) 190. (b) (d) The equation of two lines of regression is 4x + 3y + 7 = 0 & 3x + 4y + 8 = 0. The correlation coefficient between x & y is (a) (c) 189. 10 11 0.9 0.7 (b) (d) x 100 Y 200 and V= find bvu 2 3 0.8 None of these A bag contains 5 red & 3 black balls and the second one 4 red and 5 black balls. One of these is selected at random and a draw of two balls is made from it. What is the chance that one of them is red and the other is black? (a) 275 504 (b) 273 504 (c) 175 504 (d) None of these Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 215 MODEL TEST PAPER - 8 192. A purse contains 3 silver and 4 Gold coins and a second purse contains 4 silver and 3 Gold coins. If a coin is selected at random from one of the two purses, what is chance that it is a silver coin. (a) (b) 1 4 (c) 193. 1 2 3 4 (d) None of these Find mean of the probability distribution of number of sixes in two tosses of unbiased dice. (a) (b) 2 3 (c) 194. 1 3 1 4 (d) None of these Find the probability distribution (when x = 2) of the number of sixes in a single throw of three dice. (a) (b) 1 216 (c) 195. 75 216 15 216 (d) None of these A Chartered Accountant applies of a job in two firms X and Y. He estimates that the probability of his being selected in firm X is 0.7, and being rejected at Y is 0.5 and the probability of atleast one of his applications being rejected is 0.6. What is the probability that he will be selected in one of the firms? (a) (c) 196. 0.8 0.9 (b) (d) 0.7 None of these 1 log log x + dx ( ) 2 Evaluate ( log x ) (a) x log (log x) x +c log x (b) x (log x)2 (c) x log (log x) + x +c log x (d) None of these 216 The Institute of Chartered Accountants of India x +c log x Common Proficiency Test (CPT) Volume - II 197. Is equal to is a (a) (c) 198. Reflexive relation Equivalence relation odd function even function Neither odd nor even function None of these For the function f(x) = 121+x, the domain of real values of x where 0 < x < 9 the range is (a) (c) 200. (b) (d) If f(x) = x2 + 2, then the given function is (a) (b) (c) (d) 199. Symmetric relation Transitive relation 12 < f(x) < 1210 0 < f(x) < 12 (b) (d) 0 < f(x) < 1210 None of these Is greater than over the set of real number s is (a) (c) Transitive relation Reflexive relation (b) (d) Symmetric relation Equivalence relation YYY Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 217 Answer of Model Test Papers Model Test Paper BOS/CPT 8 SECTION A : FUNDAMENTALS OF ACCOUNTING 1. (d) 2. (a) 3. (d) 4. (c) 5. (b) 6. (a) 7. (a) 8. (b) 9. (a) 10. (d) 11. (a) 12. (d) 13. (c) 14. (a) 15. (c) 16. (a) 17. (a) 18. (a) 19. (c) 20. (a) 21. (c) 22. (d) 23. (c) 24. (a) 25. (a) 26. (b) 27. (a) 28. (d) 29. (c) 30. (d) 31. (b) 32. (d) 33. (c) 34. (a) 35. (b) 36. (c) 37. (d) 38. (a) 39. (c) 40. (d) 41. (b) 42. (c) 43. (c) 44. (d) 45. (c) 46. (b) 47. (c) 48. (a) 49. (c) 50. (b) 51. (d) 52. (c) 53. (b) 54. (c) 55. (a) 56. (d) 57. (b) 58. (a) 59. (a 60. (b) SECTION B : MERCANTILE LAWS (40 MARKS) 61. (d) 62. (a) 63. (c) 64. (b) 65. (c) 66. (d) 67. (c) 68. (d) 69. (d) 70. (a) 71. (d) 72. (c) 73. (c) 74. (b) 75. (b) 76. (a) 77. (b) 78. (a) 79. (d) 80. (c) 81. (d) 82. (c) 83. (b) 84. (b) 85. (d) 86. (c) 87. (a) 88. (c) 89. (a) 90. (a) 91. (a) 92. (c) 93. (d) 94. (d) 95. (c) 96. (a) 97. (a) 98. (a) 99. (c) 100. (a) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 289 ANSWERS Answer of Model Test Papers Model Test Paper BOS/CPT 8 SECTION C : GENERAL ECONOMICS (50 MARKS) 101 (b) 111 (c) 121 (b) 131 (a) 141 (c) 102 (b) 112 (a) 122 (b) 132 (b) 142 (c) 103 (a) 113 (d) 123 (c) 133 (a) 143 (c) 104 (a) 114 (d) 124 (a) 134 (d) 144 (d) 105 (a) 115 (a) 125 (a) 135 (b) 145 (d) 106 (b) 116 (d) 126 (a) 136 (c) 146 (d) 107 (a) 117 (b) 127 (b) 137 (b) 147 (d) 108 (b) 118 (b) 128 (d) 138 (b) 148 (a) 109 (c) 119 (d) 129 (c) 139 (d) 149 (a) 110 (d) 120 (a) 130 (c) 140 (d) 150 (d) SECTION D : QUANTITATIVE APTITUDE (50 MARKS) 151. (b) 152. (a) 153. (b) 154. (c) 155. (a) 156. (c) 157. (c) 158. (c) 159. (a) 160. (b) 161. (b) 162. (c) 163. (c) 164. (a) 165. (b) 166. (b) 167. (c) 168. (a) 169. (a) 170. (b) 171. (b) 172. (a) 173. (b) 174. (d) 175. (a) 176. (a) 177. (c) 178. (b) 179. (b) 180. (b) 181. (a) 182. (c) 183. (a) 184. (b) 185. (a) 186. (c) 187. (a) 188. (c) 189. (d) 190. (b) 191. (a) 192. (a) 193. (a) 194. (c) 195. (a) 196. (a) 197. (d) 198. (b) 199. (a) 200. (a) 290 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II = n n 2 [2a+(n 1)d] + [2a + (n 3)d] (n 1)[2a + (n 2)d] 2 2 = an + = (n 1)n (n 3 ) (n 2 ) d + a (n 2 ) + d 2 a (n 1) (n 1) (n 2 )d 2 2 (n 3 )(n 2 ) (n 1) n+ (n 1) (n 2 ) d 2 2 n 2 n + n 2 5n 2 + 6 2n 2 4 + 6n d 2 = 2d =d 2 Ans. (a) 200. d A3 1 = A(n 1) 3 a + 3d 1 = (3+3 d) 3 = 3 + (n 1)d a + (n 1)d 3 6 n 10 d= 7n = a + (N 1) d 31 = 3+ (n + 2 1) 28 = (n+1) Ans. (c) 6 n 10 6 n = 13 n 10 13 Model Test Paper BOS/CPT 8 151. The first no. divide by 8 between 100 and 200 is 104 The last no. divide by 8 between 100 and 200 is 200 The total number divide by 104 and 200 is 13. All number divide by 8 also divide by 2 is 13 Ans. (b) 152. Sum of 1st n odd number Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 395 ANSWERS S = 1+3+5+ ... + (2n 1) Since S = n [2 a + (n 1)d ] 2 S = n/2 [2.1 + (n 1)2] = = S n (1+n 1) n(n) = n2 Ans. (a) 153. Let the number be x. According to the given condition of the problem is 36x = x + 1050 36x = 1050 x = 1050 35 x = 30 Ans. (b) n(n + 1) 154. The formula is 1 + 2 + 3 + ........ + n = 2 3 3 3 12 (12 + 1) 1 + 2 + 3 + ........ + 12 = 2 3 3 3 = 2 3 [6(13 )] 2 = 2 3 [78 ] 2 = 6084 Ans. (c) 155. Let S = 1+9+24+46+75+........+t n shifting 1 places to the right in the RHS S = 1+9+24+46+75+...........t n-1 +t n subtracting term by term, 0=1+8+15+22+29+............+(t n -tn-1 ) - t n Transposing t n = 1+8+15+22+29+ ............ to n th term 396 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II = n {2.1+(n 1)7} 2 7 5 = n2 n 2 2 Now Sn = 7 5 tn = 2 n 2 2 n = 7 n(n + 1)(2 n + 1) 5 n(n + 1) 2 6 2 2 = 5 n(n + 1) 7 (2 n + 1) 2 2 6 = 4 n(n + 1) 7 n 3 2 3 Sn = n(n + 1)(7n 4 ) 6 156. Let the number to be added be x then according to the problem. 83 + x 1 = ' 263 + x 3 3(83+x) = 263 + x 249 + 3x = 263 + x 3x x = 263 249 2x = 14 x= 14 =7 2 Hence the required number is 7 Ans. (c) 157. Initially, let the number of employees be 9 and wages per head be Rs. 14. Then, total wages bill = Rs. (9 14) = Rs. 126 Further, the number of employees becomes 8 and the wages per head becomes Rs. 15. Now total wages bill = Rs. (8 15) = Rs. 120 Ratio of the wages bill = 126:120 = 21:20 Thus the wages bill is decreased in the ratio 21:20 Ans. (c) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 397 ANSWERS 158. Let C gets Rs. = x Given B = of C = (x) and A = Also, given 2 1 x of B = 2/3 ( x) = 6 3 1 1 x + x + x = 680 6 4 2 x + 3 x + 12 x = 680 12 17 x = 680 12 x = 680 12 = 480 17 Ans. (c) 159. Let us assume that when x is added to each of the four given numbers, they become in proportion. 10 + x : 18 + x = 22 + x : 38 + x Product of the means = Product of the extremes. (10+x) (38+x) = (18+x) (22+x) 380+48x + x 2 =396 + 40x + x 2 8x = 16 x=2 Required number = 2 Ans. (a) 160. Let the required numbers be x and y. Since the mean proportional between a and c is given by the relation b = ac Mean proportional = xy According to the question, xy = 24 xy = 576 (1) Again suppose that the third proportional to x and y is z. Then x:y=y:z 398 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II x:z=y:y xz = y2 z= y2 x According to the question, y2 = 192 x y 2 =192 x (2) From equation (2), x= y2 192 Putting this value of x in equation (1) y2 .y = 576 192 y 3 = 576 192 = 24 24 24 8 = 24 24 24 2 2 2 y = (24 24 24 2 2 2 2) 1/3 = 24 2 y = 48 (1) xy = 576 x (48) = 576 x= 576 =8 48 Hence the required number are 12 and 48. 161. Lt x 0 e x 1 (e x 1 e x + e x 2 + x x x e x 1 e x 1 + Lt x x 0 x e x 1 = 1 Lt x 0 x 1 1=0 Ans. (b) 0 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 399 ANSWERS 1 162. Lt e 1/ x 1 Lt 1 / x x 0 e +1 +1 e x 1 1 x 0 ex RHL e 1/ x 1 Lt + 1 / x App Lt = x 0 e +1 RHL does not exist LHL e 1/ x 1 Lt 1 / x App Lt x 0 e +1 LHL does not exist. Lt does not exist in f(x) Ans. (c) 163. Lt x 0 RHL LHL does not exist 3 x | x | 7x 5 | x | Lt + 3x x 2x = =1 7x 5x 2x Lt 4x 1 3 x ( x) = = 7 x 5 ( x ) 12 x 3 x 0 x 0 LHL RHS f(x) does not exist at x = 0 Ans. (c) 164. Lt x 0 does not exist a.1 b.1 a b Ans. (a) 165. Lt x 0 ( ) ( ) e ax 1 e bx 1 e ax e bx Lt a . b x 0 x ax bx e x 1 Lt = 1 x 0 x a b e x 1 x e x 1 . Lt x 0 x log (1 + x ) log (1 + x) e x 1 . Lt Lt x 0 x x 0 1.1 = 1 1 log (1 + x) x Ans. (b) 1 400 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 1 x 1+ x 166. Given y = d d ( 1 + x ) dx ( 1 x ) ( 1 x ) dx ( 1+ x) ( 1+ x ) 1 1 (1 x ) ( 1) ( 1+ x ) ( 1 x ) (1 + x ) 2 2 dy = dx 2 1 1 2 = (1 + x) = 1 1 2 1 1+ x 1 1 x 2 1 x 2 1+ x (1 + x) 1 (1 + x) + (1 x) (1 + x) . = 1 2 1 x 1+ x dy 1 2 1+ x 1 . = = 3/2 dx 2 1 x 1+ x 1 (1 + x ) 1 x ( ) Ans. (b) 167. Given x y= 1 + x2 1 + x 2 (1) x. dy = dx 2 1 + x2 2 2 dy = dx (2 x ) x2 (1 + x ) (1 + x ) x (1 + x ) 1+ x 2 = 2 1 + x2 1 + x2 1 + x2 = 1 2 2 1 ( ) 3 2 2 1+ x Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 401 ANSWERS dy x = dx x3 3 (1 + x ) 3 2 2 x = 2 1+ x 3 dy = [y ] 3 dx x3 Ans. (c) 168. Given x y = e x 4 Taking log on both sides ( ) ( ) log x y = log e x y y log x = (x y) log e y log x = x y y (1 + log x) = x y= x 1 + log x Differentiate on both sides 1 (1 + log x).1 x dy x = 2 dx (1 + log x ) 1 + log 1 = (1 + log x ) 2 = log x (1 + log x )2 Ans. (a) 169. Given y 3 x 5 = (x + y )8 (1) Differentiate on both sides. ( ) y 3 5 x 4 + x 5 .3 y 2 5y 3 x4 + 3 x5 y2 [ dy dy = 8 (x + y )7 1 + dx dx dy dy = 8 (x + y )7 + 8 (x + y )7 dx dx ] dy 5 2 3 x y 8 (x + y )7 = 8 (x + y )7 5 y 3 x 4 dx 402 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 8 (x + y )7 5 (x + y )8 dy 8 (x + y ) 5 y x x = = 3 8 dx 3 x 5 y 2 8 (x + y )7 (x + y ) 8 (x + y )7 y 7 3 4 = 5 8 x (x + y ) 3 (x + y )7 y (x + y ) 8 = y [8 x 5 (x + y )] y[8 x 5 x 5 y ] = x[3 (x + y ) 8 y ] x[3 x + 3 y 8 y ] = Using equation (1) y[3 x 5 y ] y = x[3 x 5 y ] x (x + y )7 Ans. (a) 170. Given y = x x i.e. x ..... y = xy Taking log on both sides ( ) log y = log x y log y = y log x Differentiate on both sides dy 1 1 dy = y. + log x. dx x y dx dy dx 1 log y y x = x dy 1 y log x y = dx y x dy y2 = dx x(1 y log x ) x. dy y2 = dx 1 y log x Ans. (b) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 403 ANSWERS 1 171. (e x 1 1 (0) dx e x )dx = 1 = 0 Ans. (b) 0 e 172. 1 + log x dx x 1 Let 1 + log x = t x = 0, t = 1 1 dt = x dx x = e, t = 2 2 t2 = + dt = 2 1 1 2 = 1 3 = 2 2 2 3 2 Ans. (a) log 3 173. 0 ex dx 1+ e x If 1+ex=t ex = 4 1 t dt dt dx x = 0, t = 2 x = log3, t = 4 4 = [log t ]2 log 4 log 2 2 = log 2 Ans. (b) log 2 1 174. 1+ 0 x 1+ x let (1 + x 2 ) = t2 2 x = 0, t = 1 x =1 t = 2 2x = 2t 2 1 t dt = 1+ t dt t dx = dx dx x 2 1 1 dt 1+ t 1 404 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II = = = = [t log (1 + t )]1 2 ( ( ( )[ ( ) ] 2 1) log (1 + 2 )+ 0 2 1) log (1 + 2 ) 2 1 log 1 + 2 log 1 Ans. (d) None of these 1 175. 1 dx 1 1 dx (1 + x) (2 + x) + + 1 x 2 x 0 0 1 1+ x [log(1 + x ) log(2 + x )]1 0 log 2 + x 0 log 2 3 Ans. (a) log 2 3 176. a + ar = 15 a (1+ r) = 15 a = ar + ar 2 + ar 3 a= ar 1 r = r r = 1/2 1 r a= 15 2 = 10 3 Sum of Series = a 10 = 20 = 1 r 1 1/ 2 Ans. (a) 20 177. a = 1 1 =1 x 1 x a b= 1 1 = 1 y 1 y b 1 1 + = 1 x + 1 y 2 (x+y) = 2.1 = 1 a b Ans. (c) 1 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 405 ANSWERS R 3 100 4 178. 90 = 2000 R = 6% Ans. (b) 6% 179. 216 = 5400 6 n 100 n = 4/6 yrs. = 8 months Ans. (b) 8 months R 2 = 200 R 100 180. I1 = 10000 I2 = 6000 R 3 = 1800 R 100 I1 + I2 = 1900 200R + 180R = 1900 380R = 1900 R = 5% Ans. (b) 5% 181.If all the observation are equal. Then standard deviation = 0 Ans. (a) 0 182. If every item is increased by 5 then mean ( x ) also increased by 5, but the value of ( x x ) 2 remain same. Standard deviation will remain same, Standard deviation = 10 Ans. (c) 10 183. S.D. = d2 = N 360 =6 10 Coefficient of variation = 100 = x SD Am 100 6 = 15 40 Ans. (a) 15 406 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II M.D 100 Am 184. Coefficient of M.D. = 44 = 5 .77 100 AM A.M. = 13.11 Ans. 13.11 185. The S.D. of two values is equal to half their difference. a b 2 S.D. = The Statement is correct Ans. (a) True 186. Computation of Correlation Coefficient x x= x2 y2 40 40 2000 2000 2500 2500 1600 1600 100 80 4000 5000 3200 100 80 = 50 , y = = 40 2 2 4000 (50) (40) = 0 2 Cov (x, y) = xy 50 50 Total y r=0 Ans. (c) 187. Given rR = 2 , 3 di2 b di2 rR = 1 ( = 55 ) n n2 1 2 6 (55 ) =1 3 n n2 1 ( ) 330 2 1 = 3 n n2 1 ( ) 1 330 = 3 n n2 1 ( ) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 407 ANSWERS ( ) ( ) n n 2 1 = 990 = 10 10 2 1 n = 10 as n must a positive Ans. (a) 188. Let us assume that 4x + 3y + 7 = 0 (1) represent the regression line of x on y and 3x + 4y + 8 = 0 regression line of y on x. (2) represent the (1) 4x = 7 3y x= 7 3 y 4 4 bxy = 3 4 (2) 4y = 8 3x y = 2 3 x 4 3 4 byx = 3 3 9 r 2 = byx. bxy = = 4 4 16 r= 9 3 3 = = = 0 .75 16 4 4 (We take the sign of n as negative since both the regression coefficient are negative). Ans. (c) 189. Ans. (d) Refer Properties 190. Given byx = 1.2 (1) U= x 100 2 x = 100 + 2U x = 100 + 2 U and v = y 200 3 y = 200 + 3 v y = 200 + 3 v 408 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II byx = = = ( x x) (y y ) E( x x)2 [2 (U U ).3(v v )] 2 [2(U U )] 2 3 (U U )(V V ) 4 (U U )2 = 3/2 bvu bvu = 2/3 byx = 2/3 1.2 = 0.8 Ans. (b) 191. Let A, is First bag is selected A2 is second bag is selected. B: In a draw of 2 balls, one is red and the other is black. The required probability P = P(A 1 B) + P (A 2 B) P(A 1 ) P (B/A 1 ) + P (A 2 ). P(B/A 2 ) = Since there are two bags, the selection of each being equally likely. P(A 1 ) = P(A 2 ) = 1/2 P(B/A 1 ) = Probability of drawing one red and one black ball in a draw of 2 balls from the 1 st bag 5 C 1 3 C 1 15 = 8C 2 28 = P(B/A 2 ) = Probability of drawing one red and one black ball in a draw of 2 balls from the 2 nd bags. = 4 C 1 5C 1 5 = 9C 2 9 (1) p = 1/2 p. = 15 1 5 + 28 2 9 15 5 135 + 140 275 + = = 56 18 504 504 Ans. (a) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 409 ANSWERS 192. Let A1 is first purse is selected. A2 is second purse is selected. Let B: In a draw of one coin, one coin must be silver The required probabilities. P = P (A1 B ) + P (A 2 B ) = P ( A1 ) .P (B / A1 ) + P ( A 2 ). P (B / A 2 ) (1) Since there are two purse, the selection of each being equally likely 1 1 P ( A1 ) = , P ( A2 ) = 2 2 P (B / A1 ) = Probability of drawing one silver coin from the first purse. = 3C 1 = 3/7 7C 1 P (B / A 2 ) = Probability of drawing one silver coin from the second purse. = 4C1 4 = 7C 1 7 3 1 4 Substituting (1) p=1/2 + 7 2 7 = 3 4 7 1 + = = 14 14 14 2 Ans. (a) 193. When two tosses of unbiased dice the total sample space. S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6) (2,1), (2,2), (2,3), (2,4), (2,5), (2,6) (3,1), (3,2), (3,3), (3,4), (3,5), (3,6) (4,1), (4,2), (4,3), (4,4), (4,5), (4,6) (5,1), (5,2), (5,3), (5,4), (5,5), (5,6) (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)} n(s) = 36 In the above sample space, let x be the number of sines getting from the experiment. Let x = 0, means no sin. = number of times = 25 x = 1, means no sin. = number of times = 10 410 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II x = 2, means no sin. = number of times = 01 36 Expected table is: x 1 2 p(x) 0 25 10 1 The required probability = Mean = Expected Value x p ( x) n( s ) = = 0 25 + 1 10 + 2 1 36 = 12 1 = 36 3 Ans. (a) 194. The experiment of throwing three dice is theoretically same as that of throwing a die thrice. Let E be the event of throwing six in a throw of die. P(E) = 1/6 and P ( E ) = 1 P(E) = 1 1/6 = 5/6 Let x denotes the random variable "number of Sixes". The possible values of x are 0, 1, 2, 3 P(x=2) = P(E 1 E 2 E 3 or E 1 E 2 E 3 or E 1 E 2 E 3 ) = P(E 1 ) . P(E 2 ) P( E 3 ) + P(E 1 ) P( E 2 ) P(E 3 )+ P( E 1 )+ P(E 2 ) P(E 3 ) = 1 1 5 1 5 1 5 1 1 . . + . . + . . 6 6 6 6 6 6 6 6 6 P(x=2) = 15 216 Ans. (c) 195. let A and B denote the events that the Chartered Accountant is selected in firms X and Y respectively. Then in the usual notations, we are given. P(A) = 0.7 P( A ) = 1 P(A) = 1=0.7=0.3 P( B ) = 0.5 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 411 ANSWERS P(B) = 1 P(B) = 1 0.5 = 0.5 ( ) and P A B = 0.6 By De Morgan's law (A B) = A B P (A B ) = 1 P (A B ) ( = 1 P A B = 1 0.6 = ) 0.4 The probability that the Chartered Accountant will be selected in one of the two firms X or Y is given by: P (AUB) = P(A) + P(B) P = 0.7 + 0.5 0.4 = (A B) 0.8 Ans. (a) 196. 1 log (log x) + dx (log x) 2 I = log (log x) = log (log x).x 1 (log x) 1 x. log (log x) (log x) x log (log x) 1 .dx + 1 (log x)2 1 x dx 1 dx + (log x) 2 . x dx + (log x )2 x log x x. log (log x) Ans. (a) d [ log (log x)] .x dx + = dx dx (log x) 2 dx 1 = dx 1 (log x)2 + (log x)2 dx x +c log x x. log (log x) x +c log x 197. 'is equal to' Satisfies Reflexive, Symnetric and transitive Relation This is Equivalence Relation. Ans. (d) Equivalence Relation. 412 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 198. f(x) = x2 +2 f( x) = ( x) 2 + 2 x2 + 2 = f( x) = f(x) f(x) is even function Ans. (b) even function. 199. f(x) = 12 1+ x = 12.12 x Range = 12 12 , 0< x<9 12 12 1 .....12 12 9 Range = 12 < f(x) < 12 10 Ans. (a) 12 f( x) 12 10 200. 'Is greater than' over the set of real number is not satisfied Reflexive and Symmetric relation it only satisfied transitive Relat ion Ans. (a) Transitive relation. Model Test Paper BOS/CPT 9 151. Given x 17 = x + y 23 23x = 17x + 17y 23x 17x = 17y 6x = 17y x= 17 y 6 17 y+y x+y 6 Now, = x y 17 y y 6 = 17 y + 6 y 6 6 17 y 6 y Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 413

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