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CA CPT : Volume 2 - Model Test Paper 9 (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 9 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. Every transaction or event has two aspects as per (a) (c) 2. Dual aspect concept Realisation concept. 24.4.2010 24.3.2010 (b) (d) 21.3.2010 None of the above Amount spent for the construction of temporary huts which were necessary for construction of the overbridge (flyover) and demolished when the flyover was ready is a (a) (b) (c) (d) 4. (b) (d) A bill was drawn on 20.1.2010 payable after 60 days, the maturity date of the bill will be (a) (c) 3. Going concern concept Cost concept Capital expenditure Deferred Revenue expenditure Revenue expenditure Both (a) and (c) Difference of total of debit and credit side of the trial balance is transferred to (a) (c) Suspense A/c P & L A/c Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Difference A/c Trading A/c 219 MODEL TEST PAPER - 9 5. In the absence of any partnership agreement, profits and losses are shared among the partners (a) (b) (c) (d) 6. Which of the following statement is not true? (a) (b) (c) (d) 7. P & L A/c All of the above Liabilities = Capital + Assets Capital = Assets Liabilities Capital = Assets + Liabilities Assets = Liabilities Capital Purchases A/c Building A/c (b) (d) Material A/c Wages A/c (b) (d) Consistency concept Accrual concept Going concern concept All of the above Writing of transaction in the Ledger is called (a) (c) 13. (b) (d) Balance Sheet P & L appropriation Fundamental accounting assumptions are (a) (c) 12. Balance Sheet None of the above Material costing Rs. 4,000 and labour charges Rs. 3,000 paid for the erection of the building is debited to (a) (c) 11. (b) (d) Which of the following is correct? (a) (b) (c) (d) 10. P & L A/c Trading A/c Carriage outward is debited to (a) (c) 9. Petty cash is an asset In case of debt becoming bad the amount should be credited to bad debts A/c Plant & Machinery is a fixed asset Goods distributed as sample is credited to Purchases A/c Returns inward is debited to (a) (c) 8. Equally In the ratio of capital In the ratio of loan given by them to the partnership firm Either (a) or (b) Casting Posting (b) (d) Balancing Journalizing (b) (d) Revenue expenditure Current assets Municipal tax Rs. 6,000 under dispute is a (a) (c) Contingent Liability Current Liabilities 220 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 14. Purpose of accommodation bill is (a) (b) (c) (d) 15. In the Journal there are (a) (c) 16. 6 columns 8 columns Nominal A/c Real A/c (b) (d) Personal A/c Dummy A/c Carriage A/c Freight A/c (b) (d) Motor A/c Freight & Motor A/c Very short-term Short term (b) (d) Long term All of the above Trading A/c Balance sheet (b) (d) P & L A/c All of the above Arjun purchased goods for Rs. 10,00,000 and sold 70% of such goods during the year ended 31st December 2009. The market value of the remaining goods was Rs. 2,00,000. He valued the closing Inventory at cost. He violated the concept of (a) (c) 22. (b) (d) Capital expenditures are recorded in the (a) (c) 21. 5 columns 7 columns Capital expenditure provides benefit (a) (c) 20. 5 columns 7 columns Freight charges paid on purchase of a new motor will be debited to (a) (c) 19. (b) (d) Joint Venture account is a (a) (c) 18. 4 columns 6 columns In the ledger there are (a) (c) 17. To facilitate trade transaction When both parties are in need of fund Provide loan for actual purchases or sales of goods All of the above Periodicity Conservatism (b) (d) Money measurement Cost A building was purchased for Rs. 4,00,000 on 1.04.2009. On 31st March, 2010, its net realizable value was Rs. 5,00,000. The value of building to be shown in the books as on 31st March, 2010 will be (a) (b) (c) (d) Cost price Net realisable value Cost or Net realisable value which ever is less Cost or Net realisable value which ever is more Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 221 MODEL TEST PAPER - 9 23. Cash sales Cash collected from customers Bad debts Opening Trade receivables Closing Trade receivables Total sales will be (a) (c) 24. (b) (c) 25. (d) 6,000 6,000 6,000 6,000 6,000 6,000 Rs. 15,000 Rs. 7,500 (b) (d) Rs. 17,500 Rs. 25,000 2:2:1 3:3:2 (b) (d) 3:3:1 none of the above 12:10 13:11 (b) (d) 10:12 None of the above A machinery is purchased for Rs. 60,000. Depreciation is to be provided annually on the basis of fixed instalment method. Useful life of the asset is 8 years and the residual value is Rs. 10,000. Rate of depreciation will be (a) (c) 29. Dr. To Sales Returns A/c Sales Return A/c Dr. To X A/c Sales Return A/c Dr. To Suspense A/c None of the above X, Y and Z are partners sharing profits in the ratio of 4:3:2. Y retires, X and Z decide to share future profits in the ratio of 5:3. Gaining ratio between X and Z will be (a) (c) 28. X A/c K and L are equal partners. They admitted M for 1/4 share in future profit. New profit sharing ratio will be (a) (c) 27. Rs. 2,63,000 Rs. 2,60,000 Ram and Shyam entered into a joint venture. Ram purchased goods costing Rs. 52,500. Shyam sold goods costing Rs. 45,000 at Rs. 60,000. Balance goods were taken over by Ram at Rs. 10,000. The profit on Joint Venture is (a) (c) 26. (b) (d) A cheque of Rs. 6,000 received from X was dishonoured and had been posted to debit of Sales returns account. Rectifying journal entry will be (a) . Rs. 2,33,000 Rs. 2,43,000 Rs. 70,000 Rs. 2,00,000 Rs. 7,000 Rs. 30,000 Rs. 16,000 10.416% 9.416% (b) (d) 10% 11% Goods worth Rs. 7,000 given as charity should be credited to (a) (c) Trustee A/c Purchases A/c 222 The Institute of Chartered Accountants of India (b) (d) Sales A/c Charity A/c Common Proficiency Test (CPT) Volume - II 30. Perpetual inventory valuation system entails (a) (b) (c) (d) 31. Ram, Shyam and Mohan are partners sharing profits in the ratio of 4:3:2. Sohan is admitted for 1/3 share in future. Profit sacrificing ratio will be (a) (c) 32. 2:3 3:2 (b) (d) 1:1 None of the above Capital A/c Revaluation A/c (b) (d) Realization A/c None of the above 2:2 1:2 (b) (d) 2:3 3:2 Goodwill is to be calculated at one and half years purchases of average profit of last 6 years. The firm earned profit during the first 3 years as Rs. 30,000, 20,000 and 20,000 and suffered losses of Rs. 5000, 3000 and 2000 in the last 3 years. Goodwill amount will be (a) (c) 36. 4:3:2 None of the above M, N and O are partners with capitals of Rs. 10,000, Rs. 7,500 and Rs. 5,000 respectively. On O s retirement his share is acquired by M and N in the ratio of 3:2 respectively. Gaining ratio will be (a) (c) 35. (b) (d) On admission of a partner, unrecorded investment worth Rs. 10,000 and unrecorded liability toward suppliers for Rs. 4,000 will be recorded in (a) (c) 34. 2:3:2 3:2:3 Y and Z are partners sharing profit in the ratio of 3:2. X is admitted as a partner. The new profit sharing ratio among Y, Z and X is 5:3:2. Sacrificing ratio will be (a) (c) 33. Maintenance of records of each receipts and issues. Direct determinatin of cost of goods issued and closing Inventory is taken as residual figure. Reconciliation of physical Inventories with the Inventory as per records. All of the above Rs. 10,000 Rs. 20,000 (b) (d) Rs. 15,000 Rs. 25,000 X started business with Rs. 1,00,000 cash and furniture Rs. 20,000. He bought goods worth Rs. 3,00,000 on credit basis. Sales amount to Rs. 5,00,000 including Rs 50,000 cash sales. Out of credit sales, Rs. 1,00,000 were outstanding at the end of the year. Cash balance after giving affect of above transactions will be (a) (c) Rs 4,50,000 Rs 5,00,000 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Rs 3,50,000 Rs 2,00,000 223 MODEL TEST PAPER - 9 37. An old furniture appearing in the books at Rs. 10,000 is to be exchanged for a new furniture of Rs. 10,000. The old furniture has been valued at Rs. 2,000 for exchange purpose. Loss on exchange will be (a) (c) 38. Rs. 25,000 Rs. 20,000 (b) (d) (b) (c) (d) Depreciation Rent paid (b) (d) Salary A/c Dr To Employee A/c Salary A/c Dr To Employee A/c To Suspense A/c Salary Dr To Employee A/c None of the above Salary paid Carriage 10,000 10,000 10,000 1,000 9,000 1,000 1,000 In the trial balance of joint stock company the following balances are given i. 10% Mortgage debentures 4,00,000 (payable after 4 years) ii. Discount allowed on issue of debenture Amount of discount written off per year will be (a) (c) 42. Rs. 30,000 Rs. 24,000 Salary paid to employee Rs. 10,000 debited to Employee A/c by Rs. 1,000. Rectifying entry will be (a) 41. Rs. 22,000 Rs. 7,000 Which of the following is a non cash expense? (a) (c) 40. (b) (d) Goods of Rs. 30,000 ( sales price ) sent on approval or return basis were included in the sales book. The profit included in the sales was 20% on cost. Inventory with the party will increase closing Inventory by (a) (c) 39. Rs. 18,000 Rs. 8,000 Rs. 2,400 Rs. 3,000 (b) (d) 10,000 Rs. 2,500 Rs. 2,600 Recovery of bad debt is a (a) (b) (c) (d) Revenue expenditure Revenue receipt Deferred revenue expenses Capital receipt 224 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 43. Capital on April 1, 2009 Capital on April 1, 2010 Drawings during the year Additional capital introduced during the year Net Profit of the year will be (a) (c) 44. Rs. 49,000 Rs. 47,000 (b) (d) Rs. 42,000 Rs. 50,000 Ignored Subtracted (b) (d) Added None of the above Capital Expenditure Deferred revenue Expenditure (b) (d) Revenue Expenditure None of the above. 21 June, 2010 22 June, 2010 (b) (d) 23 June, 2010 19 June, 2010 Which of the following errors will effect the trial balance (a) (b) (c) (d) 49. Rs. 5,000 Rs. 3,000 On 10.05.2010, A draws a bill on B for Rs. 50,000 for 40 days. June 22 is a public holiday. The maturity date of the bill will be (a) (c) 48. (b) (d) Expenses of Rs. 20,000, incurred in obtaining a license for starting the factory is (a) (c) 47. Rs. 6,000 Rs. 4,000 In bank reconciliation statement, when balance as per cash book is taken as the starting point, then interest collected by the bank Rs.9,000 and direct deposit by a customer into his bank Rs. 18,000 will be (a) (c) 46. 20,000 25,000 5,000 6,000 Raj draws a bill on Rohan for Rs. 1,00,000 for mutual accommodation. Raj discounted the bill for Rs. 98,000 from Bank and remitted Rs. 49,000 to Rohan. On the due date Raj will send to Rohan (a) (c) 45. Rs. Rs. Rs. Rs. Repairs to motor plant wrongly debited to motor plant account Total of purchases journal is short by 70,000 Wages paid on purchase of new motor plant debited to wages a/c None of three Rohit acceptance to Sumit for Rs. 15,000 renewed at 6 month on the condition that Rs. 10,000 be paid in cash immediately and a new bill of 6 months will be drawn for the remaining amount which will carry interest @ 10% p.a. The amount of interest will be (a) (c) Rs. 100 Rs. 250 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Rs. 150 Rs. 200 225 MODEL TEST PAPER - 9 50. Goods destroyed by fire Rs. 80,000 and insurance company admitted 50% claim. The loss on insurance claim will be entered in (a) (c) 51. Trading A/c All of the above. Rs. 3,500 Rs. 7,000 (b) (d) Rs. 10,500 Rs. 3,000 Furniture bought on 1st October 2008 for Rs. 40,000 was sold on 31st March, 2010 for Rs. 36,000. Depreciation is charged @ 10% p.a. on original cost. Accounting year closes on 31st March every year . Profit on sales will be (a) (c) 53. (b) (d) Following balances are given in trial balance 10% loan on (1.04.2009) Rs. 70,000 (Cr.) Interest on loan 3,500 Interest outstanding at the end of the year will be (a) (c) 52. Balance Sheet P & L A/c (b) (d) Rs. 3,000 Rs. 4,000 Rs. 1,000 Rs. 2,000 Following figures have been taken from the book of a trader Purchases 1,00,000 Sales returns 8,000 Carriage outward Sales 9,000 5,000 Office rent Purchases returns 1,60,000 4,000 Amount of gross profit will be (a) (c) 54. (b) (d) Rs. 60,000 Rs. 52,000 Rs. 61,000 Rs. 70,000 The profit for the last four years are given as follows Years Rs. 2006 10,000 2007 15,000 2008 20,000 2009 15,000 The value of goodwill on the basis of three years purchases of average profit based on last four years will be (a) (c) Rs. 15,000 Rs. 20,000 226 The Institute of Chartered Accountants of India (b) (d) Rs. 60,000 Rs. 45,000 Common Proficiency Test (CPT) Volume - II 55. Which of the following is a fixed asset? (a) (c) 56. (b) (d) Trading A/c Balance Sheet Plant & Machinery Trade receivables (b) (d) Land & Building Furniture Journalising Balancing (b) (d) Posting of an entry other than opening entry Carry forwarding Goods costing Rs. 30,000 were sold at 25% profit on selling price. Sales price will be (a) (c) 60. Capital A/c of partners P & L adjustment The words To Balance b/d or By Balance b/d are recorded in the particulars column at the time of (a) (c) 59. Building Trade receivables Which of the following is a current asset? (a) (c) 58. (b) (d) General Reserve at the time of admission of a new partner is transferred to (a) (c) 57. Cash Inventory Rs. 7,500 Rs. 37,500 (b) (d) Rs. 22,500 Rs. 40,000 On April, 2009, Gita invested capital of Rs. 60,000. She withdrew Rs. 5,000 on the first day of each month interest on drawing is provided @ 20%. The amount of interest on drawings deducted from capital will be (a) (c) Rs. 6,000 Rs. 6,500 (b) (d) Rs. 12,000 Rs. 1,000 SECTION B : MERCANTILE LAWS (40 MARKS) 61. Actual breach may be (a) (b) (c) (d) 62. A contract implied by law is known as (a) (c) 63. During the course of performance On the date of performance (a) and (b) (a) or (b) Contingent contract Quasi contract (b) (d) Alternation Implied contract Specific performance may be ordered by court if (a) (b) (c) (d) There is no standard for ascertain actual damage Pecuniary compensation is not adequate relief The act is done wholly on part of trust (a) or (b) or (c) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 227 MODEL TEST PAPER - 9 64. Which of the following is not referred to as goods (a) Stock (b) Shares (c) Money (d) Grass 65. A contract can be performed by (a) An agent of the promisor (c) (a) or (b) 66. (b) (d) The promisor himself Both (a) and (b) Which of the following statement is false? Consideration (a) (b) (c) (d) Must be of some value in law Must move at the desire of the promisor May move from any person Must be illusory 67. An executory consideration (a) Is a promise for a promise (b) Consists of a promise in future (c) Is an outstanding liability on both the parties (d) All of the above 68. _________ of a firm means the breaking up or extinction of the relationship which subsisted between all the partners of the firm (a) Registration (b) Dissolution (c) Amalgamation (d) Demerger 69. Publishing defamatory statements or agreements which are opposed to public policy are (a) Valid (b) Voidable (c) Illegal (d) Void 70. Following is not a mode of delivery (a) (c) 71. (b) (d) Constructive delivery Symbolic delivery In a breach of contract, if the promisee did not suffer any real damage, he can claim (a) (c) 72. Statutory delivery Actual delivery Exemplary damages Nominal damages (b) (d) General damages No damages In an agreement one party agrees to assist the other in recovering property, with a view to sharing the profits of litigation. It is (a) (c) Maintenance Stifling litigation 228 The Institute of Chartered Accountants of India (b) (d) Champerty None of the above Common Proficiency Test (CPT) Volume - II 73. Risk prima facie passes with (a) (b) (c) (d) 74. When the seller fails to give notice to the buyer under Section 39(3), the risk during seatransit lies with the (a) (c) 75. Whole some None of the above Yes No (b) (d) Partly yes Partly No Goods are perishable. Seller gives notice (b) (d) Seller has reserved such right All of these. Illegal & void Unlawful (b) (d) Voidable Valid Void from beginning Void if based on happening of an impossible event Enforceable if the contingent event is under the control of the promisor Wagering agreement Champerty and maintenance are the ____________agreement. (a) (c) 81. (b) (d) A contingent contract is (a) (b) (c) (d) 80. Presentable Merchantable Competitions involving games of skill are (a) (c) 79. Buyer Insurer Seller has right of resale where (a) (c) 78. (b) (d) Audit of a partnership firm s account is compulsory under the Partnership Act, 1932 (a) (c) 77. Seller Carrier A pen or pencil that will not write, a watch that will not keep time, a rubber that will not help to erase cannot be considered as (a) (c) 76. Payment of price Property or ownership Completed agreement Verification and delivery of goods Lawful Valid (b) (d) Void Voidable When both the benefits & burden devolve on the legal heir, it would be called (a) (b) (c) (d) Will Assignment Delegation Succession Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 229 MODEL TEST PAPER - 9 82. _________cannot enter with a contract. (a) (c) 83. (b) (d) Void Illegal Payment is made The contract is made (b) (d) Goods are ascertained None of the above Where a trust or charge is created Where payment is made to a third party Where payment is made by a third party None of the above A contract having reciprocal promises (b) A contract having cross promises (d) A bilateral contract An unenforceable contract Partnership Agreement Articles of Partnership (b) (d) Constitution of Partnership All of the above Property of the firm shall be held by use of the partners ___________. (a) (b) (c) (d) 90. Voidable Valid Partnership deed is also called________. (a) (c) 89. It defines the provisions of law It is fraudulent A contract involving two promises is called: (a) (c) 88. (b) (d) Privity of contract is subject to the exception ___________. (a) (b) (c) (d) 87. It is forbidden by law It is for legal consideration Under the Sale of Goods Act, 1930, the property in goods passes when________. (a) (c) 86. Agent Sole Trader A __________ agreement is one, which is enforceable at the option of one party. (a) (c) 85. (b) (d) The objects of an agreement shall not be unlawful if ___________. (a) (c) 84. Partner Lunatic For charitable purposes For private purposes of the partners For business purposes as well as private purposes Exclusively for business purposes Section 10 of the Sale of Goods Act 1930 deals with fixation of price of goods by __________. (a) (b) (c) (d) The Judge The Arbitrator The Central Government The valuation of a third party. 230 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 91. In an agreement to sell the property (ownership) in the goods passes __________. (a) (b) (c) (d) 92. A contract of sale may be__________. (a) (c) 93. Future All of the above Is lost Is at the optioning the court Is at the optioning the seller Can be exercised Price Interest (b) (d) Damages All of the above A just in personam Both (a) and (b) (b) (d) A just in rem Neither (a) nor (b) Sale Unlawful (b) (d) Agreement to sell All of the above In a contract of sale of goods, if the seller is not the owner of goods, then the title of the buyer shall: (a) (c) 99. (b) (d) A contract of sale of contingent goods is _________. (a) (c) 98. Existing Contingent An agreement to sell in respect of goods is an executory contract which creates ___________. (a) (c) 97. Absolute All of the above The rights available to an unpaid seller against the buyer are right to sue for ________. (a) (c) 96. (b) (d) Where the unpaid seller has attained a decree for the price of the goods, the right of lien _________. (a) (b) (c) (d) 95. Conditional Written Under the Sale of Goods Act, 1930, goods may be _________. (a) (c) 94. Immediately At a future date Either immediately or future date Never Be same as that of the seller Be better than that of the seller (b) (d) Not be same as that of the seller None of the above A buys a readymade shirt for his son, The shirt does not exactly fit his son. Decide. (a) (b) (c) (d) A has no right to return or exchange the same A has right to return the same He will demand for damages He may file a suit for exchange Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 231 MODEL TEST PAPER - 9 100. A buys a T.V. set from B . B agrees to deliver the set to A . After some time during the day, B sells the same to C at a higher price. Decide title of the good. (a) (c) C gets a good title Nobody gets a goods title (b) (d) A gets a good title None of these SECTION C : GENERAL ECONOMICS (50 MARKS) 101. If budget deficit is Rs. 11,350 crore and borrowings are Rs. 33,300 crore, what is fiscal deficit? (a) (c) 102. Meat and Rice Cheese and Meat More than one Less than one (b) (d) One Zero J.B. Say Adam Smith (b) (d) Robbins Alfred Marshall Alfred Marshall Hicks and Allen (b) (d) Adam Smith None of the above Cardinal Measurability of utility means: (a) (b) (c) (d) 107. (b) (d) Indifference curve analysis is propounded by: (a) (c) 106. Bread and Rice Bread and Meat Marginal utility analysis was mainly propounded by: (a) (c) 105. Rs. 44,650 crore Rs. 21,950 crore If the proportion of income spent on a good remains the same as income increases, then income elasticity for the good in: (a) (c) 104. (b) (d) Sir Robert Giffen was surprised to find out relationship of price with two other goods, which were: (a) (c) 103. Rs. 11,350 crore Rs. 33,300 crore Utility can be measured Utility cannot be measured Utility can be ranked Utility can be measured in some case Which of the following statements is false? (a) (b) (c) (d) An indifference curve is concave to the origin An indifference curve is convex to the origin A higher indifference curve is better than a lower indifferent curve An indifference curve is a curve which represents all those combinations of two goods which give same satisfaction to the consumer. 232 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 108. Identify the factor which generally keeps the price-elasticity of a demand for a good high. (a) (c) 109. Treatment of post office deposits Treatment of time deposits of banks Treatment of saving deposits of banks Treatment of currency Once in 1969 Twice in 1969 and 1980 Thrice in 1969, 1980 and 1991 None of the above Reduce CRR Increase CRR Sell securities in the open market Increase Bank Rate RBI Finance Minister (b) (d) Planning Commission Monetary Bank of India Which of the following is incorrect? (a) (b) (c) (d) 115. 1.5 1.667 Monetary Policy is given by: (a) (c) 114. (b) (d) In order to increase money supply in the country, the RBI may: (a) (b) (c) (d) 113. 0.916 1 After 1950, commercial banks in India were nationalized: (a) (b) (c) (d) 112. Its very low price None of the above The basic distinction between M1 and M2 is in the: (a) (b) (c) (d) 111. (b) (d) Suppose price of fashionable Shirts rises from Rs. 400 per piece to Rs. 700 per piece. The Shopping Mall manager observes that the rise in price causes demand for shirts to fall from 500 shirts per week to 300 shirts per week. What is the price elasticity of demand for shirts? (use Mid Point Method) (a) (c) 110. Its very high price Large number of substitutes The shape of the average cost and marginal cost curve is U The AR and MR curves of a firm under perfect competition are parallel to X-axis. At Equilibrium AR=MR At Equilibrium MC=MR The slope of indifference curve indicates: (a) (b) (c) (d) Price ratio between two commodities Marginal rate of substitution Factor substitution Level of indifference Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 233 MODEL TEST PAPER - 9 116. If the quantity of Banana demanded is 100 kg when price is Rs 40 per kg and quantity demanded is 50 kg, when price per kg of Banana is Rs. 60. Find price elasticity of demand using arc-elasticity method. (a) (b) (c) (d) 117. Suppose Mohan & Co. produces 10 units of output and incurs Rs. 30 per unit of variable cost and Rs. 5 per unit of fixed cost. In this case, total cost is: (a) (c) 118. -1.6 -2.6 (b) (d) 1.6 2.6 Economic laws are mere statement of tendencies Economics laws are as exact as physical laws Economics laws are permanent All of the above Rs. 1500 Rs. 8000 (b) (d) Rs. 1600 Rs. 2000 Under which market structure, the control of firm over price is nil? (a) (c) 123. Buyers are able to influence the price of the commodity Any units of commodity are considered by buyers to be different Buyer discriminates in their purchases based on non-price factors. There are no obstacles to the free mobility of resources. If after selling 10 units, a seller realises Rs. 12, 000 and after selling 15 units he realises Rs. 20, 000 what is the marginal revenue here? (a) (c) 122. Rs. 35 Rs. 350 Which of the following statements is correct? (a) (b) (c) (d) 121. (b) (d) If the price of petrol rises by 25% and demand for car falls by 40% then, cross elasticity between petrol and car is: (a) (c) 120. Rs. 300 Rs. 305 A condition needed for a perfectly competitive industry to exist is that: (a) (b) (c) (d) 119. 2.5 1.8 (-) 1.66 (-) 2.2 Perfect competition Oligopoly (b) (d) Monopoly Monopolistic Competition If as a result of 80 percent increase in all inputs, the output increases by 25 percent, this is a case of: (a) (c) Increasing return to scale Decreasing returns to scale 234 The Institute of Chartered Accountants of India (b) (d) Decreasing return to factor Diminishing return to factor Common Proficiency Test (CPT) Volume - II 124. When marginal product is negative, then total product is: (a) (c) 125. (b) (d) Rs.40 Rs.1 The firm should increase output The firm should do nothing The firm should hire less labour The firm should decrease price Change in quantity, divided by the change in price Change in price divided by change in output The change in PxQ due to a one unit change in output None of above Suppose that an owner is earning total revenue of Rs.1,00,000 and is increasing explicit cost of Rs.60,000. If the owner could work for another company for Rs.30,000 a year, we would conclude that: (a) (b) (c) (d) 130. Rs.20 Rs.38 Marginal Revenue is equal to (a) (b) (c) (d) 129. Always earns super profits Incurs losses Earns normal profit only May earn normal profits, super normal profits or incur losses. Suppose a firm is producing at level of output, such that MR>MC what should be the firm do to maximise profit? (a) (b) (c) (d) 128. Decreasing None of the above Assume that when price is Rs.40 quantity demanded is 9 units, and when price is Rs. 38, quantity demanded is 10 units. Based on this information, what is the marginal revenue resulting from an increase in output from 9 units to 10 units? (a) (c) 127. (b) (d) In the long run, a firm in monopolistic competition: (a) (b) (c) (d) 126. Maximum Constant The firm is earning economic profit or Rs. 10,000 The firm is earning accounting profit or Rs. 40,000 The firm is earning economic profit of Rs. 40,000 Both (a) and (b) Which is not the essential condition of pure competition? (a) (b) (c) (d) Large number of buyers and sellers Homogeneous product Freedom of entry Perfect knowledge among buyers and sellers Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 235 MODEL TEST PAPER - 9 131. What is the shape of AR curve faced by a firm under perfect competition? (a) (b) (c) (d) 132. Which of the following is the condition for equilibrium of a firm? (a) (c) 133. Structural Frictional (b) (d) Seasonal Technological Second Tenth (b) (d) Sixth Ninth CWS CDS (b) (d) Usual Status CMS Which of the following statements is correct? (a) (b) (c) (d) 138. Usual Status Current Weekly Status Current Daily Status Current Yearly Status __________ measures generally gives the lowest estimate of unemployment. (a) (c) 137. MR = AR AC = MR Every__________ person in the world is an Indian (a) (c) 136. (b) (d) When due to introduction of new equipments, some workers tend to be replaced by equipments; their unemployment is termed as __________ (a) (c) 135. AC = AR MC = MR ___________________ measure estimates the number of persons who may be said to be chronically unemployed. (a) (b) (c) (d) 134. Horizontal Vertical Positively sloped Negatively sloped Countries which are industrially well-developed generally have higher per-capital income than countries which are not. India is a capital surplus economy Agriculture sector need not depend upon industrial sector for its growth None of the above Mahalanobis model stressed upon the establishment of: (a) (b) (c) (d) Consumer goods industries Export oriented industries Agro-based industries Capital and basic goods industries 236 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 139. If income elasticity of the household for good X is 3 then it is a: (a) (c) 140. Marginal utility Consumers surplus (b) (d) Total utility Producer surplus Bank rate policy Margin requirement (b) (d) Open market operation Variable reserve requirement Liberalisation Privatisation (b) (d) Globalisation Disinvestment Reducing the peak rate of custom duties Rectifying anomalies like inverted duty structure Introduction of VAT for achieving harmonized taxation regime The tax rate on foreign companies has also been reduced from 55% to 40% Occupational structure refers to the: (a) (b) (c) (d) 147. Insurance Companies None of the above Which of the following is not an indirect Tax Reform? (a) (b) (c) (d) 146. (b) (d) Integration of the domestic economy with the world economy is called____. (a) (c) 145. Banks RBI Which of the following is not a quantitative measure of credit control? (a) (c) 144. Foreign currency assets held by RBI Gold holding of the RBI Special Drawings Rights None of the above The total area under the demand curve of good measures: (a) (c) 143. Necessity Good Inferior Good Based II framework is for: (a) (c) 142. (b) (d) Which of the following is not included in foreign exchange reserves? (a) (b) (c) (d) 141. Normal Good Luxury Good Number of workers living in a country. Size of working population in the industrial sector Distribution of working population among different occupations Nature of different occupation in the economy Which of the following is not a characteristic of a price taker? (a) (b) (c) (d) Negatively Sloped Demand Curve TR = P x Q AR = Price MR = AR Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 237 MODEL TEST PAPER - 9 148. All are features of monopoly except: (a) (b) (c) (d) 149. There is a single seller The firm is a price taker The firm produces a unique product The existence of some advertising A monopolist is able to maximize his profits when: (a) (b) (c) (d) 150. His output is maximum He charges a higher price His average cost is minimum His marginal cost is equal to marginal revenue ___________ is the difference between total receipts and total expenditure (a) (c) Fiscal Deficit Capital Deficit (b) (d) Budget Deficit Revenue Deficit SECTION D : QUANTITATIVE APTITUDE (50 MARKS) 151. If x 17 x+y = , what is equal to x + y 23 x y (a) (b) 17 32 (c) 152. 11 23 23 11 (d) None of these (b) (d) 2 None of these (b) (d) 12 None of these If 1+ 25 x = 1 + , then x is 144 12 (a) (c) 154. If (4)3 ( ) (a) (c) 153. 1 3 10 13 2 8 = 2n, then n is A number of men went to a hotel and each spent as many rupees as there were men. If the money spent was Rs. 15625; find the number of men. (a) (c) 110 145 238 The Institute of Chartered Accountants of India (b) (d) 125 None of these Common Proficiency Test (CPT) Volume - II 155. A, B and C have to distribute Rs. 1,000 between them, A and C together have Rs. 400 and B and C Rs. 700. How much does C have? (a) (c) 156. If log (a) (c) 157. 6ab 6a262 (b) (d) 8ab None of these (b) (d) 100 10000 1000 None of these 2.352 7.452 (b) (d) 3.452 None of these 36 38 (b) (d) 31 None of these (b) (d) 10 None of these If nP3 = 60, then the value of n is (a) (c) 161. a+b 1 = (log a + log b), the value of a2 + b2 is 2 2 If log 2 = 0.3010, find the number of digits in 2100 (a) (c) 160. Rs. 200 None of these If log 2 = 0.301 and log 3 = 0.477, then the value of log 225 is: (a) (c) 159. (b) (d) If log10x = 4, then the value of x is (a) (c) 158. Rs. 100 Rs. 150 3 5 Evaluate lim x 0 ax + bx 2 x a b (a) (b) log (c) 162. log ab log (a b) (d) None of these (b) (d) 0 None of these Evaluate lim x 0 (a) (c) 10x 5x 2x + 1 x 1 log 5 log 2 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 239 MODEL TEST PAPER - 9 163. Evaluate lim x 0 (a) (c) 164. (b) (d) log 5 + log 2 None of these (b) (d) 0 None of these (b) (d) 6 1 Evaluate lim x 0 (a) (c) 166. log 5 log 2 0 0 None of these e5x e 3x e 2x + 1 Evaluate lim x 0 x (a) (c) 165. 10x 5x 2x + 1 x2 e5x e 3x e 2x + 1 x 6 1 Evaluate: 1 dx x + a2 2 ( log ( x ) a )+c ( ) (a) (b) 2 2 log x + x a + c (c) 167. 2 2 log x + x + a + c x2 (d) None of these (b) 2 2 log x + x + a + c (d) None of these Evaluate: (a) (c) 168. 2 1 dx x a2 2 ( log ( x + ) a )+c 2 2 log x x a + c Evaluate 9x x2 2 ( ) 1 dx 1 2 (a) 1 3x + 1 log +c 6 3x 1 (b) 1 3x 1 log +c 6 3x + 1 (c) 1 3x + 2 log +c 3 3x + 2 (d) None of these 240 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II x -1 Evaluate (a) x 2 + 1 log x + x 2 + 1 + c (b) x 1 log x + x 1 + c (c) 169. x 2 + 1 log x + x 1 + c (d) 170. x2 + 1 dx ) ( ( ) ( ) None of these 2 Evaluate (1 x ) logx dx 2 (a) (b) x2 (1 x ) log x 1 + 9 + c (c) x2 x3 1 x log x x +c 3 9 (d) 171. (1 x ) x log x 1 x9 + c None of these 2 76 80 (b) (d) 78 None of these In an election, there are five candidates contesting for three vacancies; an elector can vote any number of candidates not exceeding the number of vacancies. In how many ways can one cast his votes? (a) (c) 173. From a panel of 4 doctors, 4 officers and one doctor who is also an officer, how many committee of 3 can be made if it has to contain at least one doctor and one officer? (a) (c) 172. 2 12 25 (b) (d) 14 None of these In how many ways can 12 different things be equally distributed among 4 groups? (a) (c) 15,400 14,400 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) 15,000 None of these 241 MODEL TEST PAPER - 9 174. The number of factors of 420 is (a) (c) 175. (b) (d) 22 None of these Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all the five balls. In how many different ways can we place the balls so that no box remains empty? (a) (c) 176. 20 25 100 150 (b) (d) 120 None of these Find the sum of the series. 243 + 324 + 432 + . to n terms (a) (b) 4n 34 n 1 3 (c) 177. 4n 36 n 1 3 3n 36 n 1 4 (d) None of these The sum of the first eight terms of a G.P. is five times the sum of the first four terms; then the common ratio is (a) (b) 2 (c) 178. 2 2 (d) None of these The sum of the following series 4 + 44 + 444 + to n term is: (a) (b) 4 10(10n 1) + n 9 9 (c) 179. 4 10(10n 1) n 9 9 10(10n 1) +n 9 (d) None of these The Arithmetic Mean between two numbers is 15 and their G.M. is 9; then the numbers are (a) (c) 180. 27,3 16, 9 (b) (d) 9, 9 None of these The product of n G.M.s between the two given numbers is equal to the n power of the single G.M. between them. This statement is (a) (c) True Cannot say 242 The Institute of Chartered Accountants of India (b) (d) False None of these Common Proficiency Test (CPT) Volume - II 181. The weighted arithmetic mean of first n natural numbers whose weights are equal to the corresponding numbers is equal to: (a) (b) 2(2n + 1) 2 (c) 182. 2n + 1 3 n(n + 1) 2 (d) None of these The mean weight of 15 persons is 110 kg. The mean weight of 5 of them is 100 and another 5 is 125 kgs. What is the mean weight of the remainder? (a) (c) 183. 100, 3 100, 4 (b) (d) 200, 6 None of these Mean Mode (b) (d) Median (a) and (b) both In which Central value arranging is required. (a) (c) 186. 105 kgs. None of these The most reliable central value is (a) (c) 185. (b) (d) The sum of diviations of certain number of items measured from 2.5 is 50 and the sum of deviations of the same series measured from 3.5 is 50. Find the number of observations and their mean? (a) (c) 184. 110 kgs. 100 kgs. Mean Median (b) (d) G.M. H.M. The chance of 53 Tuesdays in a year is (a) (b) 1 7 (c) 187. 2 7 3 7 (d) None of these Two unbiased dice are thrown. Find the probability that sum of the faces is not less than 10. (a) 1 6 (b) 5 6 (c) 2 3 (d) None of these Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 243 MODEL TEST PAPER - 9 188. The probability that a person travels by a plane is 1 2 and that he travels by train is 5 3 Find the probability of his traveling neither by plane nor by train? (a) (b) 2 15 (c) 189. 13 15 1 15 (d) None of these A card is drawn from a well shuffled pack of playing cards. Find the probability that it is either a diamond or a king. (a) (c) 190. 0.673 0.255 (b) (d) 0.237 None of these True Cannot say (b) (d) False None of these The mean and variance of a binomial distribution and 3 and 2 respectively. Find the probability that the variate takes values less than or equal to 2. (a) (c) 193. 3/13 None of these For a binomial distribution mean is 7 and its Standard Deviation is 8 . This statement is (a) (c) 192. (b) (d) A problem in statistics is given to two students A and B. The odd in favour of A solving the problem are 6 to 9 and against B Solving the problem are 12 to 10. If both A and B attempt, find the probability of the problem being solved. (a) (c) 191. 5/13 4/13 0.3767 0.3067 (b) (d) 0.3760 None of these Two digits are selected at random from the digits 1 through 9. Find the probability that their sum is even. (a) 2 7 , 9 18 (b) 5 5 , 9 18 (c) 4 5 , 9 18 (d) None of these 244 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 194. A die is thrown twice and the sum of the number appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once? (a) (c) 195. 0.7021 0.63728 (b) (d) 0.73728 None of these 2.1 2.23 (b) (d) 1.69 None of these 2.1 2.45 (b) (d) 1.69 None of these 0.1288 0.0588 (b) (d) 0.1088 None of these A population consists of 4 numbers. Find the number of sample of size 2 for with replacement condition. (a) (c) 200. None of these A random sample of size 9 is drawn without replacement from a finite population consisting of 25 units. If the number of defective units in the population be 5, find the Standard Error of the sample proportion of defectives. (a) (c) 199. (d) A simple random sample of size 36 is drawn from a finite population consisting of 101 units. If the population Standard Deviation is 12.6, find the Standard Error of sample mean when the sample is drawn without replacement. (a) (c) 198. 2 5 A simple random sample of size 36 is drawn from a finite population consisting of 101 units. If the population Standard Deviation is 12.6, find the Standard Error of sample mean when the sample is drawn with replacement. (a) (c) 197. (b) It is observed that 80% of television viewers watch Kahani Ghar Ghar Ki Programme. What is probability that at least 80% of the viewers in a random sample of five watch this programme? (a) (c) 196. 3 5 4 5 16 10 (b) (d) 6 None of these A population consists of 4 numbers. Find the number of sample of size two for without replacement condition. (a) (c) (b) (d) 16 10 6 None of these YYY Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 245 Answer of Model Test Papers Model Test Paper BOS/CPT 9 SECTION A : FUNDAMENTALS OF ACCOUNTING 1. (b) 2. (c) 3. (a) 4. (a) 5. (a) 6. (b) 7. (c) 8. (b) 9. (b) 10. (c) 11. (d) 12. (c) 13. (a) 14. (b) 15. (b) 16. (d) 17. (a) 18. (b) 19. (b) 20. (c) 21. (c) 22. (a) 23. (b) 24. (a) 25. (b) 26. (c) 27. (c) 28. (a) 29. (c) 30. (d) 31. (b) 32. (b) 33. (c) 34. (d) 35. (b) 36. (c) 37. (c) 38. (a) 39. (a) 40. (b) 41. (b) 42. (b) 43. (c) 44. (d) 45. (b) 46. (a) 47. (a) 48. (b) 49. (c) 50. (c) 51. (a) 52. (d) 53. (b) 54. (d) 55. (b) 56. (a) 57. (c) 58. (d) 59. (d) 60. (c) SECTION B : MERCANTILE LAWS (40 MARKS) 61. (b) 62. (c) 63. (d) 64. (c) 65. (c) 66. (d) 67. (d) 68. (b) 69. (c) 70. (a) 71. (c) 72. (b) 73. (b) 74. (a) 75. (c) 76. (c) 77. (d) 78. (d) 79. (b) 80. (b) 81. (d) 82. (c) 83. (c) 84. (a) 85. (b) 86. (a) 87. (a) 88. (d) 89. (d) 90. (d) 91. (b) 92. (d) 93. (d) 94. (d) 95. (d) 96. (a) 97. (b) 98. (a) 99. (a) 100. (a) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 291 ANSWERS Answer of Model Test Papers Model Test Paper BOS/CPT 9 SECTION C : GENERAL ECONOMICS (50 MARKS) 101 (b) 111 (b) 121 (b) 131 (a) 141 (a) 102 (c) 112 (a) 122 (a) 132 (c) 142 (b) 103 (b) 113 (a) 123 (c) 133 (a) 143 (c) 104 (d) 114 (c) 124 (b) 134 (d) 144 (b) 105 (c) 115 (b) 125 (c) 135 (b) 145 (d) 106 (a) 116 (c) 126 (a) 136 (b) 146 (c) 107 (a) 117 (d) 127 (a) 137 (a) 147 (a) 108 (c) 118 (d) 128 (c) 138 (d) 148 (b) 109 (a) 119 (a) 129 (d) 139 (c) 149 (d) 110 (b) 120 (a) 130 (d) 140 (d) 150 (b) SECTION D : QUANTITATIVE APTITUDE (50 MARKS) 151. (c) 152. (a) 153. (a) 154. (b) 155. (a) 156. (a) 157. (c) 158. (a) 159. (b) 160. (c) 161. (a) 162. (b) 163. (a) 164. (b) 165. (a) 166. (a) 167. (c) 168. (b) 169. (a) 170. (c) 171. (a) 172. (c) 173. (a) 174. (b) 175. (b) 176. (a) 177. (c) 178. (a) 179. (a) 180. (a) 181. (a) 182. (b) 183. (a) 184. (a) 185. (c) 186. (b) 187. (a) 188. (b) 189. (c) 190. (a) 191. (b) 192. (a) 193. (c) 194. (b) 195. (b) 196. (d) 197. (b) 198. (b) 199. (a) 200. (b) 292 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 ANSWERS = 23 y 23 = 11y 11 x + y 23 = x y 11 1+ 152. Given x 25 = 1+ 12 144 Squaring on both sides: 1+ 25 x = 1 + 144 12 2 144 + 25 x2 2x = 1+ + 144 144 12 169 144 + x 2 + 24 x = 144 144 x 2 + 24 x 25 = 0 (x + 25 ) (x 1) = 0 x = 25 , x = 1 x = 1 ( negative neglected) Ans. (a) (4 )3 ( 153. Given ( ) i.e. (2 ) 2 3 ) 8 2 = 2n 8 1 (2 ) 2 = 2 n 26 2 4 = 2n 2 10 = 2 n n = 10 Ans. (a) 154. Let total number of men went to a hotel = x Given, A man Spent Rupees = Total number of men = x Given Data = x + x = 15625 414 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II x 2 = 15625 x = 15625 = 125 Ans. (b) 155. Given A + B + C = 1000 (1) A + C = 400 (2) B + C = 700 (3) (2) A = 400 C (3) B = 700 C (1) 400 C + 700 C + C = 1000 C = 100 Ans. (a) a b 156. Given log = 1/2 (log a + log b) 2 2 log a b = log a + log b 2 2 a b log = log ab 2 2 a b = ab 2 2 a b = ab 4 (a b) 2 = 4ab a 2 + b 2 2 ab = 4 ab a 2 + b 2 = 6ab Ans. (a) 157. Given log10 x = 4 x = 10 4 Ans. (c) x = 10000 158. log 225 = log (9 25) = log 9 + log 25 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 415 ANSWERS = log 3 2 + log 5 2 = 2log 3 + 2 log 5 = 2log 3 + 2 log 10/2 = 2log 3 + 2 log 10 2 log 2 = 2 0.477 + 2 2 (0.301) log 225 = 2.352 Ans. (a) 159. Let 2 100 = x Taking log on both sides. log 2 100 = log x 100 log 2 = log x log x = 100 0.3010 log x = 30.1000 the no. of digits in 2 100 is 31 Ans. (b) 160. Given nP3 = n! = 60 (n 3 ) ! n(n 1) (n 2) = 60 = 5 4 3 n=5 Ans. (c) 161. Lt x 0 a x +bx 2 (a x 1) + (b x 1) Lt x 0 x x Lt x 0 a x 1 b x 1 + Lt x 0 x x a x 1 = log a Lt e x 0 x App Lt = log a + log b = log (ab) Ans. (a) 162. Lt x 0 log (ab) 10 x 5 x 2 x + 1 x (10 x 1) (5 x 1) (2 x 1) Lt x 0 x x x 416 The Institute of Chartered Accountants of India a x 1 = log a Lt x e 0 x Common Proficiency Test (CPT) Volume - II App Lt = log 10 log 5 log 2 = 10 log = log 1 0 5 2 Ans. (b) 0 163. Lt 10 x 5 x 2 x 1 x2 x 0 Lt x 0 Lt x 0 [5 x 2 x 5 x 2 x 1] 5 x (2 x 1) 1 (2 x 1) = x2 x2 (2 x 1) (5 x 1) (2 x 1)(5 x 1) Lt Lt x 0 x 0 x x x2 log 2 log 5 Ans. (a) 164. Lt x 0 log 5 log 2 e 5x e 3x e 2x + 1 x (e 5 x 1) (e 3 x 1) (e 2 x 1) 2 3. Lt 5 x 0 5x 3x 2x App Lt 5.1 3.1 2.1 = e x 1 = 1 Lt x 0 x 5 3 2 =0 Ans. (b) 0 165. Lt x 0 Lt (e 3 x .e 2 x e 3 x e 2 x 1) e 5x e 3x e 2x 1 = Lt x 0 x2 x2 [e 3x (e 2 x 1) 1(e 2 x 1) x 0 x 2 ] Lt [(e x 0 3x 1) (e 2 x 1) x 2 ] e 2x 1 e 3x 1 Lt Lt x 0 x x 0 x App Lt 3 2=6 Ans. (a) 6 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 417 ANSWERS Let 1 166. Given dx x2 + a 2 x2 + a 2 = z x x2 + a 2 z=x+ dz 1 (2 x ) dx = 1+ 2 dx 2 x +a2 x2 + a 2 + x = 2 x +a 2 z = 2 x + a2 = 167. dz = z 2 2 log x+ x +a + c Let dx x2 + a 2 dx 2 2 x +a 1 = dz z = log z + c dx x2 a 2 x2 a 2 = z x z=x+ x2 a 2 1 dz (2 x ) = 1 + = 1+ 2 dx 2 x a2 x2 a 2 + x = 2 x a 2 = x 2 x a2 z 2 x a2 dx dz = z x2 a 2 = 1 x2 a 2 dx = 1 2 dz +c 2 2 log (z) = log x+ x a Ans. (c) +c 418 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 168. Let t = 3x dt = 3 dx 1 dt 1 = 3 3 t2 1 I= 1 t 2 12 = 1 1 t 1 log +c 3 2 +1 t +1 = dt 1 3x 1 log +c 6 3x +1 Ans. (b) x 1 169. Let I = x2 + 1 dx dx x2 + 1 x I = x2 + 1 1 x = x2 + 1 dx 1 x2 + 1 dx I = I1 I 2 (say) I1 = x x2 + 1 dx Let t = x 2 + 1 dt = 2x dx I1 = 1 dt t 2 = 1 1 / 2 t dt 2 = 1 t1 / 2 = t = x2 + 1 2 1/ 2 1 I2 = = 2 log x + x +1 2 x +1 dx Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 419 ANSWERS I = I1 I2 I = 2 x 2 + 1 log x + x +1 + c Ans. (a) 170. Let I = 2 (1 x ) log x dx I = log x (1 x 2 ) dx [Here (log x) i s to be take n as first function and (1 x 2 ) as second function] Integrating by parts: x3 log x x 3 x2 x 3 x log x x2 x 3 = I = = I 1 x3 x x 3 dx x2 1 3 x log x x3 x 3 *3 +c = x2 1 3 3 x log x x x 9 dx +c Ans. (c) 171. Among 4 doctors, 4 officers and 1 doctor who is also an officer committee of 3 can be form in such manner. (i) 1 doctor, 1 officer, 1 doctor who is also officer = 4 C1 4 c 1 1 = 16 (ii) 2 doctor and doctor officer = 4 C 2 1 =6 (iii) 2 officer and doctor officer = 4 C 2 1= 6 (iv) 2 doctor and 1 officer = 4 C 2 4 C 1 = 24 (v) 1 doctor and 2 officer = 4 C 1 4 C 2 = 24 Total no. of ways = 16 + 6 + 6 + 24 + 24 = 76 Ans. (a) 76 172. Elector can vote for one or more vacancies in such manner (i) For 3 vacancies 5 C 3 = 10 420 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II (ii) For 2 vacancies 5 C 2 = 10 (iii) For 1 vacancy 5 C1 = 5 Total ways = 10 + 10 + 5 = 25 Ans. (c) 25 173. No. of ways in which 12 different thing distributed in 4 groups. = 12 ! = 15400 (3 !) 4 Ans. (a) 15,400 174. Factor of 420 is = {2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 30, 28, 35, 42, 60, 84, 105, 210, 140, 420} No. of factor of 420 = 22 Ans. (b) 22. 175. Five balls are kept in 3 boxes as no box will empty = (5 C 4 c 3 c ) 3 ! = (5 4 1) 6 = 120 ways. 1 1 3 Ans. (b) 120 ways. 176. 243 + 324 + 432 + n terms 3 5 .1 + 3 4 .4 + 3 3 .4 2 + n terms a = 35 r =4/3 4 n 3 5 . 1 3 Sn = = 35.3 4 1 3 = 4n 3 6 n 1 3 Ans. (a) 4n 3 6 n 1 3 177. S 8 =5.S 4 4 n 1 3 [ ] [ ] a r8 1 5 .a r 4 1 = r 1 r 1 (r + 1) = 5 4 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 421 ANSWERS r4 = 4 = ( 2) r= 2 Ans. (c) 4 2 178. 4+44+444 ... n terms 4 [9 + 99 + 999 + ..... n terms ] 9 4 [(10 1)+(100 1) + (1000 1) + ... n terms) 9 = = 4 9 = Ans. (a) 179. 10 (10 n 1) 4 10 (10 n 1) n n 9 9 10 1 4 10 (10 n 1) n 9 9 a +b = 15 and 2 ab = 9 ab = 81 a = (30 b) & (30 b)b = 01 b 2 30b + 81 = 0 b = 27, 3 and a = 3, 27 Nos are 27, 3 Ans. (a) 27, 3 180. Product of n Gm between two No. is equal to n th Power of single Gm between two nos. This statement is correct. Ans. (a) True 181. The weighted arithmetic mean of first a natural numbers whose weights are equal to the corresponding number is equal to 2n + 1 3 Ans. (a) 182. x = 2n + 1 3 w 1 x1 + w 2 x 2 + w 3 x 3 ( x1 + x 2 + x 3 ) 100 5 = 125 5 + w 3 5 15 1650 = 500 + 625 + 5.w 3 110 = 525 = 105 kg. 5 Ans. (b) 105 Kgs. w3 = 422 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 183. x n 2.5 = 50 x 2.5n = 50 (i) x 3.5n = 50 (ii) [Eg. (i) Eg. (ii)] 1.0n = 100 n = 100 x = 300 x 300 mean = = =3 n 100 Ans. (a) 100, 3 184. The most reliable value is mean. Ans. (a) Mean 185. In which Central Value arranging is required Median Ans. (c) Median 186. There are 365 days in a normal year (without leap year) No. 365 = 7 52 + 1 In a year will contain at least 52 Tuesday The possible remaining one Tuesday Let A be the event of getting 53 Tuesday in the year. P (A) = 1/7 Ans. (b) 187. Given two unbiased dice are thrown, then the simple space are: 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 Sample space of sum of the faces is not less than 10 A = {(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)} n(A) = 6 n ( A) 6 1 = = Required probability = n(S ) 36 6 Ans. (a) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 423 ANSWERS 188. Let A be the person travels by a plane P(A) = 1 5 Let B be the person travels by a train 2 3 P (B) = Probability of his travelling neither by plane nor by train. P(AB) = P(A). P(B) (Since A and B are mutually exclusive conditional probability) = 1 2 2 = 5 3 15 Ans. (b) 189. Let A denote the event of drawing a diamond and B denote the event of drawing a King 13 1 = from a pack of Cards. Then we have P(A) = 52 4 4 1 = and P(B) = 52 13 P(AUB) = P(A) + P(B) P(A B) = 1 1 + P ( A B ) (1) 4 13 There is only one case favourable to the event A B vize, king of diamond. Hence, P (A B) = 1 52 (1) P(AUB) = 1 1 1 13 + 4 1 16 4 = + = = 52 13 4 13 52 52 Ans. (c) 190. Let us define the events: E 1 : A solves the problem E 2 : B solves the problem then we are given P(E 1 ) = 6 6 2 = = 6 + 9 15 5 and P (E 2 ) = 10 5 = 10 + 12 11 424 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II Assuming that A and B try to solve the problem independently. E 1 and E 2 are independent. P (E 1 E 2 ) = P(E 1 ).P(E 2 ) = 2 5 2 = 5 11 11 The problem will be solved if at least one of the students A and B solves the problem. Hence, the probability of the problem being solved is given by P (E 1 E 2 ) = P (E 1 ) + P (E 2 ) P (E 1 E 2 ) = 2 5 2 + 5 11 11 22 + 25 10 37 = = 0 .673 55 55 Ans. (a) = 191. For a Binomial distribution Mean (np) = 7; standard denation ( n pq )= 8 Variance = npq = 8 This statement in false Because Mean > variance this is the properts A Binomial distribution Ans. (b) 192. Given Mean of Binomial distribution = = np = 3 (1) and Variance of Binomial distribution = 2 = npq =.2 (2) (2 ) npq 2 = (1) np 3 q = 2/3 p + q = 1 p = 1 q = 1 2 1 = 3 3 (1) n(1/3) = 3 = n=9 p=1/3, q = 2/3, n=9 By the Binomial distribution p(x) = nC values less than or equal to 2 x p x q n x . The probability that the variate takes Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 425 ANSWERS i.e. p (x < 2) = p(x = 0) + P (x = 1) + P (x = 2). = 9C 0 (1/3) 0 (2/3) 9 0 + 9C 1 (1/3) 1 (2/3) 9 1 + 9C 2 (1/3) 2 (2/3) 9 2 = 9C 0 (1) (2/3) 9 + 9C 1 (1/3) 1 (2/3) 8 + 9C 2 (1/3) 2 (2/3) 7 = (2/3) 9 + 3 (2/3) 8 + 4 (2/3) 7 P(x < 2) = 0.3767 Ans. (a) 193. Exhaustive cases: 2 digits can be selected out of 9 digits 1 through 9 in 9 C 2 ways. Exhaustive number of cases = 9 C 2 = 9 8 = 36 1 2 Favoarable number of cases. Among the digits 1 through 9. Even digits are: 2, 4, 6 and 8 i.e. 4 in all Odd digits are 1, 3, 5, 7 and 9 i.e. 5 in all. The sum of the two digits drawn will be even if (i) Either both the selected digits are even (or) (ii) both the selected digits are odd. Two even digits can be selected out of the 4 even digits in 4 C 2 ways and two odd digits can be selected out of the 5 odd digits in 5 C 2 ways. Hence, the favourable number of cases that the sum of the two selected digits in even. = 4 C 2 + 5C 2 = 4 3 5 4 + 1 2 1 2 = 6+10 = 16 P (sum of the two selected digits is even) = Number of favourable cases Exhaustive number of cases = 16 4 = 36 9 and P(Both selected digits are odd) = 5 C 2 10 5 = = 9 C 2 36 18 Ans. (c) 426 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 194. Let S be the sample space of the experiment S = {(1,1), (1,2), ... (6,5), (6,6)} Let A = event of getting sum 6 and B = event of getting 4 at least once. A = {(1,5), (2,4), (3,3), (4,2), (5,1)} and B = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4), (5,4), (6,4)} P(A) = 5/36 and P(B) = 11 36 Also, AB = {(4,2), (2,4)} P(AB) = 2 36 The required probability = Probability of getting 4 on at l east one die given that sum is 6 = P(B|A) = = 2 / 36 2 = 5 / 36 5 P (BA) P ( AB) = P ( A) P ( A) Ans. (b) 196. Standard Error of mean = = 12 .6 36 = n 12 .6 6 Standard Error of mean = 2.1 Ans. (a) 2.1 197. Standard Error of Mean without replacement = = n 12 .6 36 N n N 1 101 36 = 2 .1 0 .65 101 1 SE = 2.1 0.806 = 1.69 Ans. (b) 1.69 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 427 ANSWERS 198. P = 5 1 = 25 5 1 4 Q = 1 = 5 5 n = 5 S.E. of proportion of defectives = PQ n 1 4 1 = 0 .032 5 5 5 = SE = 0.1088 Ans. (b) 0.1088 199. n = 2, N = 4 Total number of possible sample of size of with replacement = 4 2 = 16 Ans. (a) 200. n = 2, 16 N=4 Total number of possible sample of size without replacement = NC n = 4 C 2 = 6 Ans. (b) 6 Model Test Paper BOS/CPT 10 151. The value of 3 3 + 4 3 + 5 3 + ..... + 113 2 [ = 11(11 + 1) 3 3 1 +2 2 = (11 6 )2 (1 + 8 ) = (66 )2 (9 ) = ] 4356 9 = 4347 Ans. (c) 152. Let the two numbers are x and y Given x + y = 75 (1) x y = 20 (2) 428 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II

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