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CA CPT : Volume 2 - Model Test Paper 7 (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 7 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. Advantages of redemption of preference shares by issue of fresh equity shares are a) c) 2. No cash outflow of money b) No capital gain tax to shareholders d) New equity shares may be valued at premium All of the above. Bills receivable is . (a) (c) Personal A/c Nominal A/c (b) (d) Real A/c Both (a) and (b) 3. X Ltd. forfeited 500 equity shares of Rs. 10 each fully called up which were issued at premium of 20%. Amount payable on shares were on application Rs. 2, on allotment Rs. 5 (including premium), on first and final call Rs. 5. Only application money and allotment money were paid by the shareholder in respect of these shares. At the time of forfeiture of these shares, securities premium account will be debited by a) NIL b) Rs. 1,000 c) Rs. 1,500 d) Rs. 2,000. 4. A, B and C are in partnership sharing profits and losses in the ratio of 5:3:2. A wants to retire, so B and C agreed to continue at 2:1. Gaining ratio will be a) c) 5. 11:4 11:6 b) d) 8:22 11:17. A and B are partners of X & Co., sharing profits and losses in 3:2. C admitted, on which a revaluation of assets of the firm was made by reducing the value of plant & machinery Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 163 MODEL TEST PAPER - 7 by Rs. 5,000, Inventory by Rs. 1,500 and furniture & fittings by Rs. 1,000 and by making a provision of bad and doubtful debts at Rs. 750 on trade receivables. Amount of revaluation profit/loss will be a) c) 6. Rs. 500 by B None of the above. Nominal A/c Personal A/c (b) (d) Real A/c None of the above (b) (d) Credit Balance Debit Balance Both (a) and (c) None of the above Sales Books Cash Book (b) (d) Purchases Books None of the above Profit & Loss A/c Trading A/c (b) (d) Balance Sheet P & L appropriation Secret Reserve Capital Reserve (b) (d) General Reserve All the above Which liability is not included in the total of Balance Sheet? (a) (c) 14. b) d) Which reserve is not shown in the balance sheet? (a) (c) 13. Rs 2,500 by A Rs. 2,500 by B Outstanding Salaries given in the trial balance is recorded in (a) (c) 12. Suspense A/c Nominal A/c Total of the sales day book is posted periodically to the credit of (a) (c) 11. (b) (d) Cash column in Cash Book always has (a) (c) 10. Personal A/c Memorandum A/c Prepaid insurance is . (a) (c) 9. Revaluation profit of Rs. 8,250 None of the above. A and B are in partnership sharing profits and losses in the proportion of three-fourth and one-fourth respectively. On 1st April 2011, they admitted C into partnership. C purchased one-third of goodwill for Rs. 2,000 and brought Rs. 10,000 as capital. A, B and C will share profits and losses equally. Sacrifice of the partner will be a) c) 8. b) d) Sale or return day book is a (a) (c) 7. Revaluation loss of Rs. 8,250 Revaluation profit of Rs. 3,300 Current Liability Fixed Liability (b) (d) Contingent Liability All of the above Which of the following statement is false? a) A bill of exchange must be in writing 164 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II b) c) d) 15. Revenue expenditures are recorded in the (a) (c) 16. (b) (d) Increase in gross profit None of the above. By balance b/d By balance c/d (b) (d) To balance b/d To balance c/d Maturity date is an emergency holiday Maturity date is a public holiday b) d) Maturity date is an unforeseen holiday Both (a) and (b) Rs. 100 Rs. 300 b) d) Rs. 200 Rs. 50 Which of the following statement is false? a) b) c) d) 21. Increase in Trade receivables Decrease in gross profit On 1st January, 2011, A sells goods for Rs. 10,000 to B and draws a bill at three months for the amount. B accepts it and returns it to A. On 1st March, 2011, B retires his acceptance under rebate of 12% per annum. What will be the amount of rebate? a) c) 20. Trading A/c. All the above The preceding working day will be the maturity date when a) c) 19. (b) (d) In case of opening Credit Balance the word ..are written on the Credit side. (a) (c) 18. Manufacturing A/c. P & L A/c. Goods purchased from Mohan for Rs. 4,000 passed through the Sales books. The rectification of this error will result in (a) (c) 17. Promissory note should be properly stamped On occasion of maturity date falling on any gazetted holiday, next day will be the maturity date Promissory Note is signed by the maker of the note Joint venture is a short duration special purpose partnership Co-venturers may contribute funds for running the venture or supply Inventory from their regular business Co-venturers share profits/losses of the venture at an agreed ratio likewise partnership Going concern assumption of accounting is appropriate for joint venture accounting. Narang purchased goods for Rs. 3,00,000 and sold 4/5 of goods amounting Rs. 5,00,000 and paid expenses amounting Rs. 1,10,000 for the year 2009. Besides that he paid Rs. 7,000 for an electricity bill of March 2008 and advance salaries amounting Rs. 10,000 was paid for the month of April 2010. He calculated net profit Rs. 1,50,000. The profit calculated by him is correct according to (a) (c) Conservatism concept Cost concept Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Matching concept Entity concept 165 MODEL TEST PAPER - 7 22. A trader purchased goods for Rs. 5,00,000 and sold 55% of such goods during the accounting year ended 31st Dec. 2009. The market value of the remaining goods was Rs. 1,00,000. He valued the closing Inventory at cost. He violated the concept of (a) (c) 23. Rs. 24,000 Rs. 22,000 (b) (d) Rs. 18,000 Rs. 34,000 Rs.15,000 Rs.14,000 Rs.1,60,000 Rs.7,000 Rs.20,000 (b) (d) Rs. 1,50,000 Rs. 1,51,000 Rs. 1,60,000 Rs. 1,86,000 Bank overdraft as per Cash book is Rs. 15,000 Cheque deposited but not cleared Rs. 4,000 Cheque issued but not cashed Rs. 6,000 Bank overdraft as per Bank statement will be (a) (c) 27. Dr. Salary A/c Rs.15,000 and Cr. Purchases A/c Rs. 15,000 Dr. Naresh Rs.20,000 and Cr. Purchases A/c Rs. 20,000 Dr. Salary A/c Rs.20,000 and Cr. Purchases A/c Rs. 20,000 None of the above Opening Trade receivables Bad debts during the year Cash received from customers Closing Trade receivables Cash sales Total sales will be (a) (c) 26. Conservatism Money measurement Cost of goods sold Rs. 20,000 Closing Inventory Rs. 8,000 Opening Inventory Rs. 6,000 Amount of purchases will be (a) (c) 25. (b) (d) Inventory worth Rs. 20,000 (cost price Rs.15,000) taken by Naresh who is a clerk in the office. The same is to be deducted from his salary in the subsequent month. Journal entry will be (a) (b) (c) (d) 24. Cost Periodicity Rs. 13,000 Rs. 25,000 (b) (d) Bank balance as per pass book Cheque issued but not presented Cheque deposited but not cleared Bank balance as per cash book will be -: (a) (c) Rs. 22,000 Rs. 18,000 166 The Institute of Chartered Accountants of India Rs. 5,000 Rs. 17,000 Rs 20,000 Rs 7,000 Rs 5,000 (b) (d) Rs. 32,000 Rs. 8,000 Common Proficiency Test (CPT) Volume - II 28. A company can issue redeemable preference shares (a) (c) 29. Journal Proper Purchases book Rs. 5,000 Rs. 10,000 (b) (d) Rs. 8,000 Rs. 6,000 Added in the total liability of the company Deducted in the liability of the company Added in the assets of the company Both (a) and (c) Owners of the company Trade receivables of the company (b) (d) Trade Payables of the company Trustee of the company Cost of goods sold Rs. 15,000 were sold at 25% profit on selling price. The amount of sales will be (a) (c) 35. (b) (d) Debenture holders are in nature of (a) (c) 34. Cash book Sales Book Debentures issued as collateral security is . (a) (b) (c) (d) 33. Valuation of liabilities b) Valuation of assets Both (a) and (b) Arithmetical accuracy of books of accounts. Pooja and Pratibha are partners sharing profits and losses in the ratio of 3:2. Pallavi is admitted for 1/5th share and brings Rs. 10,000 as capital and necessary amount for his share of goodwill. The goodwill of the entire firm is value at Rs. 40,000. Goodwill brought by Pallavi is (a) (c) 32. At par All of the three Credit purchases of goods worth Rs. 30,000 by a dealer will be recorded in (a) (c) 31. (b) (d) Trial balance does not check a) c) d) 30. At discount At premium Rs. 20,000 Rs. 18,750 (b) (d) Rs. 11,250 Rs. 15,000 Bad Debts recovered is an example of : (a) (b) (c) (d) Increase in Asset & Owner s Equity Decrease in Asset & Owner s Equity Increase in Liability & Owner s Equity Decrease in Liability & Increase in Owner s Equity Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 167 MODEL TEST PAPER - 7 36. Bill is drawn on 20 January 2010 for 2 months. After sight date of acceptance is 29 January 2010. The maturity date of the bill will be (a) (c) 37. Sales book Sales Returns book Trading A/c P & L appropriation A/c (b) (d) P & L A/c Balance Sheet Rs. 30,000 Rs. 22,500 (b) (d) Rs. 37,500 Rs. 35,000 Rs. 68,750 Rs. 41,250 (b) (d) Rs. 13,750 Rs. 12,500 Original cost Rs. 1,50,000, Salvage value Nil, Useful Life - 5 years Depreciation for the 3rd year under sum of digits method will be (a) (c) 42. (b) (d) Machinery costing Rs. 50,000 was purchased on 1st January 2009. The installation charges amounting Rs. 5,000 were incurred. The depreciation at 25% p.a. by written down value method for the year ended 31st Dec. 2009 will be (a) (c) 41. Purchase book Cash Book MND & Company employs a team of 15 workers who were paid Rs. 2,000 each in the year ending March 31, 2009. At the start of the year April 2009, company raised salaries by 25%. The amount of salary for the year ended 31st March, 2010 will be (a) (c) 40. 23 March, 2010 29 March, 2010 Security premium is recorded in .. (a) (c) 39. (b) (d) Returns of Cash Sales is recorded in (a) (c) 38. 1 April 2010 20 March, 2010 Rs. 20,000 Rs. 25,000 (b) (d) Rs. 35,000 Rs. 30,000 A company issued Rs. 50,000 10% debentures at a discount of 5% redeemable after 5 year at a premium of 5%. Loss on issue of debentures will be (a) (c) Rs. 2,500 Rs. 5,000 (b) (d) Rs. 6,000 Rs. 7,000 43. Ramesh Ltd. purchases furniture for Rs. 20,000 payable as to Rs. 6,500 in cash and the balance by an issue of 6% debentures of Rs. 100 each at a discount of 10%. Discount amount will be (a) Rs.1,350 (b) Rs.2,000 (c) Rs. 650 (d) Rs.1,500 168 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 44. Opening Trade receivables Rs. 1,50,000 Total sales Rs. 50,000 Cash received from customers Rs. 30,000 Cash sales Rs. 15,000 Sales Returns Rs. 3,000 Bad debts Rs. 7,000 Bills received from customers Rs. 15,000 Trade receivables at the end will be (a) (c) Rs. 1,40,000 Rs. 1,20,000 (b) (d) Rs. 1,30,000 Rs. 1,50,000 45. Goods costing Rs. 3,00,000 sent out to consignee at cost plus 25%. Invoice value of goods will be (a) Rs. 3,75,000 (b) Rs. 3,50,000 (c) Rs. 2,25,000 (d) Rs. 2,50,000 46. A manager gets 10% commission on sales. Cost price of goods sold is Rs.80,000 which he sold at a margin 20% on sale. Amount of commission will be (a) (c) Rs. 16,000 Rs. 10,000 (b) (d) Rs. 9,600 Rs. 6,000 47. Adjustment entry for interest earned but not received will be (a) Dr. Cash A/c and Cr. Interest A/c (b) Dr. Accrued Interest A/c and Cr. Customer A/c (c) Dr. Accrued Interest A/c and Cr. Interest A/c (d) None of the above 48. General Manager gets 10% commission on net profit after charging such commission. Gross profit Rs. 70,000 and General expenses other than manager commission are Rs. 12,000. Commission amount will be (a) (c) 49. (b) (d) Rs. 6072.72 Rs. 5172.72 Goods sold Rs. 25,000 on approval or return basis were included in Sales Book. The profit included in the sales was at 25% on cost. At the year end, closing Inventory will increase by (a) (c) 50. Rs. 5272.72 Rs. 5372.72 Rs. 5,000 Rs. 15,000 (b) (d) Rs. 20,000 Rs. 45,000 Balance as per Pass Book Rs. 27,400 (i) Cheque issued but not presented Rs. 73,000 (ii) Cheque deposited but not yet recorded by bank Rs. 47,700 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 169 MODEL TEST PAPER - 7 Balance as per cash book will be (a) (c) 51. (b) (d) Rs. 93,300 None of the above When Overdraft as per pass book Rs. 450 is the starting point then what will be the treatment of the following items in the Bank Reconciliation Statement? 1. Cheque drawn but not presented for payment Rs. 105 2. Cheque sent for collection but not credited by bank Rs. 300 (a) (c) 52. Rs. 52,700 Rs. 2100 Rs. 645 Rs. 855 (b) (d) Rs. 255 Rs. 45 If sales Rs. 70,000 and Cost of goods sold is Rs. 24,000. The gross profit is (a) (c) Rs. 56,000 Rs. 46,000 (b) (d) Rs. 94,000 None of these 53. Calculate amount of proposed dividend on the basis of following informations : 1. 50,000 equity share of Rs.100 each fully called up 2. Calls in arrears Rs. 50,000 3. Proposed dividend 20% (a) Rs. 10,00,000 (b) Rs. 9,84,000 (c) Rs. 9,90,000 (d) Rs. 9,80,000 54. Rs. 30,000 claim for workman compensation under dispute is a (a) (c) 55. 56. 12% loan Rs. 17,000 Interest on loan Rs. 700 Outstanding interest on loan will be (a) Rs. 2,040 (c) Rs. 2,740 (b) (d) Current liability Contingent liability (b) (d) Rs. 1,340 None of the above Trial balance shows the following balance Capital - Rs. 30,000 (Cr.) Payment of advance income tax - Rs. 1,500 Income tax paid - Rs. 4,000 Capital A/c balance at the end of the year will be (a) (c) 57. Fixed assets Current asset Rs. 24,400 Rs. 27,500 (b) (d) Rs. 24,500 None of the above Ashish s acceptance to Mohit for Rs. 10,000 discharged by a cash payment of Rs. 2,000 and a new bill for the balance plus Rs. 300 for interest. The amount of new bill will be (a) (c) Rs. 8,000 Rs. 12,300 170 The Institute of Chartered Accountants of India (b) (d) Rs.10,300 Rs. 8,300 Common Proficiency Test (CPT) Volume - II 58. On 1st April, 2010 Ram Ltd. issued Rs. 5,00,000 14% debentures at a discount of 10% repayable at the end of 5 years. Amount of discount to be written off every year will be (a) (c) 59. (b) (d) Rs. 5,000 None of the above Sohan Ltd. forfeited 1000 shares of Rs. 10 each fully called up for non payment of final call of Rs. 4 per share. All of these shares were reissued as fully paid for Rs. 6 per share. Amount transferred to capital reserve will be (a) (c) 60. Rs. 10,000 Rs. 50,000 Rs. 6,000 Rs. 2,000 (b) (d) Rs. 4,000 NIL Advantages of double entry system are a) b) c) d) The profit earned or loss suffered during a period can be ascertained together with details By the use of this system the accuracy of the accounting work can be established, through the device of trial balance. Result of one year may be compared with those of previous years and reasons for the changes may be ascertained. All of the above. SECTION B : MERCANTILE LAWS (40 MARKS) 61. Only those agreements, which are valid are (a) (c) 62. State Parties (b) (d) Statute Custom In writing Both (a) and (b) (b) (d) Oral Either (a) or (b) A voidable contract is one which (a) (b) (c) (d) 65. Proposal None of the above An agreement enforceable by law under the Indian Contract Act, 1872 may be (a) (c) 64. (b) (d) Contractual rights and duties are created by (a) (c) 63. Contract Offer Can be enforced at the option of aggrieved party Can be enforced at the option of both the parties Cannot be enforced in court of law Courts prohibit Which of the following is not the legal requirement of a valid acceptance? (a) (b) It must be communicable It must be absolute and unconditional Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 171 MODEL TEST PAPER - 7 (c) (d) 66. Which are of the following is an essential element of a valid contract? (a) (c) 67. Void agreement Voidable contract (b) (d) Valid Unenforceable Void None of the above Promisor Third party (b) (d) Promisee None of the above Inadequate Illusory (b) (d) Real Both (a) & (b) Consideration may be past Consideration may be future (b) (d) Consideration may be present All of the above Fraud Misrepresentation (b) (d) Undue Influence Coercion A contract with the minor, which is beneficial for him is (a) (c) 75. (b) (d) A wrong representation when made without any intention to decline the other party amounts to (a) (c) 74. Valid contract Void contract Which of the following statement is true? (a) (c) 73. Agreement and contract All of the above Contract will be valid, if the consideration is (a) (c) 72. Standard form of contracts by promise (b) Promissory Estoppel (d) The consideration must be at the desire of the (a) (c) 71. Consideration All of the above An agreement without consideration is (a) (c) 70. (b) (d) Contract which ceases to be enforceable by law becomes a (a) (c) 69. Free consent Competent parties A contract to perform a promise could arise by (a) (c) 68. It must be presumed It must be accepted by a person who has the authority to accept Void ab initio Valid (b) (d) Voidable Illegal Where the consent of both the parties is given by mistake the contract is (a) (c) Valid Voidable 172 The Institute of Chartered Accountants of India (b) (d) Void Illegal Common Proficiency Test (CPT) Volume - II 76. To make a contract voidable coercion must have been exercised against (a) (c) 77. If parties to it have no contractual capacity If it is done by mutual mistake If it is for lawful consideration If its consent is not free Voidable Valid (b) (d) Void Illegal By mutual Agreement By impossibility of performance By breach of contract By all the above Discharge of contract Waiver of contract (b) (d) Breach of contract Recession of a contract A contract can be discharged by performance in the ways of _____________. (a) (c) 84. Is fraudulent is forbidden by law Would defeat the provision of any law All of the above __________ signifies that the parties are not further bound under the contract. (a) (c) 83. In the same sense All of the above A contract can be discharged ____________. (a) (b) (c) (d) 82. (b) (d) A ___________ agreement is one, which is enforceable at the option of one party. (a) (c) 81. At the same time At different time Which of the following agreements will not be declared expressly void? (a) (b) (c) (d) 80. Any other person (a) and (b) Consideration and object of an agreement is unlawful if it (a) (b) (c) (d) 79. (b) (d) Under the Indian Contract Act, 1872 consent means agreeing on the same thing (a) (c) 78. Only the promisor (a) or (b) Offer to perform (a) or (b) (b) (d) Actual performance (a) and (b) A contract dependent on the happening or non happening of future uncertain event, is a _____________. (a) (c) Uncertain contract Contingent contract Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Void Contract Voidable contract 173 MODEL TEST PAPER - 7 85. A contingent contract dependant on the happening of future uncertain event can be enforced when the event __________. (a) (c) 86. (b) (d) Ascertained goods All of the above Consideration Both (a) and (b) (b) (d) Ownership None of the above Claim damages Reject the goods (b) (d) Repudiate the contract None of the above The sample Either (a) or (b) (b) (d) The description Both (a) and (b) The goods are not of perishable nature The seller has not given notice of resale to the buyer The buyer has not paid the price within a reasonable time All of the above. Each partner is ______ of every other partner in every matter connected with the partnership business. (a) (c) 93. Specific goods Unascertained goods The unpaid seller can exercise the right to resell the goods when______. (a) (b) (c) (d) 92. Actionable claim All of these In case of sale of goods by sample as well as by description, the goods should correspond with________. (a) (c) 91. (b) (d) When a breach of condition is treated as a breach of warranty, the buyer can _________. (a) (c) 90. Money Immovable property __________ may or may not pass between bailee and bailer. (a) (c) 89. Becomes impossible Either of these Under the Sale of Goods Act, 1930 existing goods are classified as ________. (a) (c) 88. (b) (d) The term goods for the purpose of Sale of Goods Act, 1930 does not include__________. (a) (c) 87. Happens Does not happen Bailor Principal (b) (d) Agent Pledgor The right of lien is available to the unpaid seller, only when __________. (a) (b) (c) (d) Seller is not in possession of goods Seller is in possession of the goods Seller delivered the goods to the carrier Seller has delivered the goods to the buyer 174 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 94. In a partnership firm, the decisions can be made by rule of majority when decisions relates to __________. (a) (c) 95. Buyer Any of the above Unlawful Non-monetary (b) (d) Lawful Monetary At any time during life of partnership firm At anytime after filing a suit After dissolution of a firm Either (b) or (c) Purchase Production (b) (d) Sale Manufacture A enters with a contract with B to sell him 100 bales of cotton and afterwards discovers that B was acting as agent for C . Decide. (a) (b) (c) (d) 100. (b) (d) ___________is a bargain between the buyer and the seller (a) (c) 99. Seller Court The registration of firm may be effected __________. (a) (b) (c) (d) 98. Fundamental decisions Buying and selling of property Price means ___________ consideration for sale of goods (a) (c) 97. (b) (d) If the seller makes use of pretended bidding to raise the price, the sale is voidable at the option of the (a) (c) 96. Policy decisions Ordinary routine matters A may sue B only A may sue C only A may sue either B or C A may sue either B or C or both for the price of cotton Anticipatory breach comes under_____ (a) (b) (c) (d) Law of Contractual relationship Law of Mutual consent Law of Mutaul agency Law of Limitation SECTION C : GENERAL ECONOMICS (50 MARKS) 101. We mainly study the following in micro economics: (a) (c) Location of a Industry Factor pricing Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Study of firms All of the above 175 MODEL TEST PAPER - 7 102. When we study why saving rates are high or low, we are studying: (a) (c) 103. (b) (d) Stock Concept None of the above Positive Income elasticity Zero (b) (d) Negative Income elasticity Both (a) and (b) Negative Positive (b) (d) Zero Less than one .7 .65 (b) (d) -.67 .77 Increasing return to a factor Diminishing returns to scale (b) (d) Decreasing return to a factor None of the above Under which market structure, average revenue of a firm is equal to its marginal revenue (a) (c) 111. Flow Concept Both (a) and (b) If as a result of 90 percent increase in all inputs, the output increase by 75 percent this is a case of (a) (c) 110. Desire Means to purchase Willingness to use those means for that purchase All of above If the price of Banana rises from Rs 30 per dozen to Rs. 40 per dozen and the supply increases from 240 dozen to 300 dozens elasticity of supply is: (use Arc Elasticity Method) (a) (c) 109. When to produce? For whom to produce? If two goods are substitutes like tea and coffee, then the cross elasticity is: (a) (c) 108. (b) (d) Inferior goods have: (a) (c) 107. How to produce? What to produce? Quantity demanded is a: (a) (c) 106. Micro Economics Both (a) and (b) Effective Demand depends on: (a) (b) (c) (d) 105. (b) (d) Which of the following is not a central problem of the economy? (a) (c) 104. Macro Economics Econometrics Monopoly Oligopoly (b) (d) Monopolistic competition None of the above (b) (d) WTO ADB Special Drawing Rights has link with: (a) (c) World Bank IMF 176 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 112. Banking Regulation Act, of India pertains to the year: (a) (c) 113. (b) (d) 177 149 1st January, 1995 1st January, 2001 (b) (d) 1st January, 1991 1st January, 1996 It functions as a short term credit institution. It functions as a long term credit institution. It is a reservoir of the currencies of all the member nations. It grants loan for financing current transactions. Mutual Trade Agreements Multiple Trade Agreements Mutilated Trade Union Agreements Multilateral Trade Agreements IMF IBRD (b) (d) GATT None of the above (b) (d) Depreciation allowance Corporate dividend tax NDP does not include: (a) (c) 120. 148 188 The predecessor of WTO was: (a) (c) 119. SLR Margin Requirements MTA stands for (a) (b) (c) (d) 118. (b) (d) Which of the following is not the function of IMF? (a) (b) (c) (d) 117. CRR Both (a) and (b) The WTO came into existence on: (a) (c) 116. 1949 1934 The present membership of IMF is: (a) (c) 115. (b) (d) ______________ refers to that portion of total deposits which a commercial is required to keep with itself in the form of liquid Assets. (a) (c) 114. 1945 1943 Payment made for direct taxes Undistributed profits Which of the following would not be included in GNP? (a) (b) (c) (d) Mohan purchases a shirt to wear Sai Ram purchases a new Mercedes Benz of S-class Yes bank purchases new computers for its shares business Aditi grows Tulsi plant in her home Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 177 MODEL TEST PAPER - 7 121. Full employment is the level at which there is: (a) (c) 122. Balance of Current Account All of the above Goods and invisible items Foreign Direct Investment (b) (d) Government Loans from abroad None of the above Fiscal policy Revenue policy (b) (d) Monetary policy None of the above Payments made to factors of production Payments made by one sector to another Payments made for no return service Repayment of loan Product Method Income Method (b) (d) Expenditure Method Deductive Method The Indian Road network is one of the longest in the world The village road network connects around 65 percent of all weather roads The National highways carry more than 40 percent of the total road traffic Most of the State Electricity Boards are running on profits Electricity generated from radio active elements is called: (a) (c) 130. (b) (d) Which of the following statements is incorrect? (a) (b) (c) (d) 129. Balance of Trade Balance of capital Account Which of the following is also known as value added method of measuring National Income? (a) (c) 128. Agricultural Sector Mining Transfer payments are: (a) (b) (c) (d) 127. (b) (d) Service Tax is an instrument of: (a) (c) 126. Transport Sector Service Sector In the Balance of payment statement, current account includes: (a) (c) 125. Zero unemployment None of the above Balance of payments is a broader term than: (a) (c) 124. (b) (d) In which sector of the Indian Economy will we find a high rate of disguised unemployment? (a) (c) 123. Normal rate of unemployment Least supply of labour Thermal electricity Tidal Energy (b) (d) Hyder Electricity Atomic energy According to the latest data, PLF is lowest in: (a) (c) South eastern region West eastern region 178 The Institute of Chartered Accountants of India (b) (d) North eastern region Eastern region Common Proficiency Test (CPT) Volume - II 131. Plant load factor measures (a) (b) (c) (d) 132. In the theory of demographic transaction in the first stage: (a) (b) (c) (d) 133. Price is equal to AVC Total revenue is equal to TVC Total loss of the firm is equal to TFC All of the above Rationality on the parts of consumers Ordinal measurement of satisfaction Cardinal measurement of satisfaction Consistent consumption pattern behavior of consumer NCAER NSS (b) (d) CSO RBI Suppose the total cost of production of commodity x is Rs. 1,25,000. Out of this implicit cost is Rs. 35,000 and normal profit is Rs. 25,000. What will be explicit cost of commodity x ? (a) (c) 138. 50 20 Which one of the following agencies in India is responsible for computation of National income? (a) (c) 137. (b) (d) The indifference curve approach does not assume: (a) (b) (c) (d) 136. 10 17.5 At shut down point: (a) (b) (c) (d) 135. Birth rate falls and death rate falls Birth rate falls and death rate rises Birth rate is high and death rate is high Birth rate rises, death rate falls Indian accommodates _____________ percent of world population. (a) (c) 134. Operational efficiency of Hydel plant Operational efficiency of Atomic plant Operational efficiency of Thermal plant Operational efficiency of Tidal plant Rs. 90,000 Rs. 65,000 (b) (d) Rs. 60,000 Rs. 1,00,000 Over the planning period, the relative share of area under food grains in gross cropped area in India has: (a) (c) Decreased Remained the same Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Increased Increased initially and then decreased 179 MODEL TEST PAPER - 7 139. The LAC curve (a) (b) (c) (d) 140. Over the planning period the share of industrial sector in the GDP of the India has: (a) (c) 141. RBI World Bank Health, Literacy and employment National Income, size of population and general price level National Income, per capita Income and per capita consumption Physical resource, monetary resource and population size Monopoly Monopolistic competition (b) (d) Perfect competition Oligopoly Fishery Animal Husbandry (b) (d) Forestry None of the above Sugar Oilseeds (b) (d) Cotton None of the above Which of the following was not prevailing in the country at the time of Independence? (a) (c) 147. (b) (d) Which of the following is not a commercial crop? (a) (c) 146. SBI UTI Which of the following is not including in the primary sector? (a) (c) 145. Decreased Remained above 40% Excess Capacity is the essential characteristic of the firm in the market form of: (a) (c) 144. (b) (d) Human Development Index is a composite index: (a) (b) (c) (d) 143. Increased Remained Constant Which bank among the following is responsible for issuing currency notes in India? (a) (c) 142. Falls when the LMC curve falls Rises when the LMC curve rises Goes through the lowest point of the LMC curve Falls when LMC < LAC and rises when LMC > LAC Zamindari System Mahalwari system (b) (d) Ryotwari system None of the above Agriculture provides employment to about ______% of people living in the country (2011-12) (a) (c) 53 10 180 The Institute of Chartered Accountants of India (b) (d) 80 90 Common Proficiency Test (CPT) Volume - II 148. UNDP stands for (a) (b) (c) (d) 149. Which one is a direct tax among the following? (a) (c) 150. Unlimited National Developed Programme United Nation Development Programme United Nation Development Project United National Development Programme Wealth Tax Service Tax (b) (d) Excise Duty None of the above (b) (d) Price line None of the above The other name of Budget line is: (a) (c) Demand line Supply line SECTION D : QUANTITATIVE APTITUDE (50 MARKS) 151. One third of a number is greater than one fourth of its successor by 1. Find the number (a) (c) 152. 17 15 (b) (d) A student on being asked to multiply the fraction by 16 None of these 16 of a certain fraction made the mistake of dividing 17 16 33 and so got an answer which exceeded the correct answer by Find 17 340 the correct answer. (a) (b) 46 58 (c) 153. 64 85 64 58 (d) None of these 5 4 2 4 of of a number is 8 more than of of the same number. What is half of that 7 15 5 9 number? (a) (c) 154. 630 105 (b) (d) 210 None of these The sum of two numbers is 14 and their difference is 10. Find the product of the two numbers. (a) (c) 24 36 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) 30 None of these 181 MODEL TEST PAPER - 7 156. The difference of two numbers is 11 and 1 th of their sum is 9. The numbers are: 5 (a) (c) 155. (b) (d) 30, 19 28, 17 (b) (d) 256:2401 None of these (b) (d) 2: 5 None of these (b) 9:25 (d) 125:27 (b) (d) 2:5 None of these (b) (d) 30 None of these The sub duplicate ratio of 16:49 is (a) (c) 157. 4:7 4:9 Duplicate ratio of 4:5 is (a) (c) 158. 31, 20 29, 18 16:25 64:125 Triplicate ratio of 3:5 is (a) (c) 159. 27:125 33 :5 3 40 20 The ratio of two numbers is 4:1. If 5 is added to both the numbers, the ratio of the new numbers obtained becomes 3:1. Then the numbers are (a) (c) 162. 2:6 5:2 The 4th proportion of 6, 8 and 15 is (a) (c) 161. 1 The sub triplicate ratio 8:125 is (a) (c) 160. 1 30, 20 20, 10 (b) (d) 40, 10 None of these The ratio of the money with A and B is 3:4 and that with B and C is 4:5. If A has Rs. 300, how much money does C have? (a) (c) 400 500 (b) (d) 300 None of these 163. Two numbers are in the Ratio 5:6. If 5 is subtracted from each number, the ratio becomes 4:5. Then the number are: (a) (c) 20, 30 25, 30 182 The Institute of Chartered Accountants of India (b) (d) 20, 25 None of these Common Proficiency Test (CPT) Volume - II 164. If 1 add 1 to each of the two given numbers their ratio is 1:2. If 1 subtract 5 from each the ratio is 5:11. Then the numbers are (a) (c) 165. 13 12 (b) (d) 15 None of these 140 105 (b) (d) 130 None of these 10 5 (b) (d) 7 None of these 82 47 (b) (d) 41 None of these A committee is to be formed of 3 persons out of 12. Find the number of ways of forming such a committee. (a) (c) 171. 15 None of these A two digit number is obtained by either multiplying sum of the digits by 8 and adding 1 or by multiplying the difference of the digits by 13 and adding 3. Then the number is: (a) (c) 170. (b) (d) If 28C2r : 24C2r 4 = 225:11, then the value of r is (a) (c) 169. 13 17 There are 7 man and 3 ladies. Find the numbers of ways in which a committee of 6 can be formed of them if the committee is to include atleast two ladies. (a) (c) 168. 35, 71 None of these Seven times a two digit number is equal to four time the number obtained by reversing the order of digits, and the sum of the digits of number is 3. then the number is: (a) (c) 167. (b) (d) What must be subtracted from each term of the ratio 27:43 to make it equal to 7:15? (a) (c) 166. 71, 25 35, 51 210 220 (b) (d) 230 None of these A gentlemen invites 6 of his friends to a party. In how many different arrangements they along with the wife of the gentleman can sit at a round table for a dinner if the host and his wife always sit side by side? (a) (c) 1440 1445 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (e) 144 None of these 183 MODEL TEST PAPER - 7 172. x 3 x 9 Evaluate lim x 9 (a) (b) 1 3 (c) 173. 1 6 2 3 (d) None of these (b) 1 2 2a (d) None of these x + a 2a x a Evaluate lim x a 1 (a) (c) 174. 2 a 1 3 2a 6 + 5x 2 Find lim x 4 x + 15 x 2 (a) (b) 1 4 (c) 175. 1 2 1 3 (d) None of these (b) (d) 1 None of these Evaluate (a) (c) 176. lim x a bx x2 0 2 dy ex -e-x ; if y = Evaluate dx ex +e-x (a) (e 4 x 4 ) x 2 +e 184 The Institute of Chartered Accountants of India (b) (e x + e x ) 2 Common Proficiency Test (CPT) Volume - II 1 (c) (e dy 177. x + e x ) (d) (1 + x ) 2 1+ x (a) None of these x ;if y = Find dx 2 (1 x ) 1 x (b) (1 + x ) (d) 3 None of these 3 1 x (c) 178. Find (1 + x ) 4 dy ;if y = x + x dx 2 x +1 (a) (c) 179. 4 x x + x 2 x +1 2 x 1 Evaluate (2x +1).7x (c) 7x x x (d) 2 + 2x 2 + 2x None of these (b) 2(x +1).7 x (d) .log 7 log 7 2 2 If y = log (x + x + a then find None of these 2 + 2x .log 7 dy dx 1 1 (a) 4 x 2 dy ;if y = 7 x + 2 dx (a) 180. 2 x 1 (b) x2 + a2 (b) x2 + a2 x (c) x2 + a2 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (d) None of these 185 MODEL TEST PAPER - 7 x 181. (a) (c) 182. 2 2y (b) (d) 2y None of these If the demand law is x = 10 - p 2 then the elasticity of demand at point p = 2 (a) (c) 183. dy If (x y) e x - y = a; then y + x is dx 2/3 2/5 (b) (d) 3/2 None of these x3 dx Evaluate : x +1 (a) (b) x3 log (x+1) + c (c) x3 x 2 + x log (x + 1) + c 3 2 (d) None of these (b) ex e x c (d) None of these (a) x2 + x 2 log (x 2 + 1) + c 2 (b) x 2 + x + 2 log (x 2 + 1) + c (c) 184. x + log (x+1) + c x3 x + 2 tan 1 x + c 3 (d) None of these e 4x + e 2x dx Evaluate e 3x (a) (c) 185. 186. 1 2x 1 e 4x + c 2 4e e 2x 1 e 4x +c x4 + 1 dx Evaluate 2 x +1 Evaluate log (x +1)dx (a) x log (x+1) x + log (x+1) + c (b) x 2 log (x + 1) - x 2 + log (x 2 + 1) + c (c) x log (x + 1) - x 2 + log (x + 1) + c (d) None of these 186 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 187. Evaluate (a) (c) 188. { 2 (1 + x) 3{ } }+ c 2 2 2 (1 + x) 3 x 3 + c 3 2 3 x 2 3 (b) (d) { } 3 3 2 (1 + x) 2 x 2 + c 3 None of these x2 - x + 2 dx Evaluate 3 x + x 2 + 2x (a) (b) (c) (d) 189. dx x + 1+x log x + 3/2 log (x 1) + 4/3 log (x2 + 2) + log c log x + 2/3 log (x2 1) + 3/4 log (x2 +2) + log c log x + 2/3 log (x 1) + 4/3 log (x + 2) + log c None of these Evaluate 3x 2 1 dx +13x -10 (a) (b) 3x 2 1 log 2 +c 17 3x + 15 (c) 190. 3x 2 2 1 log 2 +c 17 3x + 15 3x + 15 1 log 17 3x 2 (d) None of these (b) (d) -ex f(x) + c None of these Evaluate: (a) (c) e {f(x) + f'(x)} dx x ex f(x) + c ex f (x) + c b 191. +c Evaluate: a logx dx x (a) 1 b log(ba).log 2 a (b) b log(ba ). log a (c) a log(b + a).log b (d) None of these Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 187 MODEL TEST PAPER - 7 192. [f(x) + f(-x)][g(x) - g(-x)]dx Evaluate: (a) (c) 0 1 (b) (d) 193. Evaluate: (b) (d) 0 None of these (b) (d) 1 None of these 2 3 1 3 1 3 (a) b a (c) 1 1 3 b3 + a 3 2 Evaluate: 0 (a) (c) None of these dx (a+b-x) a 194. 1 1 3 3 b a 3 (b) (d) b 1 None of these x dx x+ 2-x 1 1 1 1 x 195. Evaluate: log x dx 0 (a) (c) 196. In how many ways can 7 departments be distributed among 3 ministers, if every ministers gets at least one but not more than 3 departments? (a) (c) 197. 1 0 1050 1200 (b) (d) 1000 None of these Find the number of words of three letters that can be formed with the letters of the word CALCUTTA . (a) (d) 90 98 188 The Institute of Chartered Accountants of India (b) (d) 96 None of these Common Proficiency Test (CPT) Volume - II 198. How many number of numbers three digits can be made from the digits of the number 1,2,3,4,3,2? (a) (c) 199. (b) (d) 42 None of these If Sn be the sum of n terms of an A.P.; the value of Sn 2Sn 1 + Sn 2 is (a) (c) 200. 40 45 d cannot calculated (b) (d) d2 None of these There are n ARITHMETIC MEANs between 3 and 31 such that the ratio of 3rd mean to (n 1)th mean is 1:3, then the value of n is (a) (c) 12 13 (b) (d) 15 None of these YYY Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 189 Answer of Model Test Papers Model Test Paper BOS/CPT 7 SECTION A : FUNDAMENTALS OF ACCOUNTING 1. (d) 2. (a) 3. (a) 4. (d) 5. (c) 6. (c) 7. (a) 8. (c) 9. (c) 10. (a) 11. (b) 12. (a) 13. (b) 14. (d) 15. (d) 16. (c) 17. (a) 18. (c) 19. (a) 20. (d) 21. (b) 22. (b) 23. (a) 24. (c) 25. (d) 26. (a) 27. (c) 28. (d) 29. (c) 30. (d) 31. (b) 32. (d) 33. (b) 34. (a) 35. (a) 36. (a) 37. (c) 38. (d) 39. (b) 40. (b) 41. (d) 42. (c) 43. (d) 44. (b) 45. (a) 46. (c) 47. (c) 48. (a) 49. (b) 50. (c) 51. (b) 52. (c) 53. (c) 54. (d) 55. (b) 56. (b) 57. (d) 58. (a) 59. (c) 60. (d) SECTION B : MERCANTILE LAWS (40 MARKS) 61. (a) 62. (c) 63. (d) 64. (a) 65. (c) 66. (d) 67. (d) 68. (c) 69. (b) 70. (a) 71. (d) 72. (d) 73. (c) 74. (c) 75. (b) 76. (c) 77. (b) 78. (d) 79. (c) 80. (a) 81. (d) 82. (a) 83. (c) 84. (c) 85. (a) 86. (d) 87. (d) 88. (a) 89. (a) 90. (d) 91. (c) 92. (b) 93. (b) 94. (c) 95. (b) 96. (d) 97. (a) 98. (b) 99. (d) 100. (a) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 287 ANSWERS Answer of Model Test Papers Model Test Paper BOS/CPT 7 SECTION C : GENERAL ECONOMICS (50 MARKS) 101 (d) 111 (c) 121 (a) 131 (c) 141 (b) 102 (a) 112 (b) 122 (b) 132 (c) 142 (a) 103 (b) 113 (b) 123 (d) 133 (c) 143 (c) 104 (d) 114 (c) 124 (a) 134 (d) 144 (d) 105 (a) 115 (a) 125 (a) 135 (c) 145 (d) 106 (b) 116 (b) 126 (c) 136 (b) 146 (d) 107 (c) 117 (d) 127 (a) 137 (c) 147 (a) 108 (d) 118 (b) 128 (d) 138 (a) 148 (b) 109 (c) 119 (b) 129 (d) 139 (d) 149 (a) 110 (d) 120 (d) 130 (b) 140 (a) 150 (b) SECTION D : QUANTITATIVE APTITUDE (50 MARKS) 151. (c) 152. (a) 153. (d) 154. (a) 155. (d) 156. (a) 157. (a) 158. (a) 159. (b) 160. (c) 161. (b) 162. (c) 163. (c) 164. (b) 165. (a) 166. (c) 167. (a) 168. (b) 169. (b) 170. (c) 171. (a) 172. (a) 173. (b) 174. (c) 175. (a) 176. (b) 177. (b) 178. (a) 179. (b) 180. (a) 181. (c) 182. (a) 183. (c) 184. (b) 185. (c) 186. (a) 187. (b) 188. (c) 189. (b) 190. (a) 191. (a) 192. (a) 193. (b) 194. (a) 195. (c) 196. (d) 197. (b) 198. (b) 199. (a) 200. (c) 288 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II x = 5 or 9 Ans. (c) 5 or 9. Model Test Paper BOS/CPT 7 151. Let the number be x. Then according to the given condition of the problem, x x +1 = +1 3 4 x x +1 =1 3 4 4 x 3 ( x + 1) =1 12 x 3 =1 12 x 3 = 12 x = 3 + 12 = 15 Hence the required number is 15 152. Let the fraction = x And Correct answer = y Given and i.e. 16 x = y (1) 17 x 33 =y+ 16 340 17 17 33 (2) x = y+ 16 340 (1) x = 17 y 16 Substitute x the value of x in equation (2) 17 17 33 y = y+ 16 16 340 289 33 y=y+ 256 340 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 377 ANSWERS 289 33 y y= 256 340 33 289 256 y = 340 256 33 33 y= 256 340 y= 33 256 340 33 y= 64 85 Ans. (a) 153. Let the number be x Given 5 4 4 (x ) = 8 + 2 (x ) 7 15 5 9 4 8 x = 8+ x 21 45 4 8 x x=8 21 45 180 168 x=8 945 12 x=8 945 x=8 945 12 x = 708.75 Ans. (d) 154. Let two numbers are x and y Given condition x + y = 14 (1) y x = 10 (2) Adding (1) and (2) 2x = 24 x = 12 (1) 12 + y = 14 378 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II y=2 Product of two numbers = x y = 12 2 = 24 Ans. (a) 155. Let two numbers are x and y. Given x y = 11 (1) And x+y =9 5 i.e. x + y = 45 (2) (1) and (2) 2x = 56 Adding X = 28 (1) 28 y = 11 y = 11 28 = 17 y = 17 The two numbers are 28, 17. Ans. (d) 156. Sub duplicate Ratio of 16:49 = 16 : 49 = 4:7 Ans. (a) 157. Duplicate Ratio of 4 : 5 = 4 2 : 5 2 = 16 : 25 Ans. (a) 158. Triplicate Ratio of 3 : 5 = 3 3 : 5 3 = 27 : 125 Ans. (a) 159. The sub triplicate Ratio of 8 : 125 = 3 8 : 3 125 = 2:5 Ans. (b) 160. 4 th Proportion of 6, 8 and 15 is 6x = 6 15 = 8 x 15 8 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 379 ANSWERS = 15 8 6 = x 20 Ans. (c) 161. Let the two numbers be x and y. According to the First condition of the problem, x 4 = y 1 x = 4y (1) According to the second condition of the problem, x+5 3 = y+5 1 x + 5 = 3 (y + 5) x + 5 = 3y + 15 x 3y = 15 5 = 10 (2) Put x = 4y from (1) in (2), we get 4y 3y = 10 y = 10 (1) x = 4 (10) = 40 Hence the required numbers are 40 and 10. Ans. (b) 162. Let A having money = 3x B having money = 4x C having money = 5x Given 3x = 300 x = 1 00 C = 5x = 5 100 = 500 Ans. (c) 163. Let the two numbers be x and y. According to the first condition of the problem. x 5 = y 6 6x = 5y 6x 5y = 0 (1) 380 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II According to the second condition of the problem x 5 4 = y 5 5 5(x 5) = 4 (y 5) 5x 25 = 4y 20 5x 4y = 5 (2) (1) 5 30x 25y = 0 (3) (2) 5 30x 24y = 30 Subtracting (3) from (4), we get y = 30 (1) 6 x 5 (30) = 0 6x = 150 x= 150 = 25 6 Hence the required numbers are 25 and 30 Ans. (c) 164. Let the given numbers be x and y. Then accord ing to the given conditions of the problem. x +1 1 = y +1 2 2x + 2 = y + 1 2x y = 1 and (1) x 5 5 = y 5 11 11x 55 = 5y 25 11x 5y = 30 (2) (1) 11 22x 11y = 11 (3) (2) 2 22x 10y = 60 (4) (3) (4) y = 71 y = 71 (1) 2x 71 = 1 2x = 70 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 381 ANSWERS x = 35 Hence, the required numbers are 35 and 71 Ans. (b) 165. Let the number to be subtracted be x. Then according to the problem 27 x 7 = 43 x 15 15 (27 x) = 7 (43 x) 405 15x = 301 7x 15x 7x = 405 301 8x = 104 x= 104 = 13 8 Hence the required number is 13 Ans. (a) 166. Let the unit digit = x and ten digits = y x+y = 3 (1) and the number = 10y + x Reversing the order of digits Units digit = y and ten's digit = x Number = 10x + y According to the given condition of the problem 7(10y + x) = 4(10x+y) 70y + 7x = 40x + 4y 70x 40x + 70y 4y = 0 33x + 66y = 0 x+2y = 0 92) Adding (1) and (2) we get 3y = 3 y=1 382 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II (1) x + 1 = 3 x = 3 1 = 2 Hence, the required number is 12 167. The committee of six must include atleast 2 ladies. i.e. two or more ladies. As there are only 3 ladies, the following possibilities arise: The committee of 6 consists of (i) 4 men and 2 ladies, (ii) 3 men and 3 ladies. The number of ways for (i) = 7 C 4 + 3 C 2 = 35 3 = 105 The number of ways for (ii) = 7 C 3 3 C 3 = 35 1 = 35 Hence the total number of ways of forming a committee so as to include atleast two ladies = 105 + 35 = 140 Ans. (a) 168. We have nCr = n! r!(n 4 )! Now substituting for n and r, we get 28 C 2r = 28 ! (2 r )!(28 2 r )! 24C 2r 4 = 24 ! (2 r 4 )!{24 (2 r 4 )}! 24 ! (2 r 4 )! (28 2 r )! = Given 28 C 2 r : 24 C 2 r 4 = 225:11 = = 28 C 2 r 24 C 2 r 4 = (2 r 4 )! (28 2 r )! 28 ! (2 r )!(28 2 r )! 24 ! (2 r 4 )! (28 2 r )! 28 27 26 25 24 ! 24 ! 2 r (2r 1)(2 r 2 )(2 r 3 )(2 r 4 )! (28 2 r )! 225 28 27 26 25 = 2 r (2 r 1)(2 r 2 )(2 r 3 ) 11 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 383 ANSWERS 2r (2r 1) (2r 2) (2r 3) = = 11 28 3 26 = 11 7 4 3 13 2 = 11 12 13 14 = 14 13 12 11 11 28 27 26 25 225 2r = 14 r=7 Ans. (b) 169. Let in the number unit's digit = x and ten's digit = y Number = 10y + x According to the given conditions of the problem, 8 (x+y) + 1 = 10y + x (or) 8x + 8y + 1 = 10y + x 8x x + 8y 10y + 1 = 0 7x 2y + 1 = 0 (1) and 13 (y x) + 2 = 10y + x 13y 13x + 2 = 10y + x x + 13x + 10y 13y 2 = 0 14x 3y 2 = 0 (2) (1) 2 14x 4y + 2 = 0 (3) (2) (3) y 4 = 0 y=4 Put y = 4 in (1), we get 7x 8 + 1 = 0 7x = 7 x=1 Hence, the required number is 41 Ans. (b) 384 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 170. We want to find out the number of combination of 12 things taken 3 at a time and this is by: 12 ! 3!(12 3 )! 12 C 3 = = 12 ! 12 11 10 9! = 3! 9! 3! 9! = 12 11 10 3 2 = 220 Ans. (c) 172. Lt x 9 x 3 = Lt x 9 x 9 App lt = Ans. (a) 173. x 3 x 3 1 1 = 3+3 6 1 6 x + 0 2a Lt x 9 x 0 Lt x 9 Lt x 9 1 x +3 x + a 2a x 0 ( ( ) 2a ) x + a 2a x+a + (x a ) x + a 2a = Lt x a ( x a ) x + a + 2 a (x a ) x + a + 2a ( ) ( ) App Lt 1 1 = a + a + 2a 2 2a ( ) Ans. (b) 174. Lt x 1 2 2a 6 + 5x 2 4 x + 15 x 2 6 5 + 2 x Lt x2 4 x x 2 15 + x App Lt. 5+0 1 = 15 + 0 3 Ans. (c) 1 3 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 385 ANSWERS 175. Lt a bx x x a b Lt 2 x x x 2 App Lt. (0 0) = 0 Ans.(a) 176. y = = = 0 e x e x dy = dx e x + e x e 2 x + e 2 x + 2 e 2 x e 2 x + 2 x (e + e x 2 ) 1 x2 178. y = (e + e x ) 2 (e + e x ) 2 (1 + x) 4 Ans. (b) 4 x 4 (1 + x) 2 .1 x.2 (1 + x) (1 + x) = x dy x y = = 2 dx (1 + x) = d x d (e e x ) (e x e x ). (e x + e x ) dx dx (e x + e x )2 (e x + e x )(e x + e x ) (e x e x )(e x e x ) (e x + e x ) 2 Ans. (b) 177. (e x + e x ) 4 (1 + x) 2 = d d x x (1 + x) 2 dx dx (1 + x) 4 1 + x2 + 2x 2 x 2 x2 (1 + x) 4 1 x = (1 + x) 3 1 x (1 + x) 3 x+ x dy d 1 / 2 d = t . (x + x ) dx dt dx = 1 . 1+ 2 x + 2 x x 1 386 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 2 x +1 = 4 x x+ x 2 x +1 Ans. (a) 179. y = 7 x 2 4 x x+ x +2 x dy d t d 2 = 7 . ( x + 2 x) dx dt dx = 7x 2 +2 x .log 7. (2x+2) 2 dy = 2( x + 1).7 x + 2 . log 7 dx Ans. (b) 2 ( x + 1).7 x 2 +2 . log 7 2 2 180. y = log x+ x +a dy d d 2 2 = log t. x+ x +a dx dt dx = 1 . 1 + . 2 x 2 x2 + a 2 x + x2 + a 2 1 x2 + a 2 + x 2 2 2 x +a x+ x +a2 = dy = dx 1 x2 + a 2 Ans. (a) 181. Given 1 x2 + a 2 (x y ) e x x y =a Differentiate on both sides. Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 387 ANSWERS (x y ). e e x x y x x y dy x (x y ) (1) x. 1 dx + e x y 1 dy = 0 dx (x y )2 dy x y x + x dx dy + 1 = 0 (x y ) dx dy dx + 1 dy = 0 (x y ) dx y+x x dy y dy + +1 =0 x y x y dx dx dy x y 1 = 1 dx x y x y dy x x + y y x + y = dx x y x y dy y 2 y x = dx x y x y dy 2 y x = dx y y 2y x dy + x = y +x dx y = 2y x + x y dy + x = 2y dx Ans. (c) 182. Given demand law x = 10 p 2 x = (10 p 2 )1 / 2 1 1 dx 1 = (10 p 2 ) 2 ( 2p ) dp 2 388 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 1( 2p ) 2 10 p 2 p dx = dp ed = = 10 p 2 p dx . x dp p p . 1/ 2 (10 p ) 2 10 p 2 when p = 2 2 2 . 6 6 ed = ed = 2/3 ed = 2 3 Ans. (a) Alternate 183. x3 dx x +1 1 dx x +1 = x = x3 x2 +x log(x+1) + c 3 2 3 x +1 Ans. (c) 184. e 4x + e 2x e 3 x dx = e 4x e 2x e 3 x + e 3 x dx = e x dx + e x dx = e x e x + c Ans. (b) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 389 ANSWERS 185. x4 + 1 2 2 x 1 + 2 dx x 2 + 1 dx = x +1 1 dx x +1 = x = x3 x + 2 tan 1 x + c 3 2 dx dx + 2 2 Ans. (c) log ( x + 1) dx 186. Let I = log ( x + 1).1dx I= Integrating by parts [Here log (x+1) is to be taken as first function and unity as second function] I = [log (x+1] integral of '1' integral of [d/dx (log (x+1)] + integral of '1'] 1 = log (x+1).x x + 1 .x dx = x log (x+1) = x log(x+1) 1 dx x +1 = x log (x+1) [x log (x+1)] x +1 1 dx x +1 1 I = x log (x+1) x + log (x+1) +c 1 187. Consider x + 1+ x x 1+ x x (1 + x) 1+ x x = dx I= = 1 + x dx I = I1 I I1 = = x + 1+ x x dx 2 1 + x dx 390 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II Let z = 1 + x dz = dx I1 = 1 + x dx = = z dz 2 3/2 z 3 = 2 (1 + x) 3 / 2 3 I = 2/3 (1+x) 3/2 {(1 + x ) 3/2 I = 2/3 x3 / 2 +c 3/2 } x3 / 2 + c 188. Consider x 3 + x 2 2 x = x( x 2 + x 2 ) = x( x 2 + 2 x x 2 ) = x {x(x+2) (x+2)} = x (x 1) (x + 2) We may write Let x2 x + 2 x3 + x2 2 x = x2 x + 2 x( x 1) ( x + 2 ) x2 x + 2 A B C = + + x( x 1) ( x + 2 ) x x 1 x + 2 (or) x 2 x + 2 = A(x 1) (x + 2) + Bx(x + 2) + Cx(x 1) Substituting x = 1, We find 2 = 3B B = 2/3 Substituting x = 2, We find 8 = 6c i.e. C = 4/3 Substituting x = 0, We find 2 = 2A A= 1 I= x2 x + 2 dx 2 dx 4 dx x 3 + x 2 2 x dx = x + 3 x 1 + 3 x + 2 I = log x + 2/3 log (x 1) + 4/3 log (x+2) + log c Ans. (c) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 391 ANSWERS 1 3 x 2 + 13 x 10 dx 189. Let I = = = = 1 1 dx 3 x 2 + 13 x 10 3 3 1 1 dx 2 2 3 2 13 13 13 10 x + 2. x + 6 3 6 6 1 3 1 (x + 13 / 6 )2 289 dx 36 Let t = x+13/6 dt = dx I = 1/3 = = 1 t 2 (17 / 6)2 dt 1 1 t 17 / 6 . log 3 2 (17 / 6 ) t + 17 / 6 1 6 t 17 log 17 6 t + 17 1 6 ( x + 13 / 6 ) 17 log = 17 13 x + + 17 6 6 = 1 3x 2 log +c 17 3 x + 15 Ans. (b) 190. x e {f(x ) + f ( x)} dx By the method of integration by parts, we may write d x x f( x) ex dx dx e f(x )dx = f(x ) e dx dx = e x f (x ) e x f ( x) dx 392 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II e Transposing b a f( x) dx + e x f ( x) dx = e x f (x ) x x e {f( x) + f ( x)} dx = e f(x ) (or) 191. x log x dx Let log x = t x x = a, t = log a 1 dt = x dx log a log b log b t2 t.dt . log a 2 [(log b ) (log a ) ] 21 1 2 2 b log( ab ). log a [f( x) + f( x)][g( x) g( x)] dx 0.[g( x) g( x)]dx 0 Ans. (a) b 193. 2 1 b log( ab ). log 2 a Ans. (a) 192. x = b, t = log b 0 dx (a + b x)2 / 3 Let a + b x = t x = a, t = b a 1 = a t 2 / 3 dt b 3 [ ] b t1 / 3 a Ans. (b) 2 b t 2 / 3 x = b, t = a dt a [ 3 b1 / 3 a 1 / 3 [ dt dx 3. b1 / 3 a 1 / 3 ] ] x dx x + 2 x ... (i) 2 194. I = 2 x 2 x + x ... (ii) [f(x) = f(a x)] 0 I= 0 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 393 ANSWERS 2 dx = [x]0 2 2I = =2 0 I= Ans. (a) 1 2 = 1 2 1 1 195. I = 1 1 1 x 1 dx log dx ... (i) log x x 0 0 1 I= 1 1+ x dx 1 x log 0 1 I= 1 log 0 2I [f( x) = f(a x)] = x 1 x log dx ... (ii) 1 x x 0 0 Ans. (c) I=0 0 196. No. of ways in which 7 dept distributed among 3 minister = (7 = (120 + 330) 6 = 1980 C3 ) 4 C 3 1 ) + (7 C 3 4 C 2 x 3 ! Ans. (d) None of these 197. No. of selections of letters (i) 2 like and 1 different = 3 C1 2 C1 = 3 2 = 6 (ii) 3 different = 5 C 3 = 10 Total no. of ways of selection letters = 16 Total words = 16 3! = 96 words. Ans. (b) 96 198. No. of ways to form three digit nos. by using (1, 2, 3, 4, 3, 2) are 42. Ans. (b) 42 199. S n + S n 2 2 .S n 1 = 2. n n 2 [2a+(n 2 1)d] [2 a + (n 1)d ] + 2 2 n 1 [2a + (n 1 1)d] 2 394 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

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