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CA CPT : Volume 2 - Model Test Paper 1 (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 1 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. Which of the following is/are current asset? (a) (c) 2. Wages, Carriage Inward, Octroi Postage, Wages, Carriage Inward Purchase, Wages, Coal Expenses Both (a) and (c) Manufacturing A/c Trading A/c (b) (d) Balance Sheet Profit and Loss A/c (b) (d) Business Entity All of the above The accounting equation is based on (a) (c) 5. Bill receivable All of the above Suspense Account given in the Trial Balance will be entered in the : (a) (c) 4. (b) (d) Which of the following sets of expense are the direct expenses of business? (a) (b) (c) (d) 3. Inventory Prepaid Expenses Dual aspect Going concern The maximum number of shares that a company may issue in accordance with its instrument of incorporation is known as its a) c) Issued share capital Subscribed share capital Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India b) d) Paid-up share capital Authorised share capital. 1 MODEL TEST PAPER - 1 6. Interest receivable from Mohan, a Borrower Account is(a) (c) 7. (c) (d) Purchase Book Bill Receivable Book Bearer Cheque Crossed Cheque (b) (d) Promissory Note Bills of Exchange A part of the cash book A statement showing the causes of differences between the balance of cash book and passbook. A part of financial statement None of the above Cash A/c Machinery A/c (b) (d) Profit & Loss A/c Installation expenses A/c Contingent liability Secured Loan (b) (d) Provision None of the above Only real A/c Personal A/c (b) (d) Real A/c and Nominal A/c Both (b) and (c) Error which affect only one account can be (a) (c) 15. (b) (d) A Trial Balance contains the balances of (a) (c) 14. Journal Proper Sales Book When obligation is not probable or the amount expected to be paid to settle the liability cannot be measured with sufficient reliability, it is called (a) (c) 13. Personal A/c and Real A/c All accounts The Installation expenses for a new machinery will be debited to (a) (c) 12. (b) (d) Bank Reconciliation statement is (a) (b) 11. Real A/c and Nominal A/c Only Nominal A/c Which of the following instruments is not a negotiable instrument (a) (c) 10. Artificial Personal Account None of these Opening and closing entries are recorded in : (a) (c) 9. (b) (d) Normally, the following accounts are balanced (a) (c) 8. Natural Personal Account Representative Personal Account Error of complete omission Compensatory errors (b) (d) Error of posting None of the above Valuing the Inventory in trade at net realisable value or cost price whichever is lower, is an example of the convention (a) (c) Conservatism Dual aspect 2 The Institute of Chartered Accountants of India (b) (d) Consistency All of the above Common Proficiency Test (CPT) Volume - II 16. In case goods are manufactured and segregated for specified consumers the best method for valuation of inventory would be (a) (c) 17. Cash sale only Total sales exceeding invoice value/cost Credit sales None of the above Fully in cash Fully transferred to loan A/c to be paid on with some interest on it. Partly in cash and partly as loan repayment with agreed interest Any of the above As per Section 12 of Negotiable Instruments Act, which of the following is not a foreign bill? (a) (b) (c) (d) 22. Asset side of the Balance Sheet Liability of the Balance Sheet Profit and Loss A/c (Dr. balance) None of the above Claim of the retiring partner is payable in the following form (a) (b) (c) (d) 21. Fictitious assets Kept in the business for use over a long period Meant for resale Meant for conversion into cash as quickly as possible Overriding commission is generally calculated on (a) (b) (c) (d) 20. Simple average Specific identification method Income earned but not received is shown in (a) (b) (c) (d) 19. (b) (d) Fixed assets are (a) (b) (c) (d) 18. FIFO Base stock A bill drawn outside India and made payable outside India. A bill drawn outside India and made payable in India. A bill drawn outside India on a person resident in India. A bill drawn in India on a person resident outside India and made payable outside India. Kishan, the acceptor of the bill has to honour a bill on 31st March, 2010. Due to financial crisis, he is unable to pay the amount of bill of Rs. 40,000. Therefore he approaches Karan, the drawer of that bill on 20th March, 2010 for extension of the bill for further 2 months. Karan agrees to extend the credit period by drawing a new bill for Rs. 42,000 together with interest of Rs. 2,000 in cash. In this case old bill of Rs. 40,000 will be considered as (a) (c) Dishonoured Cancelled Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Retired Discounted 3 MODEL TEST PAPER - 1 23. Goodwill of the firm is valued at three year s purchase of the average profit of the last five years. The profits are as under 2010 2009 2008 2007 2006 1,60,000 20,000 1,20,000 1,00,000 80,000 (Profit) (Loss) (Profit) (Profit) (Profit) Goodwill amount will be (a) (c) 24. Rs.3,200 Rs.6,400 (b) (d) Rs.4,600 Rs.8,000 Rs. 1,000 Rs. 4,800 (b) (d) Rs. 1,600 Rs. 3,000 On 1 Jan. 2010 Ankur of Delhi consigned 200 cases, cost price Rs. 3,750 at proforma invoice of 25% profit on sales to his agent Mani of Manipur. Balance of Goods Sent on Consignment A/c transferred to General Trading A/c will be (a) (c) 27. Rs. 2,64,000 Rs. 2,28,000 Dabur Ltd. forfeited 400 shares of Rs. 10 each fully called up, on which the holder has paid only application money of Rs. 4 per share. Out of these 250 shares were reissued at Rs. 12 per share fully paid up. Capital reserve will be credited (a) (c) 26. (b) (d) Rama Ltd. forfeited 800 shares of Anil of Rs. 10 each fully called up for non-payment of final call of Rs. 2 per share and reissued to Ankit as fully paid up for Rs. 10 per share. Amount transferred to capital reserve will be (a) (c) 25. Rs. 2,76,000 Rs. 2,60,000 Rs. 5,000 Rs. 8,000 (b) (d) Rs. 3,750 None of the above A manager gets 5% commission on net profit after charging such commission, gross profit Rs. 58,000 and expenses of indirect nature other than manager s commission are Rs. 16,000. Commission amount will be (a) (c) Rs. 2,900 Rs. 1,500 4 The Institute of Chartered Accountants of India (b) (d) Rs. 2,000 Rs. 2,200 Common Proficiency Test (CPT) Volume - II 28. Particulars Salaries Interest on loan Bad debts Wages Gross Profit Net Profit will be (a) (c) 29. Rs. 15,300 Rs. 17,200 (b) (d) Rs. 9,200 Rs. 10,800 (b) (d) 1,200 2,000 Rs. 13,000 Rs. 16,000 Rs. 10,000 Rs. 2,200 Rs. 3,000 Rs. 1,600 Rs. 13,600 Rs. 6,400 Rs. 25,000 Rs. 28,000 (b) (d) Rs. 35,000 Rs. 5,600 Suspense A/c Dr. 6000 ; To Labour A/c 6000 Wages A/c Dr. 6000 ; To Suspense A/c 6000 Wages A/c Dr. 6000 ; To Cash A/c 6000 None of the above Anu and Anubhav are partners sharing profits in the ratio 5 : 3, they admitted Anup giving him 3/10th share of profits. if Anup acquires 1/5th share from Anu and 1/10th share from Anubhav, new profit sharing ratio will be (a) (c) 33. Interest on investment received Freight inward The total of wages for the month of Jan, 2010 amounting Rs. 6000 was not posted. Rectifying entry for the same will be (a) (b) (c) (d) 32. Amount Goods purchased Rs. 100000; sales Rs. 90000. If margin 20% on sales then closing Inventory will be (a) (c) 31. 4,000 5,000 1,200 1,000 25,000 Particulars (i) Balance as per cash book on 31.03.2010 (ii) Cheques sent to bank but not entered in cash book (iii) Cheques issued and presented on 7th April, 2010 (iv) Bill paid by Bank not entered in the cash book Balance on as per passbook will be (a) (c) 30. Amount 5:6:3 17 : 11 : 12 (b) (d) 18 : 24 : 38 4:3:2 Mr. Om sold goods worth Rs. 2,50,000 to Mr. Jai. Mr. Jai accepted a bill on 1.11.10, payable after 2 months. Mr. Om discounted this bill @ 18% p.a. on 15.11.10. On the due date Mr. Jai failed to discharge the bill. Later Mr. Jai become insolvent and 50 paise is recovered from Mr. Jai s estate. How much amount of bad debts will be recorded in the books of Om. (a) (c) Rs. 1,25,000 Rs. 94,370 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Rs. 1,36,500 Rs. 1,14,000 5 MODEL TEST PAPER - 1 34. A, B and C are the partners sharing profits in the ratio 4 : 3 : 2. C died on 30.06.2010 and profits for the accounting year 2009-10 were Rs. 72000. How much share in profits for the period 1st April, 2010 to 30th June 2010 will credited to C s account (a) (c) 35. (b) (d) 13th August 15th August Rs. 2,40,000 and Rs. 60,000 Rs. 4,00,000 and Rs. 1,60,000 (b) (d) Rs. 3,00,000 and Rs. 10,000 Rs. 3,00,000 and Rs. 60,000 Memorandum Joint Venture A/c Joint Bank A/c (b) (d) Joint Venture A/c Co-venturer A/c Wright Ltd. issued 40000, 8% debentures of Rs. 10 each at par which are redeemable after 8 years at a premium of 20%. The amount of loss on redemption of debentures to be written off every year will be (a) (c) 39. 12th August 14th August Which of these is not a part of double entry system? (a) (c) 38. Rs. 16,000 Rs. 12,000 Goods costing Rs. 2,40,000 were sent on consignment basis. Goods are invoiced at cost + 25%. The Invoice price and loading will be (a) (c) 37. (b) (d) A bill is drawn on 12th June for 2 months. The due date of the bill will be (a) (c) 36. Rs. 4,000 Rs. 18,000 Rs. 60,000 Rs. 10,000 (b) (d) Rs. 50,000 Rs. 8,000 Chetan Ltd. recorded the following information as on March 31, 2010 Inventory (1-4-2009) Purchases Sales Rs. 40,000 Rs. 80,000 Rs. 1,00,000 It is noticed that goods worth Rs. 30,000 were destroy due to fire against this, the insurance company accepted a claim of Rs. 14,000. The company sells goods at cost plus 33.33%. The value of closing inventory, after taking into account the above transaction is (a) (c) 40. Rs. 75,000 Rs. 25,000 (b) (d) Rs. 15,000 Rs. NIL Riya and Piya are partners in a firm. During the year 2009, Riya withdraw Rs. 1000 p.m. and Piya withdraw Rs. 500 p.m. on the first day of each month for personal use. Interest on drawing is to be charged @ 10% p.a. Total interest on drawings will be (a) (c) Rs. 975 Rs. 900 6 The Institute of Chartered Accountants of India (b) (d) Rs. 650 Rs. 325 Common Proficiency Test (CPT) Volume - II 41. Mohan drew a bill on Gopal for Rs. 100000 for 3 months, proceeds are to be shared equally. Mohan got the bill discounted at 12% p.a. and remits required proceeds to Gopal. The amount of such remittance will be (a) (c) 42. 1:1:1 Cannot be calculated Rs. 1,25,000 Rs. 1,27,500 (b) (d) Rs. 1,35,000 Rs. 1,40,000 Rs. 1,12,000 Rs. 1,00,800 (b) (d) Rs. 1,11,111 Rs. 1,00,000. Rs. 5,00,000 Rs. 52,000 (b) (d) Rs. 50,000 Rs. 45,000 Credit balance as per passbook on 31.3.2010 is Rs. 22000. Cheques deposited but not cleared amount to Rs. 2000 and cheques issued but not presented of Rs. 8000. Balance as per cash book should be (a) (c) 47. (b) (d) Machinery costing Rs. 500000 was purchased on 1.4.2008. The installation charges amounting Rs. 20000 were incurred. The depreciation at 10% per annum on straight line method for the year ended 31st March, 2010 will be (a) (c) 46. 3:2:1 2:2:1 10,000 litres of oil were consigned to a wholesaler the cost being Rs. 100 per litre by incurring freight Rs.8,000. 10% of loss of oil unavoidable. 8,000 litres were sold by the consignee. The remaining Inventory of 1000 litres will be valued at (a) (c) 45. Rs. 48,500 Rs. 97,000 Gattu and Bittu entered into a joint venture where Gattu bought goods of the value Rs. 1,00,000 and consigned them to Bittu to be sold by him on joint venture, profits being divided equally. Gattu paid Rs. 10,000 for freight and insurance. Bittu sold the goods for Rs. 1,50,000. Commission payable to Bittu Rs. 5,000. The amount to be remitted by Bittu to Gattu will be (a) (c) 44. (b) (d) R and S are partners sharing profits and losses equally. They admitted A for 1/3 share in the firm. The new profits sharing ratio will be (a) (c) 43. Rs. 24,250 Rs. 50,000 Rs. 32,000 Rs. 28,000 (b) (d) Rs. 16,000 Rs. 18,000 A Company forfeited 2,000 shares Rs. 10 each held by Mr. Mohan for non payment of allotment money of Rs. 3 per share. The called-up value per share was Rs. 8. On forfeiture, the amount debited to share capital will be (a) (c) Rs. 6,000 Rs. 1,000 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Rs. 20,000 Rs. 16,000 7 MODEL TEST PAPER - 1 48. Bill of Rs. 5000 accepted by Rajan was endorsed by Rohit to Raj on account of final settlement of Rs. 5200. The benefit of Rs. 200 earned by Rohit was (a) (b) (c) (d) 49. Ankur purchased goods costing Rs. 5,000 at an invoice price, which is 50% above cost. On invoice price he enjoyed 15% trade discount and Rs. 375 cash discount on cash payment of goods in lump sum at the time of purchase. The purchase price to be recorded in the books before cash discount will be (a) (c) 50. Rs. 7,500 Rs. 6,000 Rs. 3,00,00,000 Rs. 2,25,00,000 (b) (d) Rs. 75,00,000 Rs. 7,50,00,000 Rs. 2,00,000 Rs. 2,50,000 (b) (d) Rs. 2,60,000 Rs. 1,40,000 A company offers to the public 20000 shares for subscription. The company receives application for 24000 shares. If the shares are allotted on pro-rata basis the application for 24,000 shares are to be allotted as (a) (b) (c) (d) 53. (b) (d) Gopi Ltd. purchased land and building from Mohan Ltd. for a book value of Rs. 200000. The consideration was paid by issue of 12% debentures of Rs. 100 each at a discount of 20%. The debenture account is credited with (a) (c) 52. Rs. 5,000 Rs. 6,375 Kapoor Ltd. issued 7,50,000, 12% debentures of Rs. 100 each at a premium of 10% payable Rs. 40 on application and balance on allotment. Debentures are redeemable at par after 6 years. All money due on allotment was called up and received. The amount of premium will be (a) (c) 51. Credited to discount received account by Rs. 200 Debited to discount allowed account by Rs. 200 Credited to rebate account by Rs. 200 None of the above 5 Shares for every 6 shares applied 4 Shares for every 5 shares applied 6 Shares for every 7 shares applied None of the above Arjun and Bheem are partners in the firm sharing profits and losses in the ratio 1 : 1. They have invested capital of Rs. 80,000 and Rs. 50,000 respectively. As per partnership deed, they are entitled to interest on capital @ 2.5% p.a. before sharing the profits. During the year firm earned a profit of Rs. 5000 before allowing interest. The net profit will be apportioned as (a) (b) (c) (d) Rs. 900 to Arjun, Rs. 900 to Bheem Rs. 875 to Arjun, Rs. 875 to Bheem Rs. 785 to Arjun, Rs. 785 to Bheem Rs. 965 to Arjun, Rs. 965 to Bheem 8 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 54. Following figures have been taken from the trial balance of a trader Gross Purchase Rs. 60,000 Gross Sales Rs. 1,00,000 Purchase Returns Rs. 5,000 Sales Returns Rs. 7,000 Sales Tax Rs. 12,000 Duty Drawback Rs. 6,000 The amount of G.P. will be (a) (c) 55. (b) (c) (d) Purchases Return Book Journal Proper Purchase A/c Dr. To Sales A/c Sales A/c Dr. To purchase A/c Rahul A/c Dr. To purchase A/c To sales A/c Purchases A/c Dr. Sales A/c Dr. To Rahul 300 300 300 300 600 300 300 300 300 600 Rs. 5,000 Rs. 5,250 (b) (d) Rs. 6,000 Rs. 5400 Not required to be adjusted Added (b) (d) Subtracted None of the above Purchase of Building from payment through Bank Account will (a) (c) 60. (b) (d) When drawing up a Bank Reconciliation Statement If you start with a debit balance as per the Bank statement, the unpresented cheques should be (a) (c) 59. Bill receivable Book Purchase Book Original Cost = Rs. 63000. Salvage value = 3000. Depreciation for 2nd year by units of production method, If units produced in 2nd year was 5000 and total estimated production 60000 units. (a) (c) 58. Rs. 38,000 Rs. 26,000 A purchase of goods from Rahul amounting to Rs. 300 has been wrongly entered through sales book. What will be the rectifying entry? (a) 57. (b) (d) A debit note for Rs. 500 issued by Mr. Marshall to Mr. Fisher for goods returned by Mr. Marshall is to be accounted for (a) (c) 56. Rs. 32,000 Rs. 40,000 Decrease in total liabilities Decrease in total assets (b) (d) Increase in total assets Not affect total assets. Economic life of an enterprise is split into periodic interval as per _______ concept (a) (c) Materiality Accrual Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Periodicity Conservation 9 MODEL TEST PAPER - 1 SECTION B : MERCANTILE LAWS (40 MARKS) 61. The Indian Contract Act, 1872 is extended to (a) (c) 62. Vendor Promisee Forbidden under law Punishable (b) (d) Not forbidden under law Legal agreements Cross-offers Contracts (b) (d) An agreements Promises by the person to whom it is made by third party by the stranger by legal heir A voidable agreement is enforceable by (a) (b) (c) (d) 68. (b) (d) In the case of specific offer, it can be accepted only (a) (b) (c) (d) 67. Promisor Contractor Where two parties make identical offers to each other, in ignorance of each other s offer, the offers are known as (a) (c) 66. a promise is a contract a set of promises is a contract a proposal is a contract agreements enforceable by law is a contract Void agreements are (a) (c) 65. The whole of British India All the States and Union territories of India. A person making a proposal is called. (a) (c) 64. (b) (d) Which of the following is correct? (a) (b) (c) (d) 63. The whole of India The whole of India excluding J & K None of the parties Only one of the parties All the parties to the contract One or more but not by the other or others An illegal agreement (a) (b) (c) (d) is void ab initio becomes void void ab initio as well as punishable voidable 10 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 69. A minor is a person who has not completed (a) (c) 70. Cash money All of these as much as is merited as much as is performed (b) (d) as much as is credited None of these Where the letter of acceptance is transmitted Where the letter of acceptance is received Where the proposer resides Where the acceptor resides Res extincta Uberrima fides (b) (d) Nudum Pactum Contractu Void Voidable (b) (d) Valid Illegal Duration not fixed Duration fixed Dissolved at any time Can be dissolved only at the happening of an event. The unpaid seller has the right against the goods (a) (c) 78. (b) (d) A partnership at will is one (a) (b) (c) (d) 77. Earnest money Hard money A contract made by mistake of foreign law, is (a) (c) 76. Keeping agreement in a drawer All of the above. A gratuitous or bare promise, devoid of consideration, is called(a) (c) 75. (b) (d) When the acceptance is by a letter, a contract is deemed to be made at the place (a) (b) (c) (d) 74. Fall of hammer in auction sale Cashing of a cheque Quantum meirut means (a) (c) 73. 21 years of age 19 years of age Where a certain amount is deposited as securing for performance of a contract, it is called (a) (c) 72. (b) (d) In which of the following cases, there is no communication of acceptance? (a) (c) 71. 20 years of age 18 years of age Rights of lien Right of resale (b) (d) Right of stoppage in transit all of these Contract in which only one party has to perform his promise is known as (a) (c) Executed contract Unilateral contract Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Executory contract Bilateral contract 11 MODEL TEST PAPER - 1 79. When the performance of a contract becomes subsequently impossible or unlawful, the contract becomes (a) (c) 80. Contingent contract Implied contract (b) (d) Quasi Contract Wagering contract Fraud incompetence (b) (d) Coercion Undue influence Past Future (b) (d) Present All of these Valid Illegal (b) (d) Voidable Void Registration of the partnership firm is done with _______. (a) (b) (c) (d) 87. Movable goods only Immovable goods only Both immovable and movable goods Tangible goods only When the consent of a party is obtained by fraud, the contract is____________. (a) (c) 86. Agreement to sell Auction sale Consideration may be _______. (a) (c) 85. (b) (d) _______ does not affect the free consent of the parties. (a) (c) 84. Sale Void A party agrees to pay five lakhs to another party if first party brings to earth a star from sky. This is known as _______. (a) (c) 83. Void Voidable The Sale of Goods Act, 1930 deals with the _______. (a) (b) (c) (d) 82. (b) (d) Contract for the sale of future goods is _______. (a) (c) 81. Illegal Invalid Registrar of firms Registrar of co-operative society Registrar of companies All of these An agreement to share earnings of a smuggling business is _______. (a) (c) Valid Voidable 12 The Institute of Chartered Accountants of India (b) (d) Void Contingent Common Proficiency Test (CPT) Volume - II 88. There can be a stranger to a _______. (a) (c) 89. (b) (d) Adjusted All of these A promise in return for a promise A promise in return for a agreement A promise in return for a contract Accepted promise Consideration Future consideration (b) (d) Past consideration Executory consideration Valid Voidable (b) (d) Void Illegal Valid Void (b) (d) Invalid Voidable An agreement to commit a crime is _______. (a) (c) 96. Assigned Noted Acceptance in ignorance of the offer is _______. (a) (c) 95. Express authority None of the above An agreement made without consideration is _______. (a) (c) 94. (b) (d) When one of the parties to the contract has performed his part of the promise, it is known as _______. (a) (c) 93. Implied authority Contractual authority Reciprocal promise means _______. (a) (b) (c) (d) 92. Consideration Promise An actionable claim can always be _______. (a) (c) 91. (b) (d) The authority of a partner to bind the firm is known as _________. (a) (c) 90. Contract Agreement Valid Voidable (b) (d) Void Unenforceable Communication of proposal is complete when it comes to the knowledge of _______. (a) (c) The proposer The Court Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) The person to whom it is made (a) or (b) 13 MODEL TEST PAPER - 1 97. An offer made to a specific person is known as_________. (a) (c) 98. Separate offer Standing offer An offer An agreement (b) (d) A counter offer An invitation to offer A buys an article thinking it is worth Rs. 10,000 while it is actually worth Rs. 5,000 only. Decide what will be the remedy to A? (a) (b) (c) (d) 100. (b) (d) Advertising agent invites a tender. It is known as _______. (a) (c) 99. Special offer Specific offer The agreement can be avoided on the ground of mistake The agreement cannot be avoid on the ground of mistake A can sue for return taking back Rs. 5,000 A can sue for recovery of Rs. 2,000 only A agrees to buy from B a certain horse. It turns out that the horse was dead at the time of the bargain, though neither party was aware of the fact. Decide. (a) (b) (c) (d) The agreement is void The agreement is valid A can sue for purchasing new horse in place of dead horse None of these SECTION C : GENERAL ECONOMICS (50 MARKS) 101. Monetary Policy refers to: (a) (b) (c) (d) 102. HYVP was restricted to the following crops: (a) (b) (c) (d) 103. Public Revenue and Public Expenditure Policy Policy to control money supply M1 and M2 Policy linked to banking Wheat, Rice, Bajra, Jawar and Maize Wheat, Sugar, Bajra, Jawar and Maize Wheat, Milk, Bajra, Jawar and Maize Wheat, Banana, Bajra, Jawar and Maize The Full form of ICICI is : (a) (b) (c) (d) Investment Credit and Industrial Corporation of India Indian Credit and Investment Corporation of India Industrial Credit and Investment Corporation of India International Credit and Investment Corporation of India 14 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 104. In the theory of demographic transition in the first stage : (a) (b) (c) (d) 105. NM1 refers (as per latest RBI Working Group): (a) (b) (c) (d) 106. infinity 1.25 MC > MR MC = MR (b) (d) MR > MC AC = AR Increase CRR Decrease CRR Increase buying of Government Securities None of the above When the consumer is in equilibrium his price line is _____________ to indifference curve (a) (c) 110. (b) (d) In order to control Inflation in India RBI may: (a) (b) (c) (d) 109. 1 3 A firm under perfect competition will be making minimum losses (in the short run) at a point where: (a) (c) 108. Currency + Demand Deposits + Other Deposits with RBI Currency + Demand Deposits + Post office saving deposits Currency + Demand Deposits + Money at call None of the above In the case of a straight line demand curve meeting the two axes, the price elasticity of demand at y-axis of the line would be equal to (a) (c) 107. Both birth rate and death rate are high Both birth rate and death rate are low Birth rate is high and death rate is low Birth rate is low and death rate is high Parallel Diagonally opposite (b) (d) At right angle Tangent Which of the following is not the feature of Perfect Competition? (a) (b) (c) (d) Large number of buyers and sellers Small number of buyers and sellers Free Entry and Exit Goods is Homogeneous Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 15 MODEL TEST PAPER - 1 111. In the long run under which competition a firm may earn super normal profits? (a) (c) 112. NABARD SEBI Alfred Marshal Adam Smith (b) (d) J. B. Say A.C. Pigou Less than one Zero (b) (d) One Greater than one 184 150 (b) (d) 159 177 If as a result of 10% increase in price, the quantity supplied does not change at all, it implies that the elasticity of Supply is : (a) (b) (c) (d) 119. (b) (d) The number of Member Countries of WTO in 2013 is : (a) (c) 118. SBI RBI Average fixed cost can not be: (a) (c) 117. Rate at which RBI discounts bills of banks. Rate at which SBI gives loans to other banks. Rate at which RBI borrows from general public. Rate at which liquidity is to be maintained by nationalised banks. Economics is a Science which deals with wealth was referred by : (a) (c) 116. Selling of government stake to private sector Selling of government companies to private sector Government purchasing 26% shares in private companies Taking of full control and management from Private Sector by the government Overall Credit and Monetary Policy is the ultimate responsibility of ______ in India (a) (c) 115. Perfect competition Monopoly Bank rate is the _______. (a) (b) (c) (d) 114. (b) (d) Nationalization means: (a) (b) (c) (d) 113. Monopolistic competition Oligopoly Zero Infinite Equal to one Greater than Zero but less than one The Law of variable proportions examines the Production function with: (a) (b) One factor variable and only one factor fixed One factor variable keeping quantities of other factors fixed 16 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II (c) (d) 120. In Law of negative returns (Third stage of Law of variable proportions): (a) (b) (c) (d) 121. 123. 124. 128. 11% 9% The demand curve is also known as: (a) Marginal Revenue curve (c) Average Revenue (b) (d) Marginal utility curve Average utility curve (b) (d) Inverse relationship Positive relationship (b) (d) At its minimum point At different points Supply of a good and its price have Negative relationship No relationship MC curve cuts AVC Curve At its falling point At its rising point NTPC stands for (a) (b) (c) (d) 127. (b) (d) Cardinal utility None of the above (a) (c) 126. 8% 20% Indifference Curve analysis is based on (a) Ordinal utility (b) (c) Marginal utility (d) (a) (c) 125. Total Product declines, MP is positive Total Product declines, MP is Zero Total Product declines, MP is negative Total Product in constant, MP is constant If GDP is 20% higher than last year and the rate of inflation is 9%, then production in the economy has grown by . (a) (c) 122. All factors variable None of the above National Tidal Power Corporation National Theological Power Corporation National Thermal Power Corporation National Talent and Potential Corporation PNB, SBI, Canara Bank are examples of: (a) Semi Private banks (b) (c) Private Sector banks (d) Public Sector banks Semi Public Sector banks Margin requirement for commercial bank refers to (a) Profit margins (b) CRR and SLR (c) CRR (d) Difference between amount of Security to be given by the borrowers to the bank and the amount of Loan. Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 17 MODEL TEST PAPER - 1 129. Accounting profit is equal to: (a) (b) (c) (d) 130. RBI has . (a) (c) 131. Rising None of the above RBI Prime Minister (b) (d) Ministry of Finance None of the above Universal access and enrolment Universal retention of children upto 14 years of age A Substantial improvement in the quality of education None of the above 5% 6% (b) (d) 7% 8% 6-10 6-8 (b) (d) 6-14 4-10 (b) (d) 21.23 Sq. Km area 51 Sq. Km area VSAT stands far (a) (b) (c) (d) 137. (b) (d) Gross Enrolment Ratio shows the proportion of children in elementary school in the age group of: (a) (c) 136. Falling below average cost curve The goal of National Policy on Education is to make an expenditure of of GDP. (a) (c) 135. One branch in each state of India None of the above Which is not the aim of National Policy on Education? (a) (b) (c) (d) 134. (b) (d) Fiscal Policy in India is given by: (a) (c) 133. Very few branches No branches If firm s average cost curve is falling then marginal curve must be : (a) (c) 132. Total Revenue Total variable cost Total Revenue Total direct cost Total Revenue Total cost Total Revenue Total Explicit cost and Total Implicit Cost. Very Small Aperture Terminals Various Small Aperture Terminals Very Small Application Terminals Valuable Small Aperture Terminals On an average, one post office serves: (a) (c) 18 Sq. Km area 31 Sq. Km area 18 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 138. Project Arrow is related to ________ . (a) (c) 139. (b) (d) 60 50 Delhi Karnataka (b) (d) Kerela Tamil Nadu Atomic energy Banking operations (b) (d) Lottery business Gambling and betting Sixth Fifth (b) (d) Third Seventh Number of person per square kilometer Number of person per square kilometer of land excluding forest and river Number of person per square kilometer of land excluding rivers and seas in the country Number of persons per km of land India s present density of Population is (a) (b) (c) (d) 146. 58 63.5 Density of Population refer to (a) (b) (c) (d) 145. 7.1 25.4 Every poor person in the world is an Indian (a) (c) 144. (b) (d) FDI Prohibited in all of the following except: (a) (c) 143. 9.8 12.5 Which of the following states has the highest percentage of literacy? (a) (c) 142. Postal Services Railways What is the approximate life expectancy of the people living in India? (2011) (a) (c) 141. (b) (d) Death rate in India is _______ in 2011 (a) (c) 140. Airport Services Health Services 344 persons per square kilometer 382 persons per square kilometer 390 persons per square kilometer 440 persons per square kilometer Gini Coefficient is often used to measure poverty in: (a) (c) Absolute Terms Both (a) and (b) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Relative Terms None of the above 19 MODEL TEST PAPER - 1 147. 1921 is called the year of great divide because: (a) (b) (c) (d) 148. The is defined as the number of persons in the labor force per 1000 persons (a) (c) 149. WPR CWS (b) (d) LFPR CDS An expansion in the supply of a good is caused by a: (a) (b) (c) (d) 150. India got Independence in 1921. India got divided into India and Pakistan. Bangladesh become a separate country in 1921. After 1921 India s Population growth rate turned from negative to positive. Rise in the price of good Fall in the prices of other goods. Fall in the prices of factors of production All of the above Which of the following has the lowest price elasticity of supply? (a) (c) Luxury Air conditioner (b) (d) Necessities Perishable goods SECTION D : QUANTITATIVE APTITUDE (50 MARKS) 151. 4 1 1 5 2 The value of + (64) + ( 32) 64 (a) 1 8 (b) 17 (c) 152. 17 11 7 8 (d) None of these If a2 + b2 = 45 & ab = 18, then 3 8 1 1 + is a b (a) 1 3 (b) 2 3 (c) 1 2 (d) None of these 20 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 1 153. 1 1 a2 + a 2 1 a 2 + The value of 1 a 1+ a (a) (b) a 1 2 (c) 154. a a 1 2 a 1 (d) 2 1 a (b) (d) 5 None of these 2 10 If log e . log 625 = log16 x 10 . log e , then x (a) (c) 155. 7 8 The highest score in an innings was 2 2 of the total score and the next highest was of the 9 9 remainder. These score differed by 8 runs. What was the total score in the innings? (a) (c) 156. 162 142 (b) (d) 152 1132 The third proportional to 15 and 20 is (a) (b) 80 (c) 157. 80 3 80 7 (d) None of these The mean proportional between 9 and 25 is (a) (c) 158. (b) (d) 10 None of these The ratio of the number of boys and girls in a school is 2:5. If there are 280 students in the school, find the number of girls in the school. (a) (c) 159. 16 15 200 150 (b) (d) 250 None of these A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is Rs. 35, how many coins of each type are there. (a) (c) 30 25 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) 20 None of these 21 MODEL TEST PAPER - 1 160. One-third of a number is greater than one-fourth of its successor by 1. Find the number. (a) (c) 161. (b) (d) 21 None of these (b) (d) 4 2 1 is 81 The value of log3 (a) (c) 162. 51 15 4 2 The value of log 2 2 1 is 256 (a) (b) 4 (c) 163. 16 3 3 (d) 16 3 (b) (d) 32 64 (b) (d) 32 None of these (b) (d) 102 None of these If logx 3 2 = 1 ; then value of x is 15 (a) (c) 164. If log4 [log3(log2x)] = 0; then value of x is (a) (c) 165. 10 100 1230 baskets of mangoes were loaded in three trucks. When unloaded, it was found that 5, 10 and 15 baskets were rotten in the trucks respectively, but the remaining baskets were in the ratio of 3:4:5. How many baskets were loaded initially in each truck? (a) (c) 167. 16 4 The value of logx(0.00001) = 5, then x is (a) (c) 166. 8 16 575 565 (b) (d) 515 None of these Find the ratio x : y : z from 2x + 3y 5z = 0 and 3x + 2y + 7z = 0 (a) (c) 10:12:13 31:1:13 22 The Institute of Chartered Accountants of India (b) (d) 30:2:12 None of these Common Proficiency Test (CPT) Volume - II 168. The value of loga (a) 169. A 1 logaA n (c) n A loga 1 n The value of (b) a log1/n A (d) None of these log10 4 log10 8 (a) (b) 4 3 (c) 170. 1 3 2 3 (d) None of these If log10 12.45 = 1.0952 and log10 3.79 = 0.5786, Find the value of log10 124.5 + log10379 (a) (c) 171. 10 20 (b) (d) 15 None of these 100 200 (b) (d) 105 None of these In how many ways can the letters of the word ALGEBRA be arranged without changing the relative order of the vowels? (a) (c) 174. 4.6738 None of these How many numbers between 100 and 1000 can be formed with the digits. 2, 3, 4, 0, 8, 9? (a) (c) 173. (b) (d) Find the number of even numbers greater than 100 that can be formed with the digits 0, 1, 2, 3? (a) (c) 172. 5.6738 6.6738 82 72 (b) (d) 70 None of these How many words can be formed with the letters of the word UNIVERSITY , the vowels always remaining together? (a) (c) 60480 60000 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) 60482 None of these 23 MODEL TEST PAPER - 1 175. In how many ways can the letters of the word DIRECTOR be arranged so that the three vowels are never together? (a) (c) 176. 18,000 None of these a=3 & b = 8 a 3 & b = 8 (b) (d) (b) (d) x 9 a = 3 & b=8 None of these 0 None of these 2 Evaluate lim x 3 x - 3 x 3x (a) (c) 178. (b) (d) If f(x) = 1; if x < 3 , f(x) = ax + b; if 3 < x < 3 , f(x) = 7; if 5 < x. Determine the values of a & b so that f(x) is continuous. (a) (c) 177. 180 18,002 1 2 If f(x) = 4 x2; then lim x 2 f(2) f(x) is x 2 (a) (b) (c) 179. 2 5 2 5 (d) 4 Evaluate dy ; if y = dx 2 5 1 x 1+ x 1 1 (a) (b) (1 + x) 1 x ) (1 + x) 1 x 2 ) (c) (1 + x ) 1 x 2 ) (d) None of these (a) 10x (2 log10 1) + 2 log x 2x x (b) 10x (2 log10 + 1) + 2 log x 2x x (c) 10x (2 1) + 2 log x 2x x (d) None of these 2 1 180. 2 10x + logx dy If y = ; then find . dx x 24 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 181. Evaluate x 2 x dx 2 (a) (b) 2x x 3 x 2 2x +1 2x +1 + +c 3 (log 2) 2 (log 3) 2 (c) 182. 2x x 2 x2x +1 2x +1 + +c 2 (log 2) 2 (log 2)3 2x.x 2 x 3 .2x 2x +1 +c 3 3 (log 2)3 (d) None of these (b) 1 log 3x (d) None of these Evaluate log x dx 3x (a) (c) 183. 1 log x + c 3 1 log 3 Evaluate: ( x ) 2 +c ( x) 2 log x dx x2 (a) 1 (1 + log x) + c x (b) 1 log ex + c x (c) 1 x log + c x e (d) None of these e x (x 2 + 1) 184. +c Evaluate: ( x + 1) 2 dx (a) x 1 ex +c x +1 (b) x +1 ex +c x 1 (c) x 1 e x +c x +1 (d) None of these Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 25 MODEL TEST PAPER - 1 xe x 185. Evaluate (a) (1 + x ) (c) (1 + x ) If y = x+ (a) (c) 187. if y = (d) +c 1 x x x 2 (b) xe x +c 1+ x None of these 1 dy ; then 2x is x dx (b) 1 x (d) x2 + 1 + x2 1 x2 + 1 x2 1 (a) x , then x+ 1 x None of these dy is dx 2x 3 2x (c) 188. dx ex +c 1+ x ex 186. 2 x 4 1 2x 3 (b) 2x + (d) None of these x 4 1 x3 x 4 1 3 4 x 2 x then dy is If y = log e dx x+2 (a) x 2 1 x2 4 (b) x2 +1 x2 4 (c) x 2 1 x2 + 4 (d) None of these 26 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 189. dy is dx If y = xx, then (a) (c) 190. xx (2 + log x) xx log xx log (ex) (d) None of these dy 2 If y = x e x then is dx (a) (c) 191. e x (b) x e x 2 e x2 1 2x 2 log x x 2 2 1 3x log x e x x e x 2 e x2 1 3x 3 log x 2 x2 (b) x (d) None of these If the sum of first n terms of an A.P. s Zero, then the sum of next m terms, where a is the first term of the A.P. is (a) (b) am(m + n) n 1 (c) 192. am (m + n)(n 1) am(m + n) n 1 (d) None of these First, Second and last terms of a finite A.P. are m, n and 2m respectively, then sum of the series is (a) (b) 3mn n m (c) 193. 3mn 2(n m) 3mn 2(n + m) (d) None of these The first and fifth term of an A.P. of 40 terms are 29 & 15 respectively. Find the sum of all positive terms of this A.P. (a) (c) 1605 1805 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) 1705 None of these 27 MODEL TEST PAPER - 1 194. If mth term of an A.P. is 1 1 and nth term is , then sum of mn terms is n m (a) (b) 1 (mn 1) 2 (c) 195. mn+1 1 (mn + 1) 2 (d) None of these The sum of n terms of two A.P.s are in the ratio (7n+1) : (3n+2); find the sum of their 13th terms (a) (c) 196. If 2G1 G2 2AG1 (c) 1 2 1 (b) (d) 2A G1 G2 None of these (b) 1 2 (d) 0 If the pth, qth, rth and sth terms of an A.P. are in G.P.; then p q, q r and r s are in (a) (c) 199. 16:7 None of these am+1 + b m+1 is the G.M. between the numbers a and b, then the value of m is am + bm (a) 198. (b) (d) If one Arithmetic Mean A and G.M.s G1 and G2 be inserted between any two numbers then 3 3 is equal to G1 + G2 (a) (c) 197. 6:7 7:16 A.P. Cannot determine (b) (d) G.P. None of these The value of 1.4 is (a) (b) 10 9 (c) 200. 13 9 4 9 (d) None of these The value of 0.356 is (a) 356 999 (b) 353 999 (c) 353 990 (d) None of these YYY 28 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II Answer of Model Test Papers Model Test Paper BOS/CPT 1 SECTION A : FUNDAMENTALS OF ACCOUNTING 1. (d) 2. (d) 3. (b) 4. (a) 5. (d) 6. (c) 7. (b) 8. (a) 9. (c) 10. (b) 11. (c) 12. (a) 13. (d) 14. (b) 15. (a) 16. (d) 17. (b) 18. (a) 19. (b) 20. (d) 21. (c) 22. (c) 23. (b) 24. (c) 25. (a) 26. (b) 27. (b) 28. (d) 29. (b) 30. (c) 31. (b) 32. (c) 33. (a) 34. (a) 35. (c) 36. (d) 37. (a) 38. (c) 39. (b) 40. (a) 41. (b) 42. (b) 43. (c) 44. (a) 45. (c) 46. (b) 47. (d) 48. (a) 49. (c) 50. (b) 51. (c) 52. (a) 53. (b) 54. (a) 55. (b) 56. (d) 57. (a) 58. (c) 59. (d) 60. (b) SECTION B : MERCANTILE LAWS (40 MARKS) 61. (c) 62. (d) 63. (a) 64. (b) 65. (a) 66. (a) 67. (d) 68. (c) 69. (c) 70. (b) 71. (a) 72. (a) 73. (a) 74. (b) 75. (a) 76. (c) 77. (d) 78. (c) 79. (b) 80. (b) 81. (a) 82. (a) 83. (c) 84. (d) 85. (b) 86. (a) 87. (b) 88. (b) 89. (a) 90. (a) 91. (a) 92. (d) 93. (b) 94. (b) 95. (b) 96. (b) 97. (c) 98. (d) 99. (b) 100. (a) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 275 ANSWERS Answer of Model Test Papers Model Test Paper BOS/CPT 1 SECTION C : GENERAL ECONOMICS (50 MARKS) 101 (b) 111 (d) 121 (b) 131 (c) 141 (b) 102 (a) 112 (d) 122 (a) 132 (b) 142 (c) 103 (c) 113 (a) 123 (c) 133 (d) 143 (b) 104 (a) 114 (c) 124 (d) 134 (c) 144 (a) 105 (a) 115 (b) 125 (b) 135 (b) 145 (b) 106 (b) 116 (c) 126 (c) 136 (a) 146 (b) 107 (c) 117 (b) 127 (b) 137 (b) 147 (d) 108 (a) 118 (a) 128 (d) 138 (b) 148 (b) 109 (d) 119 (b) 129 (c) 139 (b) 149 (a) 110 (b) 120 (c) 130 (c) 140 (c) 150 (d) SECTION D : QUANTITATIVE APTITUDE (50 MARKS) 151. (a) 152. (c) 153. (d) 154. (b) 155. (a) 156. (a) 157. (c) 158. (a) 159. (b) 160. (c) 161. (b) 162. (d) 163. (b) 164. (a) 165. (a) 166. (b) 167. (c) 168. (a) 169. (c) 170. (b) 171. (c) 172. (a) 173. (c) 174. (a) 175. (b) 176. (a) 177. (c) 178. (d) 179. (b) 180. (a) 181. (a) 182. (c) 183. (b) 184. (a) 185. (a) 186. (a) 187. (b) 188. (a) 189. (b) 190. (a) 191. (b) 192. (a) 193. (b) 194. (c) 195. (b) 196. (b) 197. (a) 198. (b) 199. (a) 200. (c ) 276 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II SECTION D : QUANTITATIVE APTITUDE Suggested Answers/ Hints Model Test Paper BOS/CPT 1 4 0 5 1 1 / 2 151. + (64 ) + ( 32 ) 64 4 1 4 + ( 1) 5 (32 ) 5 = 1+ = 1 1 + + 25 8 = 1 1 + + 24 8 = 1 8 + 1 + 128 137 = 1 + + 16 = 8 8 8 = 17 64 ( ) 4 5 1 8 152. Given a 2 + b 2 = 45 (1) ab = 18 (2) (2) a= 18 (3) b Substitute a = 18 in (1) b 2 18 2 + b = 45 b 324 b 2 + b 2 = 45 324 + b 4 = 45 b 2 b 4 45 b 2 + 324 = 0 Let b 2 = x x 2 45 x + 324 = 0 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 295 ANSWERS (x 36 ) (x 9 ) = 0 x = 36 , x = 9 When x = 36, b = 6 When x = 9, b = 3 18 =3 6 When, b = 6, (3) a = When b = 3, (3) a = 18 =6 3 When a = 3, b = 6 1 1 1 1 2 +1 3 1 + = + = = = a b 3 6 6 6 2 1 1 1 1 1 + = + = a b 6 3 2 When a = 6, b = 3 1 2 Ans (c) = 153. Given 1 2 a 1 +a 2 + 1 a 1 1 a 2 1+ a 1 1 1 a + a 1 a 1+ a a+ = = a +1 a (1 a ) a 1 + ( a 1+ a ( ) )( ) ( ) (a + 1) 1 + a + a 1 (1 a ) (1 a ) 1 + a = 1 a = 1 a + a a +1+ a + a a a 1+ a (1 a ) 1 + a a = 1 2a + 2 a a (1 a ) 1 + a = ( 2 a ( ( ) a +1 ( a (1 a ) 1 + a ) ) ) 296 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II = 2 1 a 154. The given equation may be written as log 2 log 5 4 log 2 4 log 10 . = log e log x log 10 log e or, log 2 ( 4 log 5 ) = logx 4 log 2 or, log 5 = log x x = 5 Ans.(b) 155. Let the total score = x. Given the condition highest score = 2 x 9 The next highest = 2 2 x x According the third condition of the problem 9 9 2x 2 2 x x =8 9 9 9 2x 2 4 x+ x = 8 9 9 81 x= 8 x 81 = 162 4 Ans. (a) 156. Let three proportionals are a, b, c Then the third proportional = c = c= [ b2 b = ac a ] 20 2 400 80 = = 15 15 3 Ans. (a) 157. Let a, b, c be the three proport ional then the mean proportional = b = ac i.e. b = = 9 25 = 3 5 15 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 297 ANSWERS Ans. (c) 158. Let the boys Ratio 2x and the girls ratio 5x Given 2x + 5x = 280 7x = 280 x= 280 = 40 7 Boys Ratio = 2 40 = 80 Girls Ratio = 5 40 = 200 159. Let x be the number of coins available in a bag 1 1 x + x + x = 35 2 4 Given 4x + 2x + x = 35 4 7 x = 35 4 x= 35 4 = 20 7 Ans. (b) 160. 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 4x 3x 3 =1 12 x 3 = 12 x = 15 Ans. (c) 1 161. Let log 3 = x 81 i.e. 3x = 1 81 298 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 1 (3 )4 = 3 x = 3 4 x = 4 Ans. (b) 162. Let log 2 1 =x 256 2 ( ) = 1 256 (2 2 ) = 1 28 (2 ) = 2 8 i.e. 2 2 x x 3/2 x 3 22 x = 2 8 3 x = 8 2 x= 16 3 Ans. (d) 163. Given log x 3 2 = 1 15 1 i.e. x 15 = 3 2 1 15 x 1 = (2 )3 Taking power 15 on both sides 1 x 15 15 15 1 = 2 3 x = 25 x = 32 Ans. (b) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 299 ANSWERS 164. Given log3[log 4 (log 2 x )] = 0 i.e. 3 = log 4 (log 2 x) 1 = log 4 (log 2 x) 41 = log 2 x log 2 x =4 24 =x 16 =x Ans. (a) 165. Given log x (0 .00001 ) = 5 i.e. x 5 = 0 .00001 1 x5 = 0 .00001 1 = x5 0 .00001 i.e. x 5 = 100000 x 5 = (10 )5 x = 10 Ans. (a) 166. Suppose the x and y baskets were loaded in the first two trucks. Total number of baskets = 1230 Number of baskets initially loaded in the third basket = 1230 (x+y ) According to the question, x 5; y 10; 1230 (x+y) 15 = 3:4:5 3 x 5 = 1230 ( x + y ) 15 5 5x 25 = 3690 3x 3y 45 8x + 3y = 3670 and 4 y 10 = 5 1230 ( x + y ) 15 (1) 5y 50 = 4920 4x 4y 60 300 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 4x + 9y = 4910 (2) Multiply equation (1) by 3, 24x + 9y = 11010 (3) Subtracting equation (2) from equation (3), we get 20x = 6100 x= 6100 = 305 20 (1) 8(305) + 3y = 3670 2440 + 3y = 3670 3y = 3670 2440 = 1230 y= 1230 = 410 3 Hence number of baskets loaded in first truck = 305. Number of baskets loaded in Second Truck = 410 and the number of baskets loaded in third truck. = 1230 (x+y) = 1230 (305 + 410) = 1230 715 = 515 Ans. (b) 167. The given equations are: 2x + 3y 5z = 0 3x + 2y + 7z = 0 By Gross-multiplication method, we have x y x = = 21 + 10 15 14 4 + 9 x y z = = 31 1 13 x : y : z = 31 : 1 : 13 Ans. (c) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 301 ANSWERS 168. log a n A = log a (A1/n ) = 1 log a A n ans. 169. (a) log10 4 log10 2 2 = log10 8 log10 2 3 = 2 log10 2 3log 10 2 = 2 3 Ans. (c) 170. log10 124.5 + log10 379 = log10 (12.45 10) + log10 (3.79 100) = log10 12.45 + log10 10 + log10 3.79 + log10 100 = 1.0952 + 0.5786 + 2 + 1 log10 124.5 + log10 379 = 4.6738 Ans. (b) 171. No. of ways to fill unit place = 2 No. of ways to fill to the place = 4 No. of ways to fill 100 th place = 3 Total no. of 3 digit even Nose 2 4 3 = 24 If 10th comes at 100th place then 3 digit no. 3 P3 = 3 Total Nos. greater than 100 = 24 (3+1) Ans. (c) 20 172. Total no. of 3 digits nos. are = 6 P3 = 120 Nos. of 3 digit if 0 comes at hundredth place = 5 P3 = 20 Total nos. greater than 100 and less than 1000 by using (2, 3, 4, 0, 8, 9) are = 120 20 = 100 Ans. (a) 100 302 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 173. No. of ways to arrange consonants = 4! No. of ways to arrange vowels = 3! 2! Total no. of words without changing order of vowels 4! 3! = 72 words. 2! = Ans. (c) 72 words 174. No. of ways in which vowels can be arranged = 4! = 12 2! No. of ways in which 4 vowels taken as together 6 consonants are arranged = 7! Total no. of words in which 4 vowels and 6 consonants are arranged = 7! 12 = 60480 Ans. (a) 60480 175. Total words without any restriction = 8! 2! = 20160 Total words if vowels comes together = 6! 3! 2! = 2160 Total words if vowels never Come together = 20160 2160 = 18000 Ans. (b) 176. f(x) = ax + b 18000 3< x < 3 f(3) = 1 a.3 + b = 1 3a + b = 1 f(5) = 7 5a + b = 7 a.5 + b = 7 a = 3, b = 8 Ans. (a) a = 3, b = 8 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 303 ANSWERS 177. x 9 (x2 9) = lt x 3 x ( x 3 ) x 3 x ( x 3 ) lt x 3 x+3 x = lt x 3 Ans. (c) 178. lim x 2 App lt. 3+3 =2 3 =2 0 (4 x 2 ) x2 4 f(2 ) f( x) x 2 x 2 x 2 lt (x+2) App lt. x 2 = 2 +2 = 4 Ans. (d) 4 179. y = 1 x dy = dx 1+ x 1+ x d d 1 x 1 x 1+ x dx dx (1 + x) 1 1 ( 1) 1 x 2 1 x 2 1 + x 1 x 1+ x (1 + x) 2 1 x 2 .(1 + x) 1 (1 + x) 1 x 2 1 Ans. (b) 180. y = 1+ x (1 + x) 1 x 2 10 x + log x x dy = dx x 10 x log e 10 + x ( d d x (10 x + log x) (10 x + log x) dx dx x ) 1 1 x 10 + log x x 2 x x 10 x. log 10 .2 x + 2 10 x log x 10 x (2 x log 10 1) + 2 log x 2 x x 2x x Ans. (a) 304 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 181. Here, considering x 2 as the first function as 2 x as the second function and applying the method of integration by parts, we may write 2 x x 2 dx = x 2 .2 x 2x 2x . dx log 2 log 2 = 2 x x2 2 log 2 log 2 x2 = 2 x x2 2 log 2 log 2 x.2 x 2x dx log 2 log 2 = 2 x x2 2 log 2 log 2 x.2 x 1 2x . log 2 log 2 log 2 = 2 x x 2 x.2 x +1 2 x +1 + +c 2 (log 2 )2 (log 2 )3 x dx Ans. (a) x =z 182. let log 1 log x = z 2 1 1 . dx = dz 2 x I= log x 2 dx = 3x 3 = 2 2 z 3 2 log x dx 2x 2 z dz 3 = z2 1 = = log 3 3 ( x ) 2 +c Ans. (c) 183. log x x 2 dx = log x . 1 x2 dx Using Integrating by parts 1 (Note: here (log x) is to be taken as first function and 2 as second function) x Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 305 ANSWERS 1 1 1 1 dx = log x dx x x x log x. x 2 = 1 log x + x = 1 1 log x + c x x = 1 (1 + log x ) + c x 1 x2 dx Ans. (b) 184. e x. 2 x x 1+ 2 = dx . e dx 2 (x + 1)2 (x + 1) x2 + 1 x2 1 2 ex + dx 2 (x + 1)2 (x + 1) = x 1 2 ex dx + 2 (x + 1) (x + 1) = x e [f( x) + f ( x)] dx = Where f (x) = x 1 x +1 = e x . f (x ) + c = x 1 e x +c x +1 Ans. (a) 185. Let I = I= = xe x (1 + x )2 dx 1+ x 1 (1 + x )2 e 1 x dx 1 1 + x (1 + x )2 e x dx 306 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 1 1 = 1+ x e = 1 x 1 + x e = ex 1 1 e x dx e x dx + 2 1+ x (1 + x) (1 + x) 2 I= ex +c 1+ x x dx (1 + x )2 e x dx 1 2 X ( 1) (1 + X) (1) (e )dx (1 + x) 2 e x dx Ans : (a) x+ 186. Given y = dy 1 = + dx 2 x = = 1 2 x 1 x ( x )(0 ) 1 ( x) 2 1 2 x 1 2x x 1 1 1 2 x x dy 1 x 1 = dx 2 x x 2x 1 dy (x 1) = 2x dx 2x x = x 1 x x = x 187. Given y= 1 x x2 + 1 + x2 1 x2 + 1 x2 1 Multiply Reciprocal of R.H.S. to R.H.S. Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 307 ANSWERS x2 + 1 + i.e. y = x2 1 x2 + 1 x2 1 x2 + 1 + x2 1 2 2 x +1 x 1 ) ( (x + 1)+ (x 1)+ 2 2 = x2 + 1 + x2 1 x2 + 1 x2 1 2 ) [ (a + b )(a b )= a ( = 2 2 b2 ] x2 + 1 x2 1 2 = 1 2 2x + 2 x2 + 1 x2 1 2 = x2 + (x + 1)(x 1) 2 2 Differentiate on both sides. [( ) ( )( ) [2 x + 2 x + 2 x 2 x] ) ] dy 1 = 2x + x 2 + 1 (2 x ) + x 2 1 (2 x ) 2 2 dx 2 x +1 x 1 ( = 2x + = 2x + dy = dx 1 3 4 2 x 1 3 4 x3 2 x4 1 2x + 2 x3 x4 1 Ans. (b) 188. Given dy = dx + 3 x x 2 4 y = log e x+2 x e 3 x 2 4 e x x+2 1 3 3 x 2 4 4 (x + 2 ) 1 (x + 2 )(1) (x 2 )(1) (x + 2 )2 3 x 2 4 x e x+2 308 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 1 3 4 4 3 x 2 x 2 x 2 x 2 + + + ex 2 x+2 4 x + 2 (x + 2 ) = 3 x 2 4 e x+2 x 3 x 2 4 x+2 = 1 4 3 4 x 2 4 + 2 (x + 2 ) x + 2 3 x 2 4 x+2 3 = (x + 2 )2 x 2 x+2 1 3 4 4 +1 1 = x 2 2 x+2 (x + 2 ) = x+2 +1 (x + 2 ) x 2 3 +1 3 2 3 = 2 x 4 +1 3 + x2 4 = x2 4 = x2 1 x2 4 Ans. (a) 189. Given y = xx Taking log on both sides. ( ) log y = log x x log y = x. log x Differenciate on both sides. 1 dy 1 = x. + log x.1 y dx x dy = y [1 + log x ] dx [ log e = 1] Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 309 ANSWERS = y [log e + log x] = y [log ex] = [log m + log n = log (mn)] xx [log ex] Ans. (b) y = xe 190. Given x2 taking log on both sides ( ) log y = log x e x2 2 log y = e x log x differenciate on both sides ( ) 2 1 2 1 dy = e x + log x e x ( 2 x) y dx x 2 1 = e x 2 x log x x 2 2 1 2 x log x dy = y.e x dx x dy e x2 x 2 = x .e dx 1 2 x 2 log x x Ans : (a) 191. Sn = 0= n [2 a + (n 1)d ] 2 n [20 + (n 1)d ] 2 2a = (1 n)d d = Sn = 2a (1 n) m [2 (a + nd ) + (m 1)d ] 2 m 2a 2a 2 a + 2 n. + (m 1) 2 1 n 1 n 1 n + 2n + m 1 Sm = ma 1 n 310 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II = ma Sm = (m + n ) 1 n ma (m + n) (n 1) Ans. (b) ma (m + n) (n 1) d = n m 192. a = m Tl = 2m 2m = m+(N 1)d 2m m = (N 1) (n m) m n +m m +1+ n m n m N= N= n n m s= S= m = N 1 n m N n [a + l] [m + 2m] 2 n m 3 mn n m Ans. (a) 3 mn n m 193. a = 29 a + 4d = 15 4d = 15 + 29 d = 14/4 = 7/2 Let n th term be 0 0 = a+ (n 1) d 0 = 29 + (n 1) 7/2 58/7 = n 1 n = 9.28 (not possible) 10th term will be positive S 31 = Sum of remaining 31 terms. 31 7 7 2 29 + 9 + (31 1) 2 2 2 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 311 ANSWERS = 31 [5 + 105 ] 2 = 31 110 = 1705 2 S 31 = 1705 (Sum of all positive nos.) Ans. (b) 1705 194. Tn = a + (n 1) d 1 = a + (m 1)d n 1 = a + (n 1)d m ...(i) ...(ii) by solving eg. (i) and e.g. (ii) a= 1 1 ,d= mn mn S mn = = mn 1 1 + (mn 1) 2 2 mn mn mn mn + 1 mn 1 1 + 2 2 mn mn mn + 1 Smn = 2 Ans. (c) 195. 1 (mn + 1) 2 S n n / 2 [12 A + (n 1)D] = S n n / 2[2 a + (n 1)d ] n 1 2 ( A + 2 d 7n + 1 = 3n + 2 n 1 2 a + d 2 Put n = 25 7 25 + 1 A + 12 D = 3 25 + 2 a + 12 d 312 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II T13 176 16 = = 16:7 t 13 77 7 Ans. (b) 16:7 a +b a, G 1 , G 2 , b 2 196. A1 = 1 b = a(r) b 3 r= a 3 3 3 G1 + G3 2 b 1 / 3 b 2 / 3 + a a a a 2 = b b b a 3 . + a 3 a 3 a a a = a +b b a 2b = a a a = 3 G 1 . G 2 . 2A = 2A G 1 G 2 1/ 3 b .a a b 1 + a 2/3 a +b .2 2 Ans. (b) 2A G 1 G 2 197. ab = a m +1 + b m +1 m a +b m a m +1 / 2 .b 1 / 2 + a 1 / 2 .b m +1 / 2 = a m +1 + b m +1 a m +1 a m +1 / 2 .b 1 / 2 = a 1 / 2 b m+1 / 2 b m +1 [ ] [ a m +1 / 2 a 1 / 2 b 1 / 2 = b m +1 / 2 a 1 / 2 b 1 / 2 a m +1 / 2 b m +1 / 2 Ans. (a) = 1 m+1/2 = 0 ] m = 1/2 1/2 198. Ans. (c) 199. Value of 1. 4 x = 1.444... 10x = 14.444... 9x = 13.00 Ans. (a) x = 13/9 13/9 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 313 ANSWERS 200. x = 0.356 10x = 3.565656... 1000x = 356.5656... 990x = 353.0 x= 353 990 353 990 Ans. (c) Model Test Paper BOS/CPT 2 151. TP +1 = 2 .Tq +1 a + (P+ 1 1) d = 2 [a+qd] a + pd = 2a + 2qd a = d (P 2q) = Tp + q +1 = T3 p +1 ( 2 P q )d 1 = 1:2 2 ( 2 P q )d 2 Ans. (a) 152. d = a = a + (P + q )d (P 2 q )d + (P + q )d = a + 3Pd (P 2 q )d + 3Pd 1:2 Tm a + (m 1)d d + (m 1)d = = Tn a + (n 1)d d + (n 1)d d + (1 + m 1)d m = m:n n d + (1 + n 1)d Ans. (b) m:n 153. 1 = a + (m 1)d n & 1 = a+ (n 1)d m 1 1 , d= mn mn a= T mn = a+ (mn 1)d 1 1 +(mn 1) mn mn Tmn = 1 Ans. (a) 1 314 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II

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