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CA CPT : Volume 2 - Model Test Paper 6 (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 6 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. What is the important object of accounting? (a) (b) (c) (d) 2. A collateral security of 8,000 10% Debentures of Rs.10 each has been issued at a premium of 25% to A in lieu of a loan of Rs. 1,00,000 taken on 1st January, 2006. At the end of the year, interest was paid on: (a) (b) (c) (d) 3. The nominal value of debentures The amount of loan outstanding Difference of loan amount and nominal value of debentures None of the above Income is measured on the basis of (a) (c) 4. To maintain records Depiction of financial position Make information available to various groups and users. All of the three Matching concept Cost concept (b) (d) Consistency concept None of the above Which of the following is long-term liability? (a) (c) Outstanding Expenses Debentures 135 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Share Capital All of the above 135 MODEL TEST PAPER - 6 5. Drawing is a type of (a) (c) 6. Goodwill Patents rights Entity concept Accrual concept (b) (d) Money measurement concept Going concern concept Market Value Historical Value (b) (d) Present Value All of the above Decrease in Capital Increase in Assets (b) (d) Decrease in Liability All of the above Decrease in Cash Increase in Cash (b) (d) Increase in Liability None of the three Final Account Subsidiary book (b) (d) Statement of day books None of the above When overdraft as per Cash Book is the starting point then wrong debit in pass book will be (a) (b) (c) (d) 14. (b) (d) Trial Balance is a (a) (c) 13. Investment Copyright Decrease in the amount of Trade Payables result in (a) (c) 12. To issue preference shares None of the above Purchase of office equipment on credit will lead to (a) (c) 11. (b) (d) Which of the following is not a valuation Principle? (a) (c) 10. To issue debentures To issue equity shares The Enterprise is liable to the owner for capital investment made by the owner as per (a) (c) 9. Withdrawal of Capital None of the above Which of the following is not an Intangible Asset? (a) (c) 8. (b) (d) The most common method of supplementing the capital available to a company is (a) (c) 7. Expenses Income Deducted from the Bank Reconciliation Statement No effect in the Bank Reconciliation Statement Added in the Bank Reconciliation Statement None of the three Profit is a part of (a) (c) Income Assets 136 The Institute of Chartered Accountants of India (b) (d) Owner s Capital All of the above Common Proficiency Test (CPT) Volume - II 15. Journal is a book of (a) (c) 16. Bank column on the Debit side Cash column on the Credit side (b) (d) Bank column on the Credit side None of the above Drawer Drawee (b) (d) Endorsee All of the above Crossed cheque Promissory note (b) (d) Bill of exchange Bearer cheque Conservatism Materiality (b) (d) Consistency Disclosure Arti places an order to Anju for supply of certain goods yet to be manufactured. On receipt of order, Anju purchases raw materials, employs workers, produced the goods and delivered them to Arti. In this case sale will be presumed to have been made at the time of (a) (c) 23. Salaries & wages of the staff For purchase of assets Small expenses relating to postages and conveyance etc. All of the above Inventories are valued at lower of cost or net reliable value by applying the principle of (a) (c) 22. In the Cash a/c Both (a) and (b) Which of the following instrument is not a negotiable instrument (a) (c) 21. (b) (d) Promissory note is prepared by (a) (c) 20. In the Bank a/c Nowhere When a cheque received is returned dishonoured, it is recorded on (a) (c) 19. All credit transactions only Original entry Petty Cash is used for payment of (a) (b) (c) (d) 18. (b) (d) Balance of Petty Cash Book is posted to ledger (a) (c) 17. All cash transactions only Secondary entry Production of goods Purchase of material (b) (d) Delivery of goods None of the above Ratan deposited a cheque on 25 January, 2010 for a sum of Rs. 20,000. The cheque was collected on 2 February, 2010. If the bank balance as per passbook as on 31 January, 2010 is Rs. 60,000; balance as per cash book will be (a) (c) Rs. 60,000 Rs. 70,000 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Rs. 40,000 Rs. 80,000 137 MODEL TEST PAPER - 6 24. The company charge interest on call in arrear at (a) (c) 25. (b) (d) Rs. 400 Rs. 200 5% 6% (b) (d) 7% 8% Rs. 60,000 Rs. 45,000 (b) (d) Rs. 36,000 Rs. 30,000 Rs. 72,000 Rs. 80,000 (b) (d) Rs. 1,08,000 Rs. 1,20,000 20% 25% (b) (d) 30% 35% (b) (d) AS-3 AS-5 Valuation of inventory is dealt within (a) (c) 32. Rs. 800 Rs. 600 An asset has a useful life of 4 years. If it is depreciated by diminishing balance method. Its book value at the end of 4 years is 24% of its original cost. Hence the rate of depreciation applied is (a) (c) 31. Subscribed capital Called-up capital Cost of motor Rs. 2,00,000, scrap value Rs. 20,000. Useful life 4 years. What will be amount of depreciation according to sum of years digit method in the first year? (a) (c) 30. (b) (d) Calculate gross profit if rate of gross profit is 25% on sales and cost of goods are Rs.1,80,000 (a) (c) 29. Authorised capital Issued capital In the absence of any agreement, the partners are entitled to interest on the loan advanced to the firm at the rate of (a) (c) 28. 10% 20% Manish & Co. Ltd. forfeited 100 shares of Rs. 10 each, Rs. 8 called up, Rs. 4 paid on application; the amount to be forfeited is (a) (c) 27. (b) (d) The maximum amount of capital that a company can raise is called (a) (c) 26. 5% 15% AS-2 AS-4 Consider the following items (1) Prepaid Salary (2) (3) Loan (4) Current Liability would include (a) (c) 1,2,3,4 4,3,1 138 The Institute of Chartered Accountants of India Accrued Interest (receivable) Bank overdraft (b) (d) 2,3,4 3,4, Common Proficiency Test (CPT) Volume - II 33. B s trial balance contains the following informationMake provision at the end of the year Rs. 10,000 Provision for bad debts at the beginning of the year Rs. 4,000 Bad Debts Rs. 6,000 The amount to be debited to Profit & Loss A/c (a) (c) 34. (b) (d) Rs. 4,500 Nil Rs. 5,000 overstated Rs. 25,000 understated (b) (d) Rs. 25,000 overstated Rs. 5,000 understated Rs. 29,500 Rs. 7,500 (b) (d) Rs. 35,000 Rs. 22,000 Ram and Shyam entered into a Joint venture for equal profits. Ram purchases goods costing Rs. 70,000. Shyam sold goods costing Rs. 60,000 at Rs. 80,000. Balance goods were taken over by Ram at same gross profit percentage as in case of sale. The value of goods taken over will be (a) (c) 38. Rs. 1,500 Rs. 6,000 X and Y entered into a joint venture sharing profits and losses equally. X provides goods from his Inventory Rs. 20,000. He pays expenses amounting to Rs. 2,000. Y incurs further expenses on carriage Rs. 3,000. He received cash for sales Rs. 35,000. He also takes over goods to the value of Rs. 5,000. What will be the amount to be remitted by Y to X? (a) (c) 37. Rs. 8,000 NIL The opening Inventory is overstated by Rs. 10,000 and closing Inventory is understated by Rs. 15,000. The impact of these on net profit for the current year is (a) (c) 36. (b) (d) A trial balance at 31st March contains the following information: 15% Loan Rs. 30,000; Interest paid Rs. 3,000 ; Interest debited to the P & L A/c is (a) (c) 35. Rs. 20,000 Rs. 12,000 Rs. 10,000 Rs. 3,333 (b) (d) Rs. 13,333 Rs. 23,333 Guarantee given to a partner Mohan by the other partner Suresh and Mahesh means (a) (b) (c) (d) In case of Loss or insufficient profit Mohan will withdraw the minimum guaranteed amount In case of Loss Mohan will not contribute towards that loss Even in case of sufficient profit Mohan will receive only the minimum guaranteed amount None of the above Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 139 MODEL TEST PAPER - 6 39. Naresh is drawing Rs. 2,000 per month at the end of the month. If the rate of interest is 10% p.a. the total interest chargeable from him in the accounting year will be (a) (c) 40. Current profit Accumulated profit Rs 2,250 Rs. 1,800 (b) (d) Rs. 3,000 Rs. 6,000 4% 6% (b) (d) 5% 7% No change in Owner s Equity Decrease in liability & Owner s Equity (b) (d) Increase in Assets & Owner s Equity None of these A share of Rs. 200 each issued at discount of 10% is forfeited for non-payment of final call @ Rs. 50 per share. The maximum loss it can bear on re-issue of shares will be (a) (c) 46. (b) (d) Goods destroyed by fire is an example of: (a) (c) 45. Goodwill Reserves & Surplus As per table A of the companies Act, 1956, a company pays interest on call in advance at the rate of (a) (c) 44. Share Profit in capital ratio Interest on capital Salary on capital Interest on loans and advances to the firm Sita and Gita are partners sharing profit in the ratio of 3:2 (Sita s capital Rs. 6,000 and Gita s capital Rs. 3,000). They admitted Rita for 1/5th share of profit . How much Rita should bring towards her capital? (a) (c) 43. Rs. 1,200 None of the above Interest on capital will be paid to the partners if provided for in the agreement but only from (a) (c) 42. (b) (d) In the absence of any agreement, partners are entitled to (a) (b) (c) (d) 41. Rs. 2,400 Rs. 1,100 Rs. 200 Rs. 20 (b) (d) Rs. 50 Rs. 130 If on a share of Rs. 50, only Rs. 40 has been called and the company has received Rs. 30 till date. The capital account should be credited with (a) (c) Rs. 50 Rs. 40 140 The Institute of Chartered Accountants of India (b) (d) Rs. 30 Rs. 20 Common Proficiency Test (CPT) Volume - II 47. There are 60,000 preference shares of Rs. 10 each fully called up. But there are call in arrears of Rs. 4,000 @ Rs. 2 per share. Company can redeem at present (a) (c) 48. (b) (d) Rs. 36,750 Rs. 1,15,000 Rs. 7,500 Rs. 15,000 (b) (d) Rs. 30,000 Rs. 22,500 10 years Over the period of redemption (b) (d) 8 years 15 years Fixed Assets Liquid Assets (b) (d) Current Assets Fictitious Assets Rs. 9,000 Rs. 12,000 (b) (d) Rs. 6,000 Rs. 10,000 At what price goods pending approval or return as on the last day of accounting year are valued? (a) (c) 55. Rs. 35,000 Rs. 38,500 Fixed asset costing Rs. 60,000 has an estimated life of 8 years. At the end of its useful life it can be sold for Rs. 12,000. Using the fixed instalment method, the annual depreciation against profit will be (a) (c) 54. 20 years 25 years Depreciation is provided on (a) (c) 53. (b) (d) Loss on issue of Debentures is generally written off in (a) (c) 52. 10 years 15 years Lal & Co. Ltd. has issued 15% debentures on 1st January, 2008 for Rs. 2,00,000. Interest if payable on 31st March and 30th September every year. Amount of outstanding interest on 31st December, 2009 will be (a) (c) 51. 56,000 shares None of the above Preference shares amounting to Rs. 75,000 are redeemed at a premium of 5% by issue of equity shares amounting to Rs. 40,000 at a premium of 10%. The amount to be transferred to capital redemption reserve account will be (a) (c) 50. (b) (d) A company cannot issue redeemable preference shares for a period exceeding (a) (c) 49. 60,000 shares 58,000 shares Cost price Average price (b) (d) Selling price Latest price Rent paid to Landlord amounting to Rs. 1,000 was credited to rent account with Rs. 10,000. In the rectifying entry rent a/c will be debited with (a) (c) Rs. 11,000 Rs. 9,000 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Rs. 1,000 Rs. 10,000 141 MODEL TEST PAPER - 6 56. Sales to A of Rs. 600 not recorded in the books would affect (a) (c) 57. Rs. 120 Rs. 300 (b) (d) Rs. Nil Rs. 180 Added by Rs. 300 Deducted by Rs. 600 (b) (d) Deducted by Rs. 300 Added by Rs. 600 Ram send 50 fans to Shyam costing Rs. 500 per fan to be sold at 20% above cost price. Sales value will be (a) (c) 60. A s A/c Sales A/c and A s A/c When overdraft as per adjusted cash book is the starting point, Bank charges of Rs. 300 recorded twice in the passbook will be (a) (c) 59. (b) (d) X draws an accommodation bill on Y for Rs. 7,000. The proceeds are to be shared by X and Y in the ratio of 3:2. The bill was discounted for Rs. 6,700. Discount borne by X will be (a) (c) 58. Sales A/c Cash A/c Rs. 25,000 Rs. 30,000 (b) (d) Rs. 20,000 Rs. 31,250 If capital at the end of the year is Rs. 40,000; capital introduced during the year Rs. 30,000; Drawings for the year is Rs. 20,000 and Loss of the year is Rs. 60,000 then capital at the beginning of the year was (a) (c) Rs. 90,000 Rs. 70,000 (b) (d) Rs. 80,000 Rs. 10,000 SECTION B : MERCANTILE LAWS (40 MARKS) 61. Which of the following is correct? When a minor has been supplied with necessaries on credit. (a) (c) 62. (b) (d) Minor s estate is liable Minor is liable at his option Which one of the following is not a wagering agreement? (a) (b) (c) (d) 63. Minor is not liable Minor is personally liable A lottery An agreement to buy a ticket for a lottery Commercial transaction, the intention of which is not to deliver the goods but only to pay the difference in price A contract of insurance Which of the following persons are not competent to contract? (a) (c) Person of Indian origin Minor 142 The Institute of Chartered Accountants of India (b) (d) Person disqualified by law All of the above Common Proficiency Test (CPT) Volume - II 64. Which are the following elements that affect the consent of the party? (a) (c) 65. Knock out agreement Partnership agreement (b) (d) Auction agreement By bidder agreement At the rate of 12% At the rate of 6% (b) (d) At the rate of 8% At the rate as it thinks fit (b) (d) Unconditional None of the above An auction sale may be (a) (c) 72. Ordinary damages are recoverable Special damage are recoverable only if the parties knew about them Remote or indirect damages are not recoverable None of these statements is incorrect Under the Sale of Goods Act, 1930 a court can award interest (a) (c) 71. When there is no exact substitute or alternative to the subject matter of the contract When it is probable that compensation in money cannot be got for non-performance (a) or (b) (a) and (b) An agreement between the bidders not to bid against each other is called (a) (c) 70. For wrongful dishonour of cheque by a banker For a breach of promise to marry Neither (a) nor (b) Either (a) or (b) Which of the following statements is not correct? (a) (b) (c) (d) 69. Agreements the consideration of which is unlawful Agreements made under the unilateral mistake of fact Agreements made under the mistake of law Contingent agreement In which of the following situations specific performance can be granted? (a) (b) (c) (d) 68. Misrepresentation All of the above Vindictive Damages are awarded (a) (b) (c) (d) 67. (b) (d) Which of the following agreements are void? (a) (b) (c) (d) 66. Undue Influence Fraud Conditional voidable The bidder at an auction sale can withdraw his bid (a) (c) Any time during auction Before payment of price Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Before fall of hammer None of these 143 MODEL TEST PAPER - 6 73. Transfer of property in goods sent on approval take place when (a) (b) (c) (d) 74. If the goods are not in existence (not produced at the time of agreement to sell), goods are to be delivered at (a) (b) (c) (d) 75. Possession of goods Both (b) and (c) Can pass a goods title to a bona fide purchaser Can choose whether to pass or not to pass the goods Cannot pass a goods title to a bona fide purchaser All of the above Result to pay the price of goods Nobody can give that the himself does not have Title is not clear Delivery is not possible If the consent is caused by coercion is to be proved by (a) (c) 80. (b) (d) Nemo-dat quad non habet means (a) (b) (c) (d) 79. Ownership of goods Custody of goods In case of a hire-purchase the hirer (a) (b) (c) (d) 78. When it is in accordance with the terms of the contract When seller is ready but not willing for giving the possession of the goods When the seller delivers the goods at the place at which they are at time of sale All of the above The property in the goods means the (a) (c) 77. The place at which they are manufactured or produced The buyer place The sellers place None of the above A buyer is deemed to have accepted the delivery of goods (a) (b) (c) (d) 76. Buyer signifies his approval When he makes the return by goods impossible When he retains goods without signifying approval for unreasonably long time All of the above Both the parties The party causing coercion (b) (d) The aggrieved party None of these In case of reciprocal promise, first to do things which are legal are ________ and second to do things which are illegal are ________. (a) (c) Valid, void Valid, illegal 144 The Institute of Chartered Accountants of India (b) (d) Void, voidable Void, void Common Proficiency Test (CPT) Volume - II 81. All agreements in restraint of trade are ________. (a) (c) 82. (b) (d) Buyer No body True False (b) (d) Partly true Partly false Sub-partner Sleeping partner (b) (d) Nominal partner All of the above Contact of sale An agreement to sell (b) (d) Not at all a contract of sale Not at all an agreement to sell Firm is automatically dissolved Firm is also declared insolvent Solvent partner has to repay the debts of the firm None of the above ________ involves selection of goods with the intention of using them in performance of the contract with the mutual consent of the seller and the buyer: (a) (c) 89. Seller Bailee When all partners, or all but one partner, of the firm are declared insolvent then ______. (a) (b) (c) (d) 88. Fraud None of the above Contract regarding the sale of unascertained goods is termed as: (a) (c) 87. (b) (d) The partner who does not take part in the conduct of the business is known as _______. (a) (c) 86. Person of unsound mind Minor Compensation shall not be given for any remote and indirect loss sustained by reason of breach it is ___________. (a) (c) 85. Valid Illegal In the absence of a contract to contrary, the ___________ is under a duty to apply for delivery of goods. (a) (c) 84. (b) (d) Doctrine of restitution does not apply against a ________. (a) (c) 83. Void Voidable Sale Appropriation of goods (b) (d) Agreement to sell Transfer of ownership Premium paid by a partnership firm on the Joint Life Policy (JLP) of partners is (a) (b) (c) (d) Debited to capital accounts of each partner Credited to capital accounts of each partner Debited to the profit & loss account of the firm Credited to the profit & loss account of the firm Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 145 MODEL TEST PAPER - 6 90. The property in the goods means _________. (a) (c) 91. (b) (c) (d) (b) (d) Sue for price None of the above Which does not have any deed Which does not have any partner Which does not provide for how long the business will continue Which cannot be dissolved A person representing himself to be a partner of the firm by words spoken or written or by him conduct Partner of a firm but the outsiders do not know him as such Partner of a partner of a firm Partner of a firm but does not take part in the business of the firm Actively takes part in the business of the firm Actively participate in co-curricular activities Actively shares the profits Makes a show of authority Ownership of goods Transfer of goods (b) (d) Custody of goods Property in real estate The time of delivery of goods should be made, unless otherwise specified with in the (a) (c) 98. Sue for damages Rescind the contract The term possession of goods refers __________. (a) (c) 97. Rights in personam None of the above Active partner is one who _______. (a) (b) (c) (d) 96. (b) (d) Partner by holding out is_________. (a) 95. Rights against goods Rghts against appropriation A partnership at will is on __________. (a) (b) (c) (d) 94. Custody of goods Both (a) and (b) When buyer repudiates the contract before the date of delivery the seller may _________. (a) (c) 93. (b) (d) Rights of seller against the buyer personally are called_________. (a) (c) 92. The possessing of goods Ownership of goods Business hours of the buyer Business hours of the seller (b) (d) Reasonable time None of the above A pledge, made by the seller, of the goods whose title was transferred to the buyer but not the possession, is_______ (a) (c) Void Illegal 146 The Institute of Chartered Accountants of India (b) (d) Valid Voidable Common Proficiency Test (CPT) Volume - II 99. A and B were two partners in a firm of sugar dealers. Unknown to B A supplies at a particular time his own stock of sugar to the firm at market price and makes profit. Decide whether (a) (b) (c) (d) 100. A can personally keep this profit A cannot keep this profit A can keep half of profit A can keep one fourth of profit A polished B shoes without being accepted by B to do so. B does not make any attempt to stop A from polishing the shoes. Decide. (a) (b) (c) (d) B is bound to pay B is not bound to pay B is bound to pay damages any incurred by A None of these SECTION C : GENERAL ECONOMICS (50 MARKS) 101. In Micro Economics we study the Economic behaviour of: (a) (c) 102. As normative science, Economics involves value judgments Robbins has made economics as a form of welfare economics The Law of Demand is always true None of the above The best quality goods are produced The highly skillful resources in the country are fully employed All resources are utilized and goods and services are produced at least cost None of the above Economic goods are goods which: (a) (b) (c) (d) 105. Firm All of the above An economy achieves productive efficiency when: (a) (b) (c) (d) 104. (b) (d) Which of the following statements is correct? (a) (b) (c) (d) 103. An Individual Industry Cannot be increased in quantity Obey the law of Micro Economics Are limited in supply and are scarce Are limited to man-made goods. Which of the following means an Economic activity? (a) (b) (c) (d) Production of Goods Production of Services Consumption of Goods and Services All of the above Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 147 MODEL TEST PAPER - 6 106. Which economy is now a myth only, as no country in the world is having that type of economy? (a) (c) 107. (b) (d) One None of the above Inferior good Necessity (b) (d) Luxury good None of the above Teaching CA students in CA Institute by a teacher Singing a song before friends Flying kite for pleasure Teaching to friends in a library any concept of Economics Land varies in fertility and uses Land is highly immobile The supply of land is perfectly elastic from the point of view of the economy The supply of land is perfectly inelastic from the point of view of the economy Ministry of Finance Planning Commission (b) (d) RBI Parliament In India, except in the Election year, Budget is given on: (a) (c) 114. Zero Infinite Fiscal Policy is given by: (a) (c) 113. Less than one Zero The following is not the characteristic of Land: (a) (b) (c) (d) 112. (b) (d) Which of the following is considered production in Economics? (a) (b) (c) (d) 111. Greater than one One The income of a household rises by 20 percent, the demand for computer rises by 50%, this means computer is a/an: (a) (c) 110. Socialist Economy None of the above If two goods are totally unrelated, then cross elasticity between them is: (a) (c) 109. (b) (d) If the proportion of income spent on a goods decreases as income rises then income elasticity is: (a) (c) 108. Capitalist Economy Mixed Economy Last day of March 1st January (b) (d) 1st day of April Last day of February (b) (d) Super Drawing Rights Special Drawing Rights SDR stands for: (a) (c) Security Drawing Rights Systematic Drawing Rights 148 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 115. PTA stands for: (a) (b) (c) (d) 116. At present the number of members of WTO are (as in 2013) (a) (c) 117. 1946 1945 (b) (d) 1947 1919 Revenue Deficit Capital Deficit (b) (d) Primary Deficit Budget Deficit An increase in revenue deficit An increase in fiscal deficit (b) (d) A decrease in revenue deficit No change in fiscal deficit Under which of the following tax system, more tax is imposed on the lower income group? (a) (c) 123. To help its member countries in the reconstruction and development of their territories To provide finance for long-term purposes To provide finance for short-term purposes To encourage private foreign investment and credit by providing guarantee of repayment of private industries An increase in SLR will result in (a) (c) 122. WTO World Bank IMF United Nation Development Associations Fiscal Deficit minus borrowings and other liabilities is equal to: (a) (c) 121. 184 167 IBRD (World Bank) was set up in: (a) (c) 120. (b) (d) Which of the following is not the function of World Bank? (a) (b) (c) (d) 119. 177 159 International Finance Corporation comes under: (a) (b) (c) (d) 118. Plurilateral Trade Agreements Private Trade Agreements Plurilateral Transaction Agreements Public Trade Agreements Regressive Value Added Tax (b) (d) Progressive Proportional Tax Open market purchase of government bonds by RBI will have the tendency to: (a) (b) (c) (d) Decrease interest rates, but increase money supply Decrease interest rates, but decrease money supply Increase interest rates, but increase money supply Increase interest rates, but decrease money supply Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 149 MODEL TEST PAPER - 6 124. Banks rate means: (a) (b) (c) (d) 125. When prices are rising and there is unemployment and recession in the economy, then the phenomenon is called: (a) (c) 126. Cost-push inflation Demand-pull inflation National Leprosy Mission National Logistic Mission (b) (d) National Law Mission National Literacy Mission Increased Remained the same (b) (d) Reduced Doubled RBI TRAI (b) (d) SEBI BSE Third largest Largest (b) (d) Second largest Tenth largest Which year is known as year of great divide for Indian population? (a) (c) 132. (b) (d) Postal network in India is __________ in the world. (a) (c) 131. Deflation Stagflation Who is regulatory authorities for securities market in India? (a) (c) 130. Stagflation Reflaction Over the year, the incidence of malaria has _____________ (a) (c) 129. (b) (d) NLM stands for: (a) (c) 128. Inflation Deflation When too much money chases too few goods the resulting inflation is called: (a) (c) 127. Rate of interest paid by banks to depositors Rate below which banks cannot lend money to borrowers Rate of interest charged by RBI on its loan to other commercial banks Rate of interest charged by commercial banks for loan given to RBI 1911 1931 (b) (d) 1921 1941 India is passing through ___________ stage of Demographic Transition. (a) (c) Fourth Second 150 The Institute of Chartered Accountants of India (b) (d) First Third Common Proficiency Test (CPT) Volume - II Use following table to answer questions 133-136. Quantity Variable Cost 0 0 5 25 10 470 15 700 20 980 25 1350 30 1850 35 2520 40 3400 45 4530 50 Fixed Cost Total Cost AVC ATC MC 5950 A firm operating in perfect competition sells as much as of its products as it chooses at a market price of Rs. 100 per unit. It Fixed cost is Rs. 300 and its Variable cost for different levels of production are shown in the above table 133. When production is 40 units, the average cost is: (a) (c) 134. Rs. 7.50 Rs. 92.50 Rs. 22 Rs. 176 (b) (d) Rs. 85 Rs. 880 To maximize profit the firm should produce: (a) (c) 136. (b) (d) In the table, marginal cost per unit that corresponds to 40 units of production is: (a) (c) 135. Rs. 4.40 Rs. 85 15 units 35 units (b) (d) 30 units 50 units If the market price drops from Rs. 100 to Rs. 56 per unit, the firm s short run response should be (a) (b) (c) (d) Shut down Produce 5 units Produce 20 units Continue to produce the same number of units as before the drop in price Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 151 MODEL TEST PAPER - 6 Use following table to answer questions 137 to 138 Hours of Labour Total Output Marginal Product 1 200 200 2 - 160 3 480 - 0 137. What is the total output when 2 hours of Labour are employed? (a) (c) 138 160 360 (b) (d) 200 400 What is the marginal product of the third hour labour? (a) (c) 120 200 (b) (d) 160 480 Use table to answer question 139-142 Mohan sweets is a small restaurant and a price taker. The table below provides the data of Mohan s Sandwich output and costs in Rupees Quantity 0 210 20 300 30 400 40 540 50 790 60 TFC TVC AVC AC MC 1060 If Sandwiches are being sold for Rs. 14 each, what is Mohan s profit maximising level of output? (a) (c) 140. 100 10 139. TC 10 Sandwiches 50 Sandwiches (b) (d) 40 Sandwiches 60 Sandwiches What is the total variable cost when 60 sandwich are produced? (a) (c) Rs. 690 Rs. 110 152 The Institute of Chartered Accountants of India (b) (d) Rs. 960 Rs. 440 Common Proficiency Test (CPT) Volume - II 141. What is average fixed cost when 20 sandwiches are produced? (a) (c) 142. (d) 19% 13% (b) (d) 29% 9% Total product divided by the number of units of variable input The additional output resulting from a one unit increase in the variable input The additional output resulting from a one unit increase in both the variable and fixed inputs None of the above Loan and advances Money at call and short notice Bills discounted and purchased Investment in Government securities Increases Decreases Remains constant First declines then rise Contraction of demand is the result of: (a) (b) (c) (d) 148. Rs. 13 Rs. 9 In the short run, when the output of a firm increases its average fixed cost: (a) (b) (c) (d) 147. (b) (d) Which of the following is the most profitable, but least liquid asset of a commercial bank? (a) (b) (c) (d) 146. Rs. 11 Rs. 14 The marginal product of a variable input is best described as: (a) (b) (c) 145. Rs. 3.33 Rs. 2.5 In July, 1991 Indian devalued the rupee by about: (a) (c) 144. (b) (d) Between 10 to 20 sandwiches, what is the marginal cost per sandwich? (a) (c) 143. Rs. 5 Rs. 10 Decrease in the number of consumers Increase in the price of the goods concerned Increase in the price of other goods Decrease in the income of purchases The indifference curve approach assumes: (a) (c) Rationality Transitivity Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Consistency All of the above 153 MODEL TEST PAPER - 6 149. According to the 2001 census the total literacy rate is: (a) (c) 150. 32.5% 65.4% (b) (d) 52.1% 75.8% At the top 15 debtor countries of the world, India is ranked ___ by the world Bank (2011) (a) (c) Fourth Eighth (b) (d) Tenth Fifteenth SECTION D : QUANTITATIVE APTITUDE (50 MARKS) 151. If one-fifth of one-third of one-half of number is 15, then number is (a) (c) 152. 400 None of these 100 1120 (b) (d) 160 200 13 15 (b) (d) 14 None of these 75 84 (b) (d) 93 57 A bag contains rupee, 50 paise and 25 paise coins in the ratio 10:14:18. If the total amount in the bag is Rs. 430, find the number of coins of each kind. (a) (c) 157. (b) (d) The sum of the digits of a two digit number is 12. If the digits are reversed, the number is decreased by 18. Find the number. (a) (c) 156. 300 500 If the sum of a number and its square is 182, what is the number? (a) (c) 155. 450 None of these Four-fifths of three-eighths of a number is 24. What is 25% of that number? (a) (c) 154. (b) (d) Three-fourth of one fifth of a number is 60. The number is (a) (c) 153. 400 500 200, 280, 360 360, 280, 200 (b) (d) 280, 200, 360 None of these Two vessels contain equal quantity of mixtures of milk and water in the ratio 5:2 and 6:1 respectively. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained. (a) (c) 3:11 12:13 154 The Institute of Chartered Accountants of India (b) (d) 11:3 None of these Common Proficiency Test (CPT) Volume - II 158. If f(x) = x + 2, g(x) = 7x than gof (x) = (a) (c) 159. 7x.x + 2.7x None of these Rs. 1,800, Rs. 1,400 Rs. 1,400, Rs. 1,200 (b) (d) Rs. 1,600, Rs. 1,200 None of these An amount of Rs. 950 is distributed among A, B & C in the ratio of 5:11:3, what is the difference between the share of B and A. (a) (c) 161. (b) (d) The ratio of the incomes of two persons is 9:7 and the ratio of their expenditures is 4:3. If each of them saves Rs. 200 per month, then their monthly incomes. (a) (c) 160. 7 x+2 (7x) + 2 300 500 (b) (d) 340 None of these e x e 1 x 1 x 1 Evaluate lim (a) (b) 1 e (c) 162. 1 e e (d) None of these (1 + x)x 1 x 0 x Evaluate lim (a) (b) n (c) 163. 1 n n (d) None of these (x + 2)5/3 (a + 2)5/3 x 0 x a Evaluate lim (a) 5 (a + 2) 2/3 3 (b) 5(a + 2)1/3 3 (c) 5 (a + 2)1/ 2 3 (d) None of these Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 155 MODEL TEST PAPER - 6 165. Evaluate lim x 0 (a) 166. log (d) None of these (b) (d) 3 2 log 10 None of these If f (x) = 3x2 + 2 & f(0) = 0 then find f(2). (a) (c) 167. 2 3 (b) log 6 (c) 2x 3x x 8 12 Evaluate x 2 x+3 dx + 6x + 4 (a) 1 log ( x 2 + 6x + 4 ) + c 2 (b) 1 x + log ( x 2 + 6x + c ) + c 2 (c) 1 log ( x + 3) + c 2 (d) None of these Evaluate x 1 e ( x + 1) x 168. 3 dx (a) (b) x2 + log (ex + 1) + c (c) (x + 1)2 + log (ex + 1) + c (d) None of these (a) (3x + 5)5 +c 3 (b) (3x + 5)5 +c 15 (c) 169. ex +c (x + 1) 2 (3x + 5) 4 +c 15 (d) None of these 4 Evaluate ( 3x + 5) dx 156 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 170. Evaluate 7x + 5 dx (a) (b) 1 (7x + 5)3/ 2 + c 21 (c) 171. 2 (7x + 5)3/ 2 + c 21 (7x + 5)3/2 + c (d) None of these Three gentlemen and three ladies are candidates for two vacancies. A voter has to vote for two candidates. In how many different ways can one cast his vote? (a) (c) 172. (b) (d) 12 None of these In a party of 40 people, each shakes hand with others. How many handshakes took place in the party? (a) (c) 173. 10 15 780 880 (b) (d) 700 None of these How many different triangles can be formed joining the angular points of a polygon of m sides? (a) (b) m(m 1) 2 (c) 174. m(m 1)(m 2) 6 m (d) None of these How many different cricket teams of 11 players can be selected from 14 cricket players of which only two can play as wicketkeeper? Given each team must have exactly one wicketkeeper? (a) (c) 175. (b) (d) 132 None of these Mr. X has 8 children of which he takes 3 at a time to the circus. Find, how many times a particular child goes to the circus? (a) (c) 176. 130 140 20 21 (b) (d) 30 None of these If ax = by = cz and x, y, z are in G.P. then log a, log b and log c are in (a) (c) A.P. A.P. and G.P. both Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) G.P. None of these 157 MODEL TEST PAPER - 6 177. The 6th term from the end of the G.P. 8, 4, 2, 1, ., (a) (b) 32 (c) 178. 1 64 1 32 (d) None of these In a finite G.P., the product of two terms equi distant from the beginning and from the end is equal to the product of the first and the last term of the G.P. This statement is (a) (c) 179. True Cannot say 1 2 (b) (d) 1 b (c) a c + is equal to x y 0 None of these (b) 2 b 2 b (d) 1 1 + is x y None of these The number of times a particular item occurs in a given data is called its (a) (c) 182. False None of these If a, b, c are in G.P., a, x, b and b, y, c are both in A.P., the value of (a) 181. (b) (d) If a, b, c are in G.P., a, x, b and b, y, c are both in A.P., then (a) (c) 180. 1 is 1, 024 Variation Cumulative frequency (b) (d) Frequency None of these The width of each of ten classes in a frequency distribution is 2.5 and the lower class boundary of the lowest class is 10.6. Which one of the following is the upper class boundary of the highest class? (a) (c) 35.6 30.6 158 The Institute of Chartered Accountants of India (b) (d) 33.1 None of these Common Proficiency Test (CPT) Volume - II 183. Let L be the lower class boundary of a class in a frequency distribution and m be the mid point of the class. Which one of the following is the higher class boundary of the class? m+2 2 (a) (c) 184. m+ 2m L m+L 2 (b) L+ (d) m 2L The mean of the values of 1, 2, 3 , n with respective frequencies x, 2x, 3x, nx is (a) (b) n 2 (c) 185. n +1 2 2n + 1 3 (d) 2n + 1 6 The mean of four observations is 10 and when a constant a is added to each observation, the mean becomes 13. The value of a is (a) (c) 186. (b) (d) 1 0.5 q pq (b) (d) p+q p True Cannot say (b) (d) False None of these The correlation coefficient of 3x and 2y is the same as the correlation coefficient Of x and y. This statement is (a) (c) 190. 0 1 The regression of y on x is 2y + 3x = 4 and the correlation coefficient between x and y is 0.8. This statement is (a) (c) 189. 3 None of these For a (m n) classification of bivariate data, the maximum number of conditional distributions is (a) (c) 188. (b) (d) For the bivariate data [(x, y)] = [(20,5), (21,4), (22,3)], the correlation coefficient between x and y is (a) (c) 187. 2 3 True Cannot say (b) (d) False None of these When the correlation coefficient r = 1, then the two repression lines are (a) (c) Perpendicular to each other Parallel to each other Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Coincide Do not exist 159 MODEL TEST PAPER - 6 191. In a binomial distribution with 6 independent trials, the probability of 3 and 4 successes is found to be 0.2457 and 0.0819 respectively. Find the parameters p and q of the binomial distribution. (a) (b) 4 9 , 13 13 (c) 192. 2 1 , 13 13 5 2 , 13 13 (d) None of these E (x.y) = E(x). E(y), where x and y are independent random variables. This is (a) (c) 193. (b) (d) True None of these E(x) E(x)2 (b) (d) E(x2) None of these Event Sample Space (b) (d) Trial None of these Which measure of dispersion has some desirable mathematical properties? (a) (c) 197. False Either (a) or (b) An attempt to produce a particular outcome which is neither certain nor impossible is called. (a) (c) 196. False None of these Mean of the probability distribution of random variable x is (a) (c) 195. (b) (d) Probability distribution is known as theoretical distribution. This is (a) (c) 194. True Either (a) or (b) Standard Deviation Q.D. (b) (d) 2 If x 1 + y + y 1 + x = 0; then (1 + x) (a) (c) dy is equal to dx 0 1 (b) (d) ( ) Mean Deviation None of these 11 None of these dy is equal to dx If y = x x 2 + 1 + log x + x 2 + 1 then (a) x2 +1 (b) 2 x +1 (c) 198. 2 x2 +1 (d) None of these 160 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 199. If y = aemx + be mx then (a) (c) 200. d2y is dx 2 my m2y (b) (d) m2y2 None of these of these If 12C5 + 2 12C4 + 12C3 = 14Cx then the value of x is: (a) (c) 5 5 or 9 (b) (d) 9 None of these YYY Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 161 Answer of Model Test Papers Model Test Paper BOS/CPT 6 SECTION A : FUNDAMENTALS OF ACCOUNTING 1. (d) 2. (b) 3. (a) 4. (c) 5. (b) 6. (a) 7. (a) 8. (a) 9. (a) 10. (c) 11. (a) 12. (d) 13. (c) 14. (b) 15. (d) 16. (b) 17. (c) 18. (b) 19. (c) 20. (a) 21. (a) 22. (b) 23. (d) 24. (a) 25. (a) 26. (b) 27. (c) 28. (a) 29. (a) 30. (b) 31. (a) 32. (d) 33. (c) 34. (b) 35. (c) 36. (a) 37. (b) 38. (a) 39. (c) 40. (d) 41. (b) 42. (a) 43. (c) 44. (a) 45. (d) 46. (c) 47. (c) 48. (b) 49. (a) 50. (a) 51. (c) 52. (a) 53. (b) 54. (a) 55. (a) 56. (d) 57. (d) 58. (a) 59. (c) 60. (a) SECTION B : MERCANTILE LAWS (40 MARKS) 61. (b) 62. (d) 63. (d) 64. (b) 65. (a) 66. (d) 67. (d) 68. (d) 69. (a) 70. (d) 71. (b) 72. (b) 73. (d) 74. (a) 75. (b) 76. (a) 77. (c) 78. (b) 79. (b) 80. (a) 81. (a) 82. (c) 83. (b) 84. (a) 85. (d) 86. (c) 87. (a) 88. (c) 89. (c) 90. (c) 91. (b) 92. (c) 93. (c) 94. (a) 95. (a) 96. (b) 97. (b) 98. (b) 99. (b) 100. (a) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 285 ANSWERS Answer of Model Test Papers Model Test Paper BOS/CPT 6 SECTION C : GENERAL ECONOMICS (50 MARKS) 101 (d) 111 (c) 121 (d) 131 (b) 141 (a) 102 (a) 112 (a) 122 (a) 132 (c) 142 (d) 103 (c) 113 (d) 123 (a) 133 (d) 143 (a) 104 (c) 114 (d) 124 (c) 134 (c) 144 (b) 105 (d) 115 (a) 125 (b) 135 (b) 145 (a) 106 (b) 116 (c) 126 (d) 136 (c) 146 (b) 107 (b) 117 (b) 127 (d) 137 (c) 147 (b) 108 (a) 118 (c) 128 (b) 138 (a) 148 (d) 109 (b) 119 (c) 129 (b) 139 (b) 149 (c) 110 (a) 120 (d) 130 (c) 140 (b) 150 (a) SECTION D : QUANTITATIVE APTITUDE (50 MARKS) 151. (b) 152. (b) 153. (d) 154. (a) 155. (a) 156. (a) 157. (b) 158. (a) 159. (a) 160. (a) 161. (b) 162. (c) 163. (a) 164. (d) 165. (b) 166. (c) 167. (a) 168. (a) 169. (b) 170. (a) 171. (c) 172. (a) 173. (a) 174. (b) 175. (c) 176. (b) 177. (c) 178. (a) 179. (c) 180. (b) 181. (b) 182. (a) 183. (c) 184. (c) 185. (c) 186. (c) 187. (b) 188. (b) 189. (b) 190. (b) 191. (b) 192. (a) 193. (b) 194. (a) 195. (b) 196. (a) 197. (c) 198. (c) 199. (c) 200. (c) 286 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II Model Test Paper BOS/CPT 6 151. Let g iven number is x Then the condition 1 1 1 x = 15 5 3 2 x = 15 30 x = 450 152. Let the number be = x. 3 1 Then given the condition = x = 60 4 5 3x = 60 20 x= 60 20 = 400 3 Ans. (b) 153. Let the number be x. Given 4 3 (x ) = 24 5 8 3 x = 24 10 x = 24 10 = 80 3 250% of x = 250% of 80 = 250 80 = 200 100 Ans. (d) 154. Let the number be x Given condition x + x 2 =182 x 2 + x 182 = 0 (x + 14 ) (x 13 )= 0 x = 14 , x = 13 x = 13 (negative reflected) Ans. (a) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 365 ANSWERS 155. Let the unit's digit of the number be x and ten's digit by y x + y = 12 (1) Then and the number = 10y + x Reversing the order of digits of the given number, Unit's digit becomes y and ten's digits becomes x New number = 10 x + y According to the given condition of the problem (10x + y) (x + 10y) = 18 9x 9y = 18 x y = 2 (2) Adding (1) and (2) 2x = 10 x=5 y = 7 The number is 75 Ans. (a) 156. Let the number of coins is x Given 10 x + 14 18 x + x = 430 2 4 40 x + 28 x + 18 x = 430 4 86 x = 430 4 x= 430 4 = 20 86 The one Rupee coins = 10x = 10 20 = 200 The 50 paise coins = 14x = 14 20 = 280 The 25 paise coins = 18x = 18 20 = 360 Ans. (a) 157. First Vessels Contain Milk Ratio 5 First Vessels Contain Water Ratio 2 366 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II Second Vessels Contain Milk Ratio 6 Second Vessels Contain Water Ratio 1 Both the Vessels Milk = 5 + 6 = 11 Both the Vessels Water = 2 + 1 = 3 The new Ratio = 11:3 Ans. (b) 158. Given f (x) = x + 2; g (x) = 7 x gof (x) = g [f(x)] = g [ 7x ] = 7 x+2 Ans. (a) 159. Let their monthly incomes be Rs. 9x and Rs. 7x respectively. Let their monthly expenditures be Rs. 4 y and Rs. 3 y respectively. 2 According ot the given condition of the problem, 9x 4y = 200 (1) 7x 3y = 200 (2) Multiply (1) by 3, we get 27x 12y = 600 Multiply (2) by 4, we get 28x 12y = 800 Subtracting (3) from (4), we get x = 200 Hence their monthly income are Rs. (9 200=1800) and Rs. (7 200 = 1400). Ans. (a) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 367 ANSWERS 160. Let x be the distributed amount of A, B and C Given 5x + 11x + 3x = 950 19x = 950 x= 950 = 50 19 The amount of A = 5x = 5 50 = 250 The amount of B = 11x = 11 50 = 550 The difference of A and B = 300 Ans. (a) 161. Lt x 1 e x e 1 e 1 x 1 Lt x 1 e ( x 1) x 1 let 1 + h x where h 0 Lt x 0 e h 1 1 = e ( h) e Ans. (b) 1/e 162. Lt x 0 (1 + x)n 1 x (1 + nx + Lt = x 0 n(n 1) x 2 + ......) 1 2! x n(n 1) x n(n 1)(n 2 ) x 2 + x n + ...... 2! 3! = Lt x 0 x App Lt n+0=n Ans. (c) n Lt ( x + 2 ) 5 / 3 (a + 2 ) 5 / 3 x a Lt 163. ( x + 2 ) 5 / 3 (a + 2 ) 5 / 3 [(x + 2 ) (a + 2 )] x 0 x 0 App Lt 368 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 5 5 .(a+2) 5/3 1 = (a+2) 2/3 3 3 5 (a+2) 2/3 3 Ans. (a) Lt 2x 3x (2 x 1) (3 x 1) Lt x 0 x x Lt 165. 2x 1 3x 1 Lt x 0 x x x 0 x 0 a x 1 = log e a Lt x 0 x log 2 log 3 2 log 3 Ans. (b) 166. f (x ) = 3 x 2 + 2 f (x ) dx = (3 x f (x ) + c = 2 ) + 2 dx 3 x3 + 2x + c 3 When f (0) = 0 c = 0 f(x) = x 3 + 2 x f(2) = 2 3 + 2 (2) = 8 + 4 = 12 Ans. (c) 167. Let I = x+3 x2 + 6 x + 4 Put x2 +6x+4 = t (2x+6)dx = dt (x+3)dx = = dt 2 x+3 dt dx = 2t x + 6x + 4 2 1 1 dt 2 t Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 369 ANSWERS 1 log(t) 2 168. 1 x+3 dx = log(x 2 +6x+4) + c 2 x + 6x + 4 e x 1 x +1 2 x dx = e dx 3 ( x + 1) ( x + 1) 3 x 2 1 2 dx 2 3 ( x + 1) ( x + 1) x = e = x e {f( x) + f ' ( x)}dx = e x f(x) x e where f(x) = 1 ( x + 1) 2 ( x 1) ex +c dx = ( x + 1) 3 ( x + 1) 2 Ans.(a) 169. 4 (3 x + 5 ) = dx = (3 x + 5 )4 +1 (4 + 1) (3 ) +c (3 x + 5 )5 + c 15 Ans. (b) 170. 7 x + 5 dx 1 = (7 x + 5 )2 = (7 x + 5 )2 +1 + c 1 + 1 (7 ) dx 1 2 3 = (7 x + 5 )2 3 (7 ) +c 2 370 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 3 2 (7 x + 5 )2 +c 21 171. Voter has option Two candidates from gentlemen = 3 c 2 = 3 (i) (ii) Two candidates from ladies = 3 c 2 = 3 (iii) One from each ladies & gentlemen = 3 c 1 3 C 1 = 9 Total options = 3 + 3 + 9 = 15 Ans. (c) 15 172. Total hand shakes in the party = 40 c 2 = 780 Ans. (a) 780 173. Total triangle formed by m sides = m C 3 m(m 1)(m 2 )(m 3 )! (m 3 )! 3! m(m 1)(m 2 ) 6 m(m 1)(m 2 ) 6 Ans. (a) 174. Cricket team of 11 among 14 players out of which one wicket keeper 12 C10 2 C1 = 66 2 = 132 Ans. (b) 132 175. No. of ways in which a particular child goes to circus = 7 C 2 1 = 21 Ans. (c) 176. ax = by = 21 cz = k (let ) log a k = x, log b k = y, log c k = z log ka = 1/x, log kb = 1/y, log kc = 1/z x, y, z in GP y 2 = xz (log b k)2 = (log a k).(log c k) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 371 ANSWERS log b k log c k log k a log k b = = log a k log b k log k k log k c log a , log b and log c in GP Ans. (b) G.P. 177. 1 1 = 8 . 1024 2 n 1 13 1 1 = 2 2 n 1 n = 14 6th team from end = (14 6+1) from beginning = 9th term 1 T9 = 8 . 2 Ans. (c) 9 1 8 1 1 = 8 . = 32 2 1/32 178. Product of 2nd term from start & last 2nd term from end = (ar) a(r) n 2= a 2 r(n 1) Product of first & last term = a ar n 1 = a 2 r n 1 Hence proved the statement. It is true statement Ans. (a) True 179. a, b, c in GP b 2 = ac a, x, b in AP x = b, y, c in AP y = a +b 2 b+c 2 2[ab + ac + ac + bc ] a c 2a 2c + = + x y a +b b +c ab + b 2 + ac + bc 2[ab + ac + ac + bc ] ab + ac + ac + bc {b 2 = ac } =2 Ans. (c) 2 a +b b +c + 1 1 x+y 2 2 180. + = ( a + b ) (b + c ) x y xy 4 2(a + 2b + c ) 2 (ab + b + ac + bc ) = 2(a + 2b + c ) ab + b 2 + b 2 + bc 372 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II = 2 2 (a + 2 b + c ) = b b (a + 2 b + c ) 2 b Ans. (b) 181. The number of times a particular item occurs in a given data is called its frequency. Ans. (b) Frequency 182. Lower class (s) = 10.6 Width = 2.5 (Class interval) Upper Class (L) of Ligh t est Class = S = 10 C.I. = 10.6 + 10 x 2.5 = 35.6 Ans. (a) 183. 35.6 Lower Class + Upper Class = Mid Value 2 L + U.Class =m 2 Upper class = (2m L) Ans. (c) 184. Mean = (2m L) 1 .x + 2 .2 x + 3 .3 x + .... n.nx n(n + 1).x / 2 = (12 + 2 2 + 3 2 + ...... n 2 ) x n(n + 1).x / 2 = (12 + 2 3 + 3 2 + ...... n 2 ) x n(n + 1).x / 2 = n (n + 1)(2 n + 1) x 2 (2 n + 1) = 6 n(n + 1) x 3 Mean = Ans. (c) (2 n + 1) 3 2n + 1 3 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 373 ANSWERS 185. x = 10, n = 4 x = n. x = 4 10 = 40 Corrected x = (40 + 4a) Corrected x = 13 = 40 + 4 a 4 40 + 4 a 4 4a = 12 a=3 Ans. (c) 3 186. From the given data, we observe that 20 + 5 = 25 21 + 4 = 25 and 22 + 3 = 25 Thus, x and y are connected by the linear relation: x + y = 25 (1) There is perfect correlation between x and y r = 1 (2) From (1) / We get y = 25 x As x increases, y decreases (by the same amount) x and y are negatively correlated (3) From (2) and (3), we conclude that r = r (x, y) = 1 Ans. (c) 187. Ans. (b) Refer Properties 188. Ans. (b) Refer Properties 189. Ans. (b) Refer Properties 190. Ans. (b) Refer Properties 191. Lt X B (n=6, p). When X denotes the number of successes. Then, by binomial probability law, the probability of r successes is givenby p(r) = P(x=r) = 6C r P rq 6 r (1) r = 0, 1, 2, ........... 6 Put r = 3 and 4 in (1) 374 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II (1) p(3) = 6C 3 p 3 q 3 = 20p 3 q 3 = 0.2457 (given) p(4) = 6C 4 p 4 q 2 = 15 p 4 q 2 = 0.0819 (given) p ( 4 ) 15 p 4 q 2 0 .0819 1 = = = p (3 ) 20 p 3 q 3 0 .2457 3 3 p 1 . = 4 q 3 9p = 4q = 4 (1 p) 13p = 4 p = 4/13 q = 1 p = 1 4/13 = 9/13 192. Ans. (a) Refer Properties 193. Ans. (b) Refer Properties 194. Ans. (a) Refer Properties 195. Ans. (b) Refer Properties 196. Which measure of dispersion has some desirable mathematical properties Standard Deviation. Ans. (a) Standard Deviation. 197. x 1 + y + y 1 + x = 0 x 1+ y = y 1+ x Eg. Both side x 2 (1 + y ) = y 2 (1 + x) 2 2 2 2 (x y )=y x x y ( x + y ) ( x y ) = xy( x y ) x 1+ x x + y +xy = 0 dy (1 + x) ( 1) ( x) (1) 1 x + x = = dx (1 + x) 2 (1 + x) 2 1 dy dy (1 + x 2 ) = 1 = 2 dx (1 + x) dx Ans. (c) y= ( 1) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 375 ANSWERS 2 x 2 + 1 + log x + x +1 198. y = x dy 1 .2x + = x. dx 2 x2 + 1 x2 = x +1 2 + x2 + 1 + x2 + x2 + 1 + 1 = x 2 + 1 .1 + x +1 2 = 1 1 + .2 x x + x2 + 1 2 x2 + 1 x2 + 1 + x x + x +1 2 2 ( x 2 + 1) x +1 2 1 1 x +1 2 = 2 1 + x2 2 1+ x 2 Ans. (c) 199. y = ae mx + be mx dy = ame mx bme mx dx ( d2y d = = ame mx bme mx 2 dx dx = am 2 e mx + bm 2 e mx = m 2 ae mx + be mx ) ( d2y ) = m2y dx 2 Ans. (c) m2y 200. 12 C 5 + 2 .12 C 4 + 12 C 3 = 14 C x (12 C 5 ) ( ) + 12 C 4 + 12 C 4 + 12 C 3 = 14 C x 13 C 5 + 13 C 4 = 14 C x [C n r + n C r 1 =n+1 C r ] 14 C 5 = 14 C x x = 5 but value 14 C 9 = 14 C 5 14 C x = 14 C 9 x=9 376 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

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