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CA CPT : Volume 2 - Model Test Paper 10 (with Answers & Explanations)

44 pages, 200 questions, 16 questions with responses, 16 total responses,    0    0
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BOARD OF STUDIES THE INSTITUTE OF CHARTERED ACCOUNTANTS OF INDIA COMMON PROFICIENCY TEST Model Test Paper BOS/CPT 10 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. Cash discount allowed to a customer should be credited to (a) (c) 2. Purchase A/c Sales A/c A transaction An event None of these A transaction as well as an event Prepaid commission has a (a) (c) 4. (b) (d) On 31st December, 2009 Ashok Ltd. purchased a machine from Mohan Ltd., for Rs. 1,75,000. This is (a) (b) (c) (d) 3. Trade receivables A/c Discount A/c Negative balance Credit balance (b) (d) Debit balance None of these The following account will have debit balance (a) (b) (c) (d) Loan to other party Capital A/c Outstanding salary Reserve for doubtful debts 247 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 247 MODEL TEST PAPER - 10 5. A sum of Rs. 50,000 was spent on painting the new plant. It is a (a) (b) (c) (d) 6. Bills receivables is a (a) (c) 7. Written down value Scrap value (b) (d) Original cost None of the above HIFO Weighted overage (b) (d) FIFO LIFO Balance Sheet Profit & Loss A/c (b) (d) Trading A/c Either (b) or (c) When each co-venturer keeps records of their own joint venture transactions When separate set of joint venture books is prepared When each co-venture keep records of all the joint venture transaction himself None of the three No partner has a right to receive salary (b) No interest is charged on drawings (d) No interest is allowed on capital All of the above. Endorsement, discounting and collection of bills of exchange is made by (a) (c) 14. Understated None of the above. In the absence of any agreement between the partners (a) (c) 13. (b) (d) Memorandum joint venture account is prepared (a) (b) (c) (d) 12. Overstated Not affected All the expenditures of revenue nature go to (a) (c) 11. Tangible fixed asset Investment Inventory should be out of godown in the sequence in which they arrive is based on (a) (c) 10. (b) (d) Under annuity method, interest is calculated on (a) (c) 9. Intangible fixed asset Current asset When closing inventory is understated, net income for the accounting period will be: (a) (c) 8. Revenue expenditure Capital expenditure Deferred revenue expenditure None of these Trade receivables Drawee (b) (d) Trade Payables Drawer Returns Inward, appearing in the trial balance are deducted from (a) (c) Purchases Sales 248 The Institute of Chartered Accountants of India (b) (d) Capital None of the above Common Proficiency Test (CPT) Volume - II 15. Drawings is deducted from (a) (c) 16. Profit & Loss A/c Balance Sheet (b) (d) Trading A/c None of the above Deferred revenue expenditure Capital expenditure (b) (d) Revenue expenditure None of the above. Rs. 4,00,000 Rs. 5,00,000 (b) (d) Rs. 5,40,000 None of the above. Renewal of the bill Dishonour of the bill (b) (d) Retirement of the bill None of the three The Balance of an account is always known by the side which is(a) (c) 22. Journal proper Both (a) and (b) Noting charges are paid at the time of (a) (c) 21. (b) (d) Cash sales Rs. 1,40,000 Total sales Rs. 5,26,000 Bad debts Rs. 14,000 Opening Trade receivables Rs. 60,000 Closing Trade receivables Rs. 32,000 Cash collected from receivables will be (a) (c) 20. Cash book Purchases Rings & pistons of an engine were changed at a cost of Rs. 5,000 to get fuel efficiency. This is a (a) (c) 19. Sales None of the above The trial balance of Rajesh Ltd. shows closing inventories of Rs. 90,000. It will be recorded in (a) (c) 18. (b) (d) Purchase of Plant & Machinery on credit basis is recorded in (a) (c) 17. Capital Purchases Shorter Equal (b) (d) Higher None of these An undervaluation of previous year s opening inventory will (a) (b) (c) (d) Cause current year s net income to be overstated Cause previous years net income to be understated Cause previous years net income to be overstated None of the above Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 249 MODEL TEST PAPER - 10 23. Parul accepted a bill for 90 days of Rs. 10,000 drawn by Rahul on 10 Feb., 2010. On 18th March, 2010, Parul wished to retire the bill, Rahul offered rebate @ 12% p.a. considering the year of 360 days rebate amount will be (a) (c) 24. Rs. 10 Rs. 8 (b) (d) Rs. 9 Rs. 5. Rs. 70,000 Rs. 1,10,000 (b) (d) Rs. 50,000 Rs. 90,000 Rs. 1,30,000 Rs. 50,000 (b) (d) Rs. 1,70,000 None of the above 15 August 14 August (b) (d) 16 August 18 August A, B and C are partners in a firm sharing profits and losses in the ratio of 2:3:5. The firm took separate life policy of Rs. 50,000, Rs. 1,00,000 and Rs. 1,50,000 for A, B and C respectively. The share of B in the policy will be (a) (c) 30. Sold goods for cash Sold goods to Ram. If a bill of exchange will mature on 15th August but it is a public holiday then the bill will mature on (a) (c) 29. (b) (d) Cost of goods sold Rs. 1,50,000 Closing Inventory Rs. 40,000 Opening Inventory Rs. 60,000 Amount of purchases will be (a) (c) 28. Sold goods Sold goods to Ram for cash If total sales during the year Rs. 1,00,000; Cash sales Rs. 20,000 and outstanding Trade receivables at the end of the year Rs. 30,000 then cash received from customers during the year will be (a) (c) 27. Rs. 150 None of the above On equity share of Rs. 10, the company has called up Rs. 9 but actually received Rs. 8. The share capital would be credited by (a) (c) 26. (b) (d) Which of the following is a credit transaction? (a) (c) 25. Rs. 184 Rs. 180 Rs. 90,000 Rs. 3,00,000 (b) (d) Rs. 1,50,000 Rs. 60,000 A company purchased a motor car for Rs. 5,00,000. Estimated useful life of the motor car is 15 years and residual value is Rs. 50,000. Rate of depreciation will be (a) (c) 9% 10% 250 The Institute of Chartered Accountants of India (b) (d) 6% 15% Common Proficiency Test (CPT) Volume - II 31. A company issued Rs. 20,000, 15% debentures at a discount of 10% redeemable after 15 year at a premium of 5%. Loss on issue of debentures will be (a) (c) 32. (b) (c) (d) Rs. 1,500 None of these Partner Capital A/c Dr. To Revaluation A/c Revaluation A/c Dr. To Partner s capital Unrecorded investment A/c Dr. To Revaluation A/c Revaluation A/c Dr. To Unrecorded investment A/c 50,000 50,000 50,000 50,000 50,000 50,000 50,000 50,000 A partner is insolvent A partner retires (b) (d) A partner is admitted All of the above Rs. 70,000 Rs. 60,000 (b) (d) Rs. 72,000 Rs. 75,000 Lal & Co. issued 10,000 debentures of Rs. 100 each at a discount of 4% redeemable after 5 years at a premium of 6%. Loss on issue of debentures will be (a) (c) 37. (b) (d) Interest on capital at 12% p.a. is to be allowed. Capital in the beginning was Rs. 6,00,000. Interest amount will be (a) (c) 36. Rs. 1,000 Rs. 1,400 Gaining ratio is applied when (a) (c) 35. Rs. 1,000 None of the above A firm had an unrecorded investment of worth Rs. 50,000. Entry in the firms journal on admission of a partner will be (a) 34. (b) (d) Raj Ltd. purchased machinery for Rs. 20,000 payable Rs. 6,500 in cash and the balance by an issue of 10% debentures of Rs. 100 each at a discount of 10%. Discount on issue of debentures will be (a) (c) 33. Rs. 1,400 Rs. 3,000 Rs. 60,000 Rs. 1,00,000 (b) (d) Rs. 1,60,000 Rs. 40,000 Dismantling and demolition charges is a (a) (b) (c) (d) Deferred Revenue expenditure Capital expenditure Revenue expenditure None of the above Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 251 MODEL TEST PAPER - 10 38. On equity share of Rs.20, the company has called up Rs.18 but actually received Rs. 16. The share capital would be credited by (a) (c) 39. Rs. 4,40,000 Rs.4,50,000 2:2:1 1:2:3 (b) (d) 1:1:1 3:2:1 5:4 5:3 (b) (d) 4:3 47:37 Rs. 15,000 Rs. 5,000 (b) (d) Rs. 25,000 None of those In January 2007, a trader purchased machinery for Rs. 1,00,000 depreciation is charged @ 20% by diminishing balance method. At the end of the third year it was sold for Rs. 31,000. Profit or loss on sale will be (a) (c) 44. (b) (d) Following figures have been taken from the trial balance of a trader: Cost of goods sold 45,000 Sales 60,000 Closing Inventory 10,000 The amount of gross profit will be (a) (c) 43. Rs. 5,00,000 Rs. 5,60,000 A, B and C are partners sharing profits and losses in the ratio of 5:4:3. C retires and if A and B share profits of C in 4:3 then new profit sharing ratio will be (a) (c) 42. Rs. 18 Rs. 10 Ram and Mohan are partners sharing profits equally. They admitted Sohan for 1/3 share in the firm. The new profit sharing ratio will be (a) (c) 41. (b) (d) Net salary paid to employees Rs. 5,00,000 in cash after deducting income tax Rs. 50,000 professional tax Rs. 10,000. Salary A/c will be debited with (a) (c) 40. Rs. 20 Rs. 16 Loss Rs.20,200 Profit Rs.20,000 (b) (d) Loss Rs.40,000 Profit Rs.20,200 Net profit before charging manager s commission is Rs. 24,000 and the manager is to be allowed a commission of 20% on the profit after charging such commission. Commission amount will be (a) (c) Rs. 4,000 Rs. 4444.44 252 The Institute of Chartered Accountants of India (b) (d) Rs. 4,800 None of the above Common Proficiency Test (CPT) Volume - II 45. Amount spent on Structural alteration under pressure of law is a (a) (c) 46. Rs. 500 Rs. 700 (b) (d) Rs. 400 Rs. 600 Rs. 15,000 Rs. 85,000 (b) (d) Rs. 13,500 None of the above 7,200 shares 2,250 shares (b) (d) 10,800 shares 6,750 shares A revenue or an asset An expenses or an asset (b) (d) A revenue or a liability None of the above (b) (d) Sales and total expenses None of the above Gross profit is the difference between (a) (c) 52. Nil : 1/12 : Nil None of the above Credit balance in the ledger will be (a) (c) 51. (b) (d) Ram Ltd. purchased the business of Rahim Ltd. for Rs. 9,00,000 payable in fully paid shares of Rs. 100 each. Shares were issued at a premium of 25%. Number of shares issued against purchased consideration will be (a) (c) 50. Nil : Nil : 1/l2 1/12 : Nil : Nil The following information pertains to Arjun Ltd. (1) Equity share capital called up Rs. 1,00,000 (2) Calls in arrear Rs. 10,000 (3) Calls in advance Rs. 10,000 (4) Proposed dividend 15% The amount of proposed dividend payable is (a) (c) 49. Revenue expenditure Deferred revenue expenditure A was holding 100 shares of Rs. 10 each of a company on which he had paid Rs. 4 on application and Rs. 3 allotment, but could not pay Rs. 2 on first call. Forfeited share A/c will be credited with (a) (c) 48. (b) (d) M, N and O share profits and losses in the ratio of 3:2:1. Upon admission of D, they agreed to share 5:4:2:1. The sacrificing ratio will be (a) (c) 47. Capital loss Capital expenditure Sales and cost of goods sold Sales and purchases Closing entry for transfer of net profit Rs. 6,300 to the capital a/c will be (a) (b) (c) (d) Trading A/c 6,300 Dr. To Balance sheet 6,300 Trading A/c 6,300 Dr. To Profit & Loss A/c 6,300 P & L A/c 6,300 Dr. To Capital A/c 6,300 Capital A/c 6,300 Dr. To P& L A/c 6,300 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 253 MODEL TEST PAPER - 10 53. The total of Discount allowed column in the Cash book for the month of July, 2010 amounting to Rs. 10,000 was not posted. Rectifying entry for the same will be (a) (b) (c) (d) 54. After preparing the trial balance the accountant find that the total of the credit side is short by Rs. 2,000. This difference will be (a) (b) (c) (d) 55. Dr. Plant repairs A/c and Cr. Cash A/c Rs. 3,000 Dr. Wages A/c and Cr. Cash A/c Rs. 3,000 Dr. Plant A/c and Cr. Cash A/c Rs. 3,000 None of the above A transaction Both (a) and (b) (b) (d) An event None of the above Rs. 8,400 Rs. 12,600 (b) (d) Rs. 15,000 Rs. 20,000 Bright stationery used stationery for business purposes Rs. 500. Amount will be credited to (a) (c) 60. Rs. 72,000 None of the above Ram sells goods at cost plus 40%. Total sales were Rs. 21,000. Cost price of the goods will be (a) (c) 59. (b) (d) On June 1, Sahil paid salary amounting Rs. 20,000. This is (a) (c) 58. Rs. 32,000 Rs. 50,000 Journal entry for wages paid Rs. 3,000 for installation of plant will be (a) (b) (c) (d) 57. Debited to Suspense A/c Credited to suspense A/c Adjusted to any of the credit balance A/c Adjusted to any of the debit balance A/c Goods purchased for Rs. 2,00,000 and were sold for Rs. 1,60,000. Margin 20% on sales. Closing Inventory is . (a) (c) 56. Discount allowed A/c Dr. 10,000 To Suspense A/c 10,000 Suspense A/c Dr. 10,000 To Discount A/c 10,000 Customer A/c Dr. 10,000 To Discount A/c 10,000 None of the above Purchases A/c Cash A/c (b) (d) Sales A/c None of the above Goods destroyed by fire Rs. 50,000 and insurance company admitted full claim. Claim receivable will be recorded in (a) (c) Trading A/c P & L A/c 254 The Institute of Chartered Accountants of India (b) (d) P & L Appropriation A/c Balance Sheet Common Proficiency Test (CPT) Volume - II SECTION B : MERCANTILE LAWS (40 MARKS) 61. Under the Sale of Goods Act, 1930 price means (a) (b) (c) (d) 62. An agreement to share the benefits of a public office (a) (c) 63. Voidable contracts Wagering agreements General offer Express offer (b) (d) Specific offer Implied offer Out of love and affection Compensation for past voluntary services Promise to pay time barred debt All of the above Accepts the goods Fails the return goods (b) (d) Adopts the transaction In all the above cases Different parties (a) or (b) (b) (d) The same parties (a) and (b) Recission of a contract means (a) (b) (c) (d) 69. (b) (d) Novation may take place between (a) (c) 68. Invalid agreements Contingent contracts In case of sale on approval, the ownership is transferred to the buyer when he (a) (c) 67. Voidable None of the above Consideration without agreement are valid in case (a) (b) (c) (d) 66. (b) (d) Offer implied from conduct of parties or from circumstances of the case is called (a) (c) 65. Valid Void Agreement which are in nature of bets and gambling are called (a) (c) 64. Consideration in money Transfer value of goods Revenue consideration Economic Exchange Value The renewal of original contract Cancellation or termination of contract Substitution of new contract Alteration of contract Discharge of contracts by implied consent does not include (a) (c) Novations Merger Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) Actual performance Waiver 255 MODEL TEST PAPER - 10 70. On the valid performance of the contractual obligation by the parties, the contract (a) (c) 71. Promisor alone Agent of the promisor Legal representatives of promisor All of these Consideration of the contract Rescind the contract Insistence on specific performance Suit for damages When only a part of the price has been paid When a cheque has been issued and the payment of the same is stopped When whole of the price has not been tendered Any one of the above With holding delivery (a) and (b) (b) (d) Stoppage in transit (a) or (b) A seller agrees to supply a crop which is to be grown by him. This is a (a) (c) 78. Repudiation Rescission When property in goods has not passed to the buyer, the unpaid seller has a right of (a) (c) 77. (b) (d) A seller is an unpaid seller (a) (b) (c) (d) 76. Alteration Innovation Which of the remedies not available to a defrauded party? (a) (b) (c) (d) 75. Acceptance of loser performance Cancellation of the existing contract Change in one or more terms of contract abandonment of rights by a party Which of the following persons can perform the contract? (a) (b) (c) (d) 74. Becomes enforceable None of above A change in nature of obligation of contract known as (a) (c) 73. (b) (d) A contract is discharged by alteration which means the (a) (b) (c) (d) 72. Is discharged Becomes void An agreement to sell Bailment (b) (d) Sale Contract for work & labour A notice given to a partner is deemed to be a notice given to the firm when notice is given to (a) (c) Any active partner Sleeping partner 256 The Institute of Chartered Accountants of India (b) (d) Any partner All the partner Common Proficiency Test (CPT) Volume - II 79. On the insolvency of a partner, the insolvent ceases to be a partner in the firm whether the firm is dissolved or not (a) (c) 80. In good faith Based on the contract between partners Either (a) or (b) Both (a) and (b) A nominal partner A working partner (b) (d) A sleeping partner A active partner Becomes enforceable Becomes void (b) (d) Is discharged None of these Limited Enterprises (b) (d) Co-operative Both (a) and (b) Which of the following needs to be given to the partners even after dissolution of the firm (a) (c) 87. Firm The other partners Only the working partners All the retiring partners A partnership firm cannot use ___________ the words as part of its name. (a) (c) 86. Future contract Implied contract On the valid performance of the contractual obligations by the parties, the contract __________. (a) (c) 85. (b) (d) A person who lends his name to the firm, without having any real interest in it is called (a) (c) 84. Void contract Contingent contract A partner may be expelled from the firm by any majority of the partners ________. (a) (b) (c) (d) 83. No Dissolve in capital ratio For loss caused to the firm by his fraud in the conduct of the business, every partner shall identify as a ________. (a) (b) (c) (d) 82. (b) (d) A contract for sale of certain goods to be manufactured by a seller is a (a) (c) 81. Yes Practically dissolved Interest on advances Remuneration (b) (d) Interest on capital None of the above. ___________ makes the agreement void and neither party can enforce the contract against the other (a) (c) A misrepresentation An object Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) A mistake A consideration 257 MODEL TEST PAPER - 10 88. A contract of sale is a contract for sale by sample if it is__________. (a) (b) (c) (d) 89. In case of ______________, the term of contract may be altered by mutual consent, but the parties to the contract will remain the same (a) (c) 90. (b) (d) Death of the offeror All of the above Definite Unambiguous (b) (d) Certain All the above Promise Contract (b) (d) Agreement None of the above Hire purchase Leasing (b) (d) Sale Instalment purchase. Communication of offer may be by ___________. (a) (c) 96. Lapse of time Counter offer Under ______________, the goods passes to the buyer only upon payment of last instalment (a) (c) 95. By the person to whom offer is made Without condition In clear terms either oral or written All of the above A proposal when accepted becomes a _____________. (a) (c) 94. Remission Alteration The terms of offer must be _____________. (a) (c) 93. (b) (d) Revocation of offer can be done by __________. (a) (c) 92. Novation Rescission Consent should be given ___________. (a) (b) (c) (d) 91. By operation of law By way of custom or usage of trade By way of an express or implied term in the contract, to that effect By decision of the seller Words only Words or conduct (b) (d) Conduct only None of the above In case letter of acceptance is lost in transit, it will be deemed to be a valid acceptance if it is proved that the letter___________. (a) (c) Sufficiently stamped Posted 258 The Institute of Chartered Accountants of India (b) (d) Correctly addressed All the above Common Proficiency Test (CPT) Volume - II 97. The juristic concept of contract consists of __________. (a) (b) (c) (d) 98. Advertisement inviting tender is __________. (a) (c) 99. An offer An agreement (b) (d) A counter offer An invitation to offer A , as surety B , makes a bond jointly with B , to C , to secure a loan from C to B , afterwards, C obtains from B a further security for the same debt. Subsequently, C gives up the further security. Decide. (a) (c) 100. Offer and acceptance Consideration and coercion Agreement and obligation Free consent and capacity A is discharged B cannot file a suit (b) (d) A is not discharged None of the above A and B bet as to whether it would rain on a promising to pay Rs. 100 to B , if it rained, and, B promising an equal amount to A , if it did not. Decide the type of agreement. (a) (c) Contingent contract Wagering contract (b) (d) Quasi contract Implied contract SECTION C : GENERAL ECONOMICS (50 MARKS) 101. If the proportion of income spent on a good increase as income increases, then income elasticity for the good is: (a) (c) 102. Less than one Infinite Cardinal measurability of utility Constancy of the marginal utility of money Rationality of human behaviour Ordinal Measurability of utility Law of diminishing marginal utility may not apply to: (a) (c) 104. (b) (d) Which is not the assumption of marginal utility analysis? (a) (b) (c) (d) 103. Greater than one One Money Pepsi, Coke etc. (b) (d) Butter Ice cream Which is not the assumption of the law of diminishing marginal utility? (a) (b) (c) (d) The different units consumed should be identifiable in all respects The different units consumed should consist of standard units There should be time gap or interval between consumption of one unit and another unit The law may not apply to hobbies, music etc. Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 259 MODEL TEST PAPER - 10 105. Concept of consumer surplus was evolved by: (a) (c) 106. Percentage Method Point Method 1 2 (b) (d) 2.5 1.25 Silver Jubilee Swarozgar Yojna Swarnajayanti Shahari Rozgar Yojna Swarnajayanti Gram Sadak Yojna Swarnajayanti Swarozgar Yojna Currency Demand Deposits Other deposits with RBI Other deposits with post office In order to increase money supply in the country RBI may: (a) (b) (c) (d) 112. (b) (d) Which of the following is not included in M1? (a) (b) (c) (d) 111. Arc Method Total outlay Method SJSRY stands for: (a) (b) (c) (d) 110. Increase in the price of other good Increase in the price of substitute goods Decrease in the income of the consumer Increase in the price of the good concerned If the local ice-cream shop raises the price of a ice cream cup from Rs 10 per cup to Rs. 15 per cup, and quantity demanded falls from 500 cups per day to 300 cups per day, the price elasticity of demand for ice-cream cup is: (use Arc Elasticity Method) (a) (c) 109. Adam Smith Robbins Which of the following method is not used for measuring elasticity of supply? (a) (c) 108. (b) (d) Contraction of demand is the result of: (a) (b) (c) (d) 107. Allen and Hicks Alfred Marshall Buy securities in the open market Sell securities in the open market Increase CRR Increase Bank rate Which is not near money? (a) (b) (c) (d) Balance in saving account Balance in current account Both (a) and (b) Time deposits 260 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 113. Monopoly power refers to the firm s ability to: (a) (b) (c) (d) 114. In the long run monopolistic competitive firm has: (a) (c) 115. (d) Planned economies allocate resources via government departments Reducing inequality should be a major priorities for mixed economies There is greater degree of consumer sovereignty in market economies Most economies have experienced problems of falling output and rising prices The prices of computer will rise The prices of computer will fall The prices of computers will change, but not enough information is given to determine the direction of the change None of the above The quantity demanded for bananas increases The demand curve for bananas shifts to the right The quantity demanded for bananas decreases The demand curve far bananas shifts to the left Suppose the short run cost function can be written as TC=250+10Q. Average Fixed cost equals: (a) (c) 119. Excess Profits All of the above As the price of Bananas rises: (a) (b) (c) (d) 118. (b) (d) The market of computers is not in equilibrium, then which of the following statements is definitely true? (a) (b) (c) 117. Excess Capacity Zero Fixed cost Which of the following is a normative statement? (a) (b) (c) (d) 116. Earn economic Profit Restrict entry into the industry Set prices above marginal cost Possess economies of scale 250/Q 10 (b) (d) 250 250/Q+10 Gopal inherited 1 acre of land from his father in 1960. Today the value of that land is Rs. 90 lakh per acre. What is the opportunity cost to Gopal for keeping that land? His father paid Rs. 50, 000 for this land. (a) (b) (c) (d) Nothing, since the land was inherited Rs.50, 000 which his father paid Rs.90 lakh, since this amount Gopal is getting now if he sells it Both (b) and (c) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 261 MODEL TEST PAPER - 10 120. Suraj is a high school senior thinking about becoming an economic research assistant. Shyam just graduated from college with an economic degree and is looking for a job as an economic research assistant. For whom is the college tuition an opportunity cost? (a) (b) (c) (d) 121. Which of the following is incorrect? (a) (b) (c) (d) 122. (b) (d) Capitalism Both (b) and (c) Man Capital (b) (d) Labour Entrepreneurs ___________ shows the relationship of output with given inputs. (a) (c) 127. Socialism Mixed Economy Which of the following is not a factor of production? (a) (c) 126. Price and output determination Existence of very few firms in the market Price rigidity Price leadership Right to own private property is found in: (a) (c) 125. Supply for commodities is directly related to its price Price is not related to supply As supply rises, price also rises Supply is not related to factors other than price Kinked demand curve in oligopoly market explains: (a) (b) (c) (d) 124. The shape of average cost is U-shaped MC Curve cuts AC curve at the minimum level of AC The AR and MR curves of the industry under perfect competition are parallel to X-axis MC curve cuts AVC curve at the minimum level of AVC Other things remaining constant, the law of supply states: (a) (b) (c) (d) 123. Suraj Shyam Both Suraj and Shyam Neither Suraj nor Shyam Demand Function Cost function (b) (d) Production Function PPC function (b) (d) Average Cost None of the above TCn TCn-1= which cost function? (a) (c) Marginal Cost Total Cost 262 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 128. Shares traded in the stock market depict characteristics close to_________. (a) (b) (c) (d) 129. Assume that when price is Rs.20, quantity demanded in 10 units, and when price is Rs. 19 quantity demanded in 11 units. Based on this information, what is the marginal revenue resulting from an increase in output from 10 units to 11 units. (a) (c) 130. Production cost Opportunity cost (b) (d) Real cost Physical cost An overall decrease in price but an increase in equilibrium quantity An overall increase in price but a decrease in equilibrium quantity No change in overall price but a reduction in equilibrium quantity An overall decrease in price and a decrease in equilibrium quantity CDS Usual Status (b) (d) CMS CWS When due to introduction of new machinery, some workers get replaced by machines. Such unemployment is called : (a) (b) (c) (d) 135. Positively sloped demand curve TR = PxQ AR = Price Marginal Revenue = Price ___________ measure generally gives the highest estimate of unemployment especially for poor economy (a) (c) 134. Rs.9 Rs.10 With a given supply curve, a decrease in demand causes: (a) (b) (c) (d) 133. (b) (d) The cost of one thing in terms of the alternative given up is known as (a) (c) 132. Re.1 Rs.19 Which of the following is not a characteristic of a price taker? (a) (b) (c) (d) 131. Perfect competition Oligopoly Monopolistic Competition Monopoly Seasonal Unemployment Mechanical Unemployment Technological Unemployment Frictional Unemployment The measure of absolute poverty is: (a) (b) (c) (d) Used only by India Not related to the income or consumption expenditure distribution Related to the distribution of income or consumption expenditure None of the above Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 263 MODEL TEST PAPER - 10 136. National Population Policy was announced in: (a) (c) 137. NABARD SIDBI (b) (d) RBI SBI Monopoly Oligopoly (b) (d) Monopolistic Competition Perfect Competition Indivisibility of Fixed Factors Division of Labour and specialization Both (a) and (b) Misuse of machinery Short run Long run Both Short run and Long run Very Short run Which of the following statements is incorrect? (a) (b) (c) (d) 144. Agriculture occupies 20% population of India Merely 15% population is below the poverty line The production techniques in India are very advance None of the above Law of variable proportion is applicable in: (a) (b) (c) (d) 143. Adults above 60 years Adults above 40 years Law of increasing return operates due to: (a) (b) (c) (d) 142. (b) (d) MR curve and AR curves coincide in (a) (c) 141. Children upto 15 years Both (a) and (b) ______________ is the top most bank for agricultural loans in India. (a) (c) 140. 1999 2005 Which of the following statements is correct? (a) (b) (c) (d) 139. (b) (d) Unproductive consumers consist of: (a) (c) 138. 2001 2000 Both AP and MP can be calculated from TP When AP rises then MP>AP When AP is maximum then MP = AP When AP falls, MP also falls but MP>AP Supply of a Commodity is a : (a) (c) Flow concept Both stock and flow concepts 264 The Institute of Chartered Accountants of India (b) (d) Stock concept None of these Common Proficiency Test (CPT) Volume - II 145. If two goods are perfect substitutes to each other, then is necessarily follows that. (a) (b) (c) (d) 146. When the price of a substitute of X commodity falls, the demand for X commodity: (a) (c) 147. Rises Any of the above Positively sloped Both (a) and (b) (b) (d) Negatively sloped Parallel to Y axis Payment of interest on loan Cost of electricity and fuel Depreciation on building Rent of godown. The relationship between the AC and MC is that (a) (b) (c) (d) 150. (b) (d) Which of the following is not a fixed cost? (a) (b) (c) (d) 149. Falls Remains unchanged Generally supply curve of industrial products is (a) (c) 148. An indifference curve relating to the two goods will be curvilinear An indifference curve relating to the two goods will be linear An indifference curve relating the two goods will be concave to the origin An indifference curve relating the two goods will be convex to the origin MC will always be less than the AC MC will be more than AC when MC is falling MC will be more than AC, when AC is rising None of the above Which of the following is not included in M2? (a) (b) (c) (d) M1 Time liabilities portion of saving deposits with bank Certificate of deposits issued by banks Term deposits with banks with maturity over one year SECTION D : QUANTITATIVE APTITUDE (50 MARKS) 151. The value of 33 + 43 + 53 + ..+ 113 (a) (c) 152. 4356 4347 (b) (d) 4348 4374 The sum of two numbers is 75 and their difference is 20. Find the difference of their squares. (a) (c) 1500 1550 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) 1600 None of these 265 MODEL TEST PAPER - 10 153. The sum of two numbers is 13 and the sum of their squares is 85. Find the numbers. (a) (c) 154. (b) (d) 8, 10 None of these The difference between the squares of two consecutive numbers is 37. Find the numbers. (a) (c) 155. 7, 6 5, 4 19, 18 10, 9 (b) (d) 20, 19 None of these The denominator of a fraction is 3 more than its numerator. If the numerator is increased by 7 and the denominator is decreased by 2, we obtain 2. The fraction is (a) (b) 5 8 (c) 156. 3 8 7 8 (d) None of these (b) (d) 27 None of these (b) (d) logax None of these If log x 3 = 1 find the value of x 6 (a) (c) 157. The value of a loga x is (a) (c) 158. 9 18 x x2 The value of 3 2-log 3 6 is (a) (b) 3 2 (c) 159. 9 5 9 4 (d) None of these If log 2 = 0.3010, log 3 = 0.04771 and log 5 = 0.6990, there log 30 (a) (c) 160. 2.5717 1.4771 (b) (d) 2.4771 None of these If log 10 12.45 = 1.0952 and log 10 3.79 = 0.5786, find the value of log10 124.5 + log10 379. (a) (c) 5.3782 2.6738 266 The Institute of Chartered Accountants of India (b) (d) 4.6738 None of these Common Proficiency Test (CPT) Volume - II 161. If np5 : np3 = 2:1; then the value of n is (a) (c) 162. (b) (d) 90 50 120 240 (b) (d) 60 70 (b) (d) 408408 4004080 80 None of these (b) (d) xe x Evaluate ( x + 1) 1 (a) ( x + 1) (c) (b) 1 x e +c x +1 2 e 2x + c (d) None of these x -1 e ( x + 1) x e 2x (a) dx ex + c ( x + 1) Evaluate 2 ( x + 1) 4084080 None of these 2 2x 167. 200 None of these In how many different ways can 17 billiard balls be arranged, if 7 of them are black, 6 red and 4 white. (a) (c) 166. 100 None of these How many numbers can be formed with the digits of the number 112321 that are greater than one lakh? (a) (c) 165. 5 None of these How many numbers greater than 1000 can be formed with the digits of the number 23416; if the digits are not repeated in the same number. (a) (c) 164. (b) (d) A room has 10 doors. In how many ways can a man enter the room by one door and come out by a different door. (a) (c) 163. 4 10 3 3 dx +c ex +c (b) ( x + 1) (d) None of these 3 ex (c) ( x + 1) 2 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 267 MODEL TEST PAPER - 10 168. Evaluate 2 0 x 2 dx x 2 + (2 x)2 (a) (b) (c) 169. 1 2 (d) None of these (b) 1 x+a +c log 2a x a (d) None of these Evaluate: x dx a2 2 (a) 1 x a +c log 2a x+a (c) 170. Evaluate: 1 x a +c log 2a x+a a 0 2 1 dx x2 (a) (b) 1 a x +c log 2a a+x (c) 171. 1 a+x +c log 2a a x 1 x a lo g 2a x+a (d) None of these If ex y + log xy + xy = 0, then dy is dx (a) y x (b) y x (c) x y (d) None of these 268 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 172. if y = x log (log x); then dy is dx (a) y log ( log x ) + 1 x (b) x log ( log x ) + 1 y (c) x log ( log x ) + 1 y (d) None of these (a) x4 + x2 + 2 (x 2 + 1) 2 (b) x4 + x2 + 2 x 2 +1 (c) (x4 +x2 +2)2 x2 +1 (d) None of these x+ 173. 174. If y = If 1 , 1 then dy is x+ dx x y x dy + = 6, then is x y dx (a) x + 17y 17x + y (b) x 17y 17x + y (c) x 17y 17x y (d) None of these (b) (d) 24990 None of these 3 175. Evaluate : 47 c 4 + 50 - jc 3 j=0 (a) (c) 249900 249000 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 269 MODEL TEST PAPER - 10 176. The first term of an A.P. is 100 and the sum of whose first 6 terms is 5 times the sum of the next 6 terms, then the c.d. is (a) (c) 177. (b) (d) 6P 2 None of these 0 1 (b) (d) 1 None of these -9 -7 , -2, , ................ is zero. 4 4 9th term 12th term (b) (d) 10th term None of these If 6 times of 6th term of an A.P. is equal to 15 times the 15th term, then its 21st term. (a) (c) 181. 6P + 2 6P 1 Which term of the sequence, (a) (c) 180. 10 None of these The sum of first m terms of an A.P. is same as the sum of first n terms, where m n; then the sum of first (m+n) terms is: (a) (c) 179. (b) (d) The sum of n terms of an A.P. is 3n2+n; then its pth term is (a) (d) 178. 10 5 1 0 (b) (d) 1 None of these The average of n numbers is x. If each of the numbers is multiplied by (n+1); then the average of new set of numbers is (a) (b) x n +1 (c) 182. x (n + 1).x (d) None of these The average weight of 8 person increases by 1.5 kg, if a person weighing 65 kg replaced by a new person, what would be the weight of the new person? (a) (c) 183. 76 kg 77 kg (b) (d) 80 kg None of these The average of marks obtained by 120 students in a certain examination is 135. If the average marks of passed students is 39 and that of the failed students is 15; what is the number of students who passed in the examination? (a) (c) 100 200 270 The Institute of Chartered Accountants of India (b) (d) 150 None of these Common Proficiency Test (CPT) Volume - II 184. The average of 17 numbers is 45. The average of first 9 of these numbers is 51 and the last 9 of these numbers is 36. Find the 9th number? (a) (c) 185. 60 75 Four Five True Either (a) or (b) 1 (c) 1 (b) (d) Three None of these (b) (d) False None of these 2 (b) 3 8 (d) None of these 4 Three balls are drawn at random from a bag containing 6 blue and 4 red balls. What is the chance that 2 balls are blue and 1 is red? (a) 1 (c) 190. 65 None of these If one card is drawn at random from a pack of playing cards; find the probability it is neither a hearts nor a club: (a) 189. (b) (d) Laspeyre s & Paasche s Index Number satisfy the time reversal test. (a) (c) 188. 14 None of these There are . Tests for Index Number (a) (c) 187. (b) (d) The average of 11 results is 30, that of the first five is 25 and that of the last five is 28. Find the value of the 6th number? (a) (d) 186. 5 18 1 4 (b) 3 2 (d) None of these 4 Find the probability of 53 Mondays in a leap year? (a) 2 7 (b) 3 7 (c) 4 7 (d) None of these Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 271 MODEL TEST PAPER - 10 191. If A & B are independent events and P(A) = 1 3 & P(B) = ; then P( AUB ) is 3 4 (a) (b) 5 6 (c) 192. 2 6 1 6 (d) None of these Two letters are drawn at random from the word HOME Find the probability that both the letters are vowel? (a) (b) 5 6 (c) 193. 1 6 2 3 (d) None of these Two letters are drawn at random from the word HOME Find the probability that at least one is vowel? (a) (b) 1 6 (c) 194. 5 6 1 3 (d) None of these Two letters are drawn at random from the word HOME Find the probability that one of the letters selected should be M. (a) (b) 1 2 (c) 195. 1 4 3 4 (d) None of these A and B are two mutually exclusive events of an experiments. If P ( not A ) = 0.65, P (AUB) = 0.65 and P(B) = p. Then the value of p is (a) (c) 196. 0.35 0.3 (b) (d) 0.60 None of these (b) (d) 1 2 n 2n 1 Find the sum of n terms of the given series (a) (c) 2n n 1 n+2 n 1 272 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 197. Let f(x) be a polynomial function of second degree and a 1, a 2, a 3 are in A.P. then f (a2) and f (a3) are in (a) (c) 198. G.P. None of these Rs. 2,470 Rs. 5,470 (b) (d) Rs. 3,470 None of these Two regression coefficient bxy and byx are 1.2 and 0.5. This is (a) (c) 200. (b) (d) A man borrows Rs. 20,000 at interest rate 4% per annum compounded annually and agrees to pay both the principal and the interest in 10 equal instalments at the end of each year. Find the value of each instalment (approx.) (Given log 104 = 2.0170 and log 6761 = 3.8300). (a) (d) 199. A.P. Either A.P. or G.P. True Either (a) or (b) (b) (d) False None of these The mean of Poisson distribution is 1.6 and variance is 2. This is (a) (c) True Either (a) or (b) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India (b) (d) False None of these 273 Answer of Model Test Papers Model Test Paper BOS/CPT 10 SECTION A : FUNDAMENTALS OF ACCOUNTING 1. (a) 2. (d) 3. (b) 4. (a) 5. (b) 6. (c) 7. (b) 8. (a) 9. (b) 10. (d) 11. (a) 12. (d) 13. (d) 14. (c) 15. (a) 16. (b) 17. (c) 18. (c) 19. (a) 20. (c) 21. (b) 22. (c) 23. (c) 24. (d) 25. (b) 26. (b) 27. (a) 28. (c) 29. (a) 30. (b) 31. (c) 32. (b) 33. (c) 34. (c) 35. (b) 36. (c) 37. (c) 38. (b) 39. (c) 40. (b) 41. (d) 42. (a) 43. (a) 44. (a) 45. (b) 46. (c) 47. (c) 48. (b) 49. (a) 50. (b) 51. (a) 52. (c) 53. (a) 54. (b) 55. (b) 56. (c) 57. (a) 58. (b) 59. (a) 60. (d) SECTION B : MERCANTILE LAWS (40 MARKS) 61. (a) 62. (c) 63. (d) 64. (d) 65. (d) 66. (d) 67. (c) 68. (b) 69. (b) 70. (a) 71. (c) 72. (c) 73. (d) 74. (b) 75. (d) 76. (c) 77. (a) 78. (a) 79. (a) 80. (b) 81. (a) 82. (d) 83. (a) 84. (b) 85. (a) 86. (a) 87. (b) 88. (c) 89. (d) 90. (d) 91. (d) 92. (d) 93. (a) 94. (a) 95. (c) 96. (d) 97. (a) 98. (d) 99. (a) 100. (c) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 293 ANSWERS Answer of Model Test Papers Model Test Paper BOS/CPT 10 SECTION C : GENERAL ECONOMICS (50 MARKS) 101 (a) 111 (a) 121 (c) 131 (c) 141 (c) 102 (d) 112 (d) 122 (a) 132 (d) 142 (a) 103 (a) 113 (b) 123 (c) 133 (a) 143 (d) 104 (c) 114 (a) 124 (d) 134 (c) 144 (a) 105 (c) 115 (b) 125 (a) 135 (b) 145 (b) 106 (d) 116 (c) 126 (b) 136 (c) 146 (a) 107 (c) 117 (c) 127 (a) 137 (c) 147 (a) 108 (d) 118 (a) 128 (a) 138 (d) 148 (b) 109 (b) 119 (c) 129 (b) 139 (a) 149 (c) 110 (d) 120 (a) 130 (a) 140 (d) 150 (d) SECTION D : QUANTITATIVE APTITUDE (50 MARKS) 151. (c) 152. (a) 153. (a) 154. (a) 155. (b) 156. (b) 157. (a) 158. (b) 159. (c) 160. (b) 161. (b) 162. (a) 163. (c) 164. (a) 165. (b) 166. (b) 167. (c) 168. (a) 169. (a) 170. (b) 171. (d) 172. (a) 173. (a) 174. (c) 175. (a) 176. (a) 177. (b) 178. (a) 179. (b) 180. (c) 181. (c) 182. (c) 183. (a) 184. (c) 185. (b) 186. (a) 187. (b) 188. (a) 189. (c) 190. (a) 191. (b) 192. (a) 193. (a) 194. (b) 195. (c) 196. (C) 197. (a) 198. (a) 199. (b) 200. (b) 294 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II ANSWERS 198. P = 5 1 = 25 5 1 4 Q = 1 = 5 5 n = 5 S.E. of proportion of defectives = PQ n 1 4 1 = 0 .032 5 5 5 = SE = 0.1088 Ans. (b) 0.1088 199. n = 2, N = 4 Total number of possible sample of size of with replacement = 4 2 = 16 Ans. (a) 200. n = 2, 16 N=4 Total number of possible sample of size without replacement = NC n = 4 C 2 = 6 Ans. (b) 6 Model Test Paper BOS/CPT 10 151. The value of 3 3 + 4 3 + 5 3 + ..... + 113 2 [ = 11(11 + 1) 3 3 1 +2 2 = (11 6 )2 (1 + 8 ) = (66 )2 (9 ) = ] 4356 9 = 4347 Ans. (c) 152. Let the two numbers are x and y Given x + y = 75 (1) x y = 20 (2) 428 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II (1)+(2) 2x = 95 x = (1) = 75 = 95 2 95 2 55 2 The difference of their squares = x 2 y 2 2 = 95 55 2 2 = 9025 3025 4 4 = 2 6000 = 1500 4 Ans. (a) 153. Let the two numbers are x and y Given x + y = 13 (1) and x 2 + y 2 = 85 (2) (1) y = 13 x Substitute y = 13 x in (2) x 2 + (13 x) 2 = 85 x 2 + 169 + x 2 26 x 85 = 0 2 x 2 26 x + 84 = 0 x 2 13 x + 42 = 0 (x 7 ) (x 6 ) = 0 x =7, x = 6 When x = 7 (1) y = 13 7 = 6 When x = 6 (1) y = 13 6 = 7 The number (7, 6) Ans. (a) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 429 ANSWERS 154. Let the two consecutive members are x and x 1 Given x 2 ( x 1) 2 = 37 x 2 ( x 2 + 1 2 x) = 37 x 2 x 2 1 + 2 x = 37 2x = 38 x = 19 x 1 = 19 1 = 18 Ans. (a) 155. Let the number be x. x (1) x+3 Given condition (1) Given condition (2) x+7 =2 x+3 2 x + 7 = 2 (x+1) = 2x + 2 x=5 (1) 5 5 = 5+3 8 3 = 156. Given log x 1 6 1 x6 = 3 ( 3) = ( 3) ( 3) ( 3) 6 x= 2 2 2 =3 3 3 x = 27 Ans. (b) 157. Let y = a log a x Taking log on both sides [ log y = log a log a x ] 430 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II = log a x. log a a a . log b log y = log x [ log b c = log c By properties] Taking Exponent on both sides. e log y = e log x y log e = x log x y=x Ans. (a) 158. Let y = 3 2 log 3 6 = 3 2 .3 log 3 6 = 9 .3 [log 3 ( 3 x 2 ) ] = 9 .3 [log 3 3 +log 3 2 ] = 9 .3 [1+log 3 2 ] = 9 .3 1.3 log 3 2 = 3 .3 log 3 (1 / 2 ) = 3.(1/2) y = 3/2 [ a log a x = x properties] Ans. (b) 159. log 30 = log (2 3 5) = log 2 + log 3 + log 5 = 0.3010 + 0.4771 + 0.6990 = 1.4771 Ans. (c) 160. log 10 124.5 + log 10 379 = log 10 (12.45 10) + log 10 (3.79 100) = log 10 12.45 + log 10 10 + log 10 3.79 + log 10 100 = 1.0952 + 0.5786 +2 log 10 124.5 + log 10 379 = 4.6738 Ans. (b) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 431 ANSWERS 161. n P5 : n P3 = 2 :1 n! n! 2 = (n 5 )! (n 3 ) ! 1 (n 3 ) ! 2 = (n 3) (n 4) = 2.1 (n 5 ) ! 1 n 3 =2 n=5 Ans. (b) 5 162. No. of ways to enter into room = 10 No. of ways to came out from a different door = 9 Total Ways = 10.9 = 90 ways Ans. (a) 90 163. Five digit Nos. by using digit (1, 2, 3, 4, 6) = 5! = 120 Four digit nos. by using digit (1, 2, 3, 4, 6) = 5 P 4 = 120 Total Nos. greater than 1000 = 120 + 120 = 240 Ans. (c) 240 164. Total Nos. of 6 digit (greater than 1 lakh) by using (1, 1, 1, 2, 2, 3) are = = 6! 3! 2! 60 Ans. (a) 60 165. No. of ways in which 17 billiard can be arranged. If 7 are black, 6 red and 4 white are = 17 ! = 4084080 7! 6! 4! Ans. (b) 4084080 166. Let I = = xe x (x + 1)2 dx (x + 1 1) ex dx (x + 1)2 432 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II (x + 1)e x dx e x dx (x + 1)2 (x + 1)2 = ex dx (x + 1) = = I ex I1 I2 = (x + 1)2 dx e x dx ( x 1) Integrating by parts. I1 1 x 1 e 2 1+ x ( x + 1) = x e dx I = ex 1 1 x ex + e dx ( x + 1)2 dx (1 + x) ( x + 1) 2 I 1 ex (1 + x) = Ans. (b) 167. e x ( x 1) x +1 2 x dx = e dx 3 ( x + 1) ( x + 1) 3 x 1 2 dx 2 3 ( x + 1) ( x + 1) = e = x e {f(x )+ f (x )}dx Where f(x) = = 1 ( x + 1) 2 e x f( x) + c e x ( x 1) ( x + 1)3 dx = ex (x + 1)2 +c Ans. (c) 168. See the text book example page No. 9.28 Ans. (a) Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 433 ANSWERS 169. dx dx x 2 a 2 = (x a ) (x + a ) 1 1 1 dx 2a x a x+a = 1 dx dx 2a x a x+a = 1 [log (x a ) log (x + a )] 2a dy x2 a 2 170. = 1 x a log 2a x + a dx 1 a 2 x 2 dx = (a + x ) (a x ) 1 1 1 = dx 2a a + x a x = 1 1 1 dx dx a x 2a a + x = 1 [log(a + x ) log (a x )] 2a = 1 a + x log 2a a x 171. e x y + log xy + xy = 0 d.wr.t.u. dy 1 dy dy e x y 1 + x + y.1 + x + y.1 = 0 dx xy dx dx e x y e x y . dy 1 dy 1 dy + + +x +y =0 dx y dx x dx 434 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II x y 1 dy 1 + + x = e x y y e y x dx 1 1 dy ( xy + 1 y.e x.y ) = ( x.e x y + 1 + xy ) x y dx dy y x.e x y + 1 + xy = . x y dx x 1 + xy y.e Ans. (d) None of these 172. y = x log (log x ) log y = log (log x) . log x 1 1 dy 1 1 + (log x). = log (log x). . . x y dx (log x) x dy y = [log (log x) + 1] dx x Ans. (a) 173. y = x + y [log (log x) + 1] x 1 x+ y= 1 x x3 + x + x x3 + 2 x = 2 x2 + 1 x +1 ( )( )( ( ) ) dy x 2 + 1 3 x 2 + 2 x 3 + 2 x (2 x ) = 2 dx x2 + 1 = 3x4 + 3 x2 + 2 x2 + 2 2x4 4 x2 (x + 1) 2 2 dy x 4 + x 2 + 2 = dx ( x 2 + 1) 2 Ans. (a) x4 + x2 + 2 ( x 2 + 1) 2 Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 435 ANSWERS x =6 y y + x 174. y+x = 6 x+y = 6 xy xy dy 6 dy = x + y. 1 dx 2 xy dx 1+ 1 3 x dy = 3 y 1 y x dx dy = dx y 1 3 y x x y 3 x x 1 3 y ( ( 3 ) ) y x x+y 3y dy 3 y xy 6 = = dx xy 3 x x + y 3 x 6 dy 17 y x x 17 y = = dx y 17 x 17 x y Ans. (c) x 17 y 17 x y 3 175. 47 C4 + 50 i C i=0 3 47 C 4 + 50 C 3 + 49 C 3 + 48 C 3 + 47 C 3 178365 + 19600 + 18424 + 17296 + 16215 249900 Ans. (a) 249900 176. a = 100 S 6 = 5. S 6 6 6 [2 a + (6 1)d ] = 5 . [2 (a + 6 d ) + (6 1)d ] 2 2 3 [200 + 5d] = 15 [200+12d + 5d] 436 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II 200+5d = 1000 + 85d 80d = 800 d = 10 Ans. (a) 10 177. S n = 3n 2 + n S1 = 4 a1 = 4 S 2 = 14 a 2 = 14 4 = 10 S 3 = 30 a 3 = 30 14=16 d=6 Tp = a + (p 1) d = 4 + (p 1) 6 Tp = (6p 2) Ans. (b) (6p 2) 178. S m = S n m n [2 a + (m 1)d ] = [2 a + (n 1)d ] 2 2 2ma 2na = (n 2 n)d (m 2 m )d 2a (m n) = (n2 n m 2 m)d 2a (m n) = (m n) (m+n 1)d 2a = (m+n 1)d S m+n = m+n [2a + (m+n 1)d] 2 m+n [( m+n 1)d + (m+n 1)d] 2 S m+n = 0 Ans. (a) 0 9 7 179. , 2 , ..... 0 4 4 a= 9 9 1 d = 2 + = 4 4 4 0= 9 1 9 1 + (n 1) = (n 1) 4 4 4 4 9 = n 1 n=10 Ans. (b) 10th term Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 437 ANSWERS 180. 6.T 6 = 15.T 15 6 (a+5d) = 15 (a+14d) 2a + 10d = 5a + 70d a = 20d 3a = 60d T 21 = a + 20d = 20 d + 20d T 21 = 0 Ans. (c) 0 181. The average of n numbers is x. If any no.is multiplied to each of datas. Then average will also multiplied by such no. New average = (n + 1) x Ans. (c) 182. Av = = (n + 1) x. x 1.5 = x n x = 12 kg. (increased weight) Weight of New person = 65 + 12 = 77 kg. Ans. (c) 77 Kg. 183. If passes students = x 35 = 39 x + 15 (120 n) 120 4200 = 39x + 1800 15x 2400 = 24x x = 100 Passed Students = 100 Ans. (a) 184. 100 x = 45 17 x = 765 Total of first 9 numbers = 9 51 = 459 Total of last 9 numbers = 9 36 = 324 Value of 9th number = (459 + 324) 765 438 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II = 18 Ans. (c) 185. 18 x = 11 30 = 330 Total of first five numbers = 5 25 = 125 Total of last five numbers = 5 28 = 140 Value of 6th number = (125 + 140) ~ 330 = 65 Ans. (b) 65 186. Ans. (a) Refer properties 187. Ans. (b) Refer Properties. 188. Let A be the hearts playing cards in a part. Let B be the club playing cards in a part. P(A) = 13 52 P(B) = 13 52 Here A and B are mutually exclusive. P (A B ) = P ( A) + P (B) = 13 13 26 1 + = = 52 52 52 2 189. Total number of balls in the bag = 6 + 4 = 10 Since three balls are drawn out of 10 balls in 10 C 3 ways Exhaustive number of Cases = 10 C 3 = 120 The number of favourable cases two balls are blue and balls is red = 6C 2 x 4C 1 = 60 Probability of 2 balls are blue and 1 is red = = 60 = 120 6c 2 4c 1 10 c 3 Ans. (c) 190. There are 366 days in a leap year. Now 366 = 7 x 52 + 2 The leap year will contain at least 52 Mondays. The possible combination for the remaining two days are: Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 439 ANSWERS (i) Sunday and Monday (ii) Monday and Tuesday (iii) Tuesday and Wednesday (iv) Wednesday and Thursday (v) Thursday and Friday (vi) Friday and Saturday (vii) Saturday and Sunday Let A be the event of getting 53 Mondays in the leap year. Therefore, only those combinations will be favourable to the event A which contain "Monday" The combination (i) and (ii) are P(A) = 2/7 favourable to the happening of A Ans. (a) 191. Given P(A) = 1/3 P(B) = 3/4 and A and B are independent events P (A B ) = 1 P (A B )1 [ ] = 1 P(A1 ).P(B1 ) = 1 {[ 1 P(A)] [1 P (B)]} = 1 3 1 1 1 3 4 = 2 1 1 3 4 [A and B are independent] 1 5 P P (A B ) = 1 = 6 6 Ans. (b) 192. Out of given 4 letters, there are two letters are vowel (O,E). Let A be the first letter is vowel. P(A) = 2/4 Let B be the second letter is vowel P(B) = 1/3 Here A and B are independent 440 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II P(AB) = P(A).P(B) 2 1 . = 1/6 4 3 = Ans. (a) 193. Out of given 4 letters, there are two letters are vowel (O, E) Let A be the first letter is vowel. i.e. P(A) = 2/4 Let B be the second letters is vowel. P(B) = 1/3 Here A and B are Mutually executive P (A B ) = P(A) + P (B) = 2 1 6 + 4 10 5 + = = = 4 3 12 12 6 Ans. (a) 194. Let A be the first letter selected M from the 'HOME'. B be the second letter selected M from the 'HOME' P(A) = 1/4, P(B) = 1/4 A and B are Mutually exclusive P(AUB) = P(A) + P(B) = 1 1 2 1 + = = 4 4 4 2 Ans. (b) 195. By addition thereon P(A or B) = P(A) + P(B) 0.65 = = [1 P('not A)] + p [1 0.65] + p p = 0.65 0.35 p = 0.30 Ans. (c) 197. Since f(x) is a Polynomial. & a 1 , a 2 , a 3 are in AP f(a 1 ), f(a 2 ), f(a 3 ) also in AP Common Proficiency Test (CPT) Volume - II The Institute of Chartered Accountants of India 441 ANSWERS f (a 1 ), f (a 2 ), f (a 3 ) also in AP Ans. (a) AP (1 + i)n 1 198. A = P i (1.04 )10 1 20,000 = P 0 .04 After solving we get P = 2470 (Approx) Ans. (a) 2470 199. byx = 1.2 & bxy = 0.5 This is wrong because bxy and byx have same sign. Ans. (b) false. 200. The mean of poison distribution is 1.6 and variance is 2. This is wrong because P d will greater than 2 Ans. (b) false. 442 The Institute of Chartered Accountants of India Common Proficiency Test (CPT) Volume - II

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