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MASTER OF COMPUTER APPLICATIONS (MCA) (3rd SEMESTER) ASSIGNMENTS 2009 (MCS-031, MCS-032, MCS-033, MCS-034, MCS-035, MCSL-036) SCHOOL OF COMPUTER AND INFORMATION SCIENCES INDIRA GANDHI NATIONAL OPEN UNIVERSITY MAIDAN GARHI, NEW DELHI – 110068 CONTENTS Course Code Assignment No. Maximum Page No. Marks MCS-031 MCA(3)/031/Assign/09 100 3 MCS-032 MCA(3)/032/Assign/09 100 5 MCS-033 MCA(3)/033/Assign/09 100 6 MCS-034 MCA(3)/034/Assign/09 100 10 MCS-035 MCA(3)/035/Assign/09 100 11 MCSL-036 MCA(3)/036/Assign/09 100 15 Important Notes Important Notes 1. Viva-voce worth 20 Marks is compulsory for each course. 1. Viva-voce worth 20 Marks is compulsory for each course. 2. Please follow the guidelines given in the MCA Programme Guide for solving, presentation 2. format and the guidelines given in the MCA Programme Guide for solving, presentation Please followsubmission of the assignment. format and submission of the assignments. 2 Course Code : MCS-031 Course Title : Design and Analysis of Algorithms Assignment Number : MCA(3)/031/Assign/09 Maximum Marks : 100 Weightage : 25% Last Dates for Submission : 15th April, 2009 (For January Session) 15th October, 2009 (For July Session) There are four questions in this assignment, which carries 80 marks. Rest 20 marks are for viva-voce. Answer all the questions. You may use illustrations and diagrams to enhance the explanations. Please go through the guidelines regarding assignments given in the MCA Programme Guide for the format of presentation. The examples, whenever asked to be given, should be different from those that are discussed in the course material. Question 1: Sort the following list of numbers in the descending order, 187, 62, 155, 343, 184, 958, 365, 427, 78, 94, 121, 388 using each of the following methods: (i) Insertion Sort (ii) Selection Sort (iii) Heap Sort (iv) Merge Sort (v) Quick Sort Further, count the number of operations, by each sorting method. (20 marks) Question 2: A directed Hamiltonian cycle DHC in a directed graph G = (V, E) is a directed cycle of length n =V, where V is the number of vertices in G. So, the cycle goes through every vertex exactly once and then returns to the starting vertex. The DHC problem is to determine if a given directed graph G has a directed Hamiltonian cycle. Show that DHC is NP-Hard. (20 marks) Question 3: Multistage Graphs Problem: A multistage graph G = (V, E) is a directed graph in which the vertices are partitioned in k 2 disjoint sets say V1, V2, ………, Vk. Further, if (u, v) is an edge in E, then, for i with 1 i < k, the edge u belongs to Vi and the vertex v belongs to Vi+1. The number of vertices in each of the first and last sets viz., V1 and Vk is one. Let the node in the first set V1 be called s and the node in the last set Vk be called t. Further, let c(i, j) be the cost of traversing from vertex i to vertex j. The Multistage Graph Problem is to find a minimum cost path from the start node s to the terminal node t. Using Dynamic Programming, suggest a solution to Multi-stage Graph Problem. (20 marks) 3 Question 4: (a) Job Sequencing with Deadlines using Greedy Method, find an optimal solution to the problem of job sequencing with Deadlines, where n = 4, (p1, p2, p3, p4) = (10, 1, 15, 7) and (d1, d2 d3, d4) = (1, 2, 1, 2). (10 marks) (b) Let G = (V, E) be a given graph and S be a subset of V. Then, S is said to be a node cover of the graph G if each of the edges in E is incident to at least one vertex in S. The size of the cover is the number of vertices in the set S. The Node Cover Problem is to determine whether a given graph G has a Node cover of size k, where k is a pre-assigned natural number. (10 marks) 4 Course Code : MCS-032 Course Title : Object Oriented Analysis and Design Assignment Number : MCA(3)/032/Assign/09 Maximum Marks : 100 Weightage : 25% Last Dates for Submission : 15th April, 2009 (For January Session) 15th October, 2009 (For July Session) There are eight questions in this assignment which carries 80 marks. Rest 20 marks are for viva-voce. Answer all the questions. Please go through the guidelines regarding assignments given in the Program Guide for the format of presentation. Question 1: What is OOAD? Explain advantages of OOAD. (10 Marks) Question 2: Explain characteristics of an Object Oriented Systems. (10 Marks) Question 3: What is Inheritances? Explain with an example, how Inheritance is shown in class diagram. (10 Marks) Question 4: What is an object? Critically explain “Object Identification is one of the major challenges in OOAD”. (10 Marks) Question 5: What is a state diagram? Explain the characteristics of the system that can be identified by examination of the state diagram of that System. (10 Marks) Question 6 : Explain different UML Diagrams used in OOAD. (10 Marks) Question 7: Explain object model and dynamic model with example. (10 Marks) Question 8: What is Unidirectional Implementation? Explain how it is different than Bi-directional Implementation with an example. (10 Marks) 5 Course Code : MCS-033 Course Title : Advanced Discrete Mathematics Assignment Number : MCA(3)/033/Assign/09 Maximum Marks : 100 Weightage : 25% Last Dates for Submission : 15th April, 2009 (For January Session) 15th October, 2009 (For July Session) There are eight questions in this assignment. Answer all questions. 20 Marks are for viva-voce. You may use illustrations and diagrams to enhance explanations. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation. Question 1: Which of the following statements are true and which are false? Give reasons for your answer. i) Neither order nor degree is defined for the recurrence relation a n = a1a 2 ...a n 1 . ii) The generating function of the recurrence relation an+2 = 3an+1 2an, where a0 = 1, a1 = 1, ex is . (x 1) (x 2) iii) The generating function of the sequence {1, 2, 3, 4, …, n …} is (1–z)-2. iv) Any graph is isomorphic to its complement. v) If (G) = 3, G has a subgraph isomorphic to K3. (10 Marks) Question 2: i) Draw the complement of the graph in Figure 2. A a B F E D C Figure 2 ii) Show that each of the graphs in Figure.3 is isomorphic to one of the subgraph of the graph in Figure 2. 6 A A B D A B E E D C C B D C Figure 3 For example, you can show that the graph in Figure 4. Is isomorphic to a subgraph of the graph in Figure 2. by producing the subgraph H with V (H) = {f, b, d, c}, E (H) = {(f,b), (b, c), (c, d), (d, f)} A B D C Figure 4 and the isomorphism g (f) = a, g (b) = B, g(c) = D, g (d) = C. b) Is it possible to draw a 6 regular graph on 11 vertices? If yes, draw such a graph. If no, give reasons for your answer. (10 Marks) Question 3: (a) Raghu goes to a grocery shop and purchases grocery for Rs. 23. He has 3 five rupee coins, 4 two rupee coins and 6 one rupee coins. In how many ways can he pay the shop keeper? Find a solution using generating functions. (6 Marks) (b) Find the general form of the solution to the linear homogeneous recurrence relation with constant coefficients for which the characteristic roots are 1 with multiplicity 1, 2 with multiplicity 2 and 2 with multiplicity 3. The relation also has a non-homogenous part which is a linear combination of n2n and (2)n. (4 Marks) Question 4: (a) How can a power series be associated with the problem in which we have to find the number of selections of fruits if we have Rs.50 with us and it is given that an Apple costs Rs. 5, a Banana Rs.2 and a Coconut Rs.3. (4 marks) (b) (i) Use Lemma 1 to find the generating function A(z) (say) for the sequence in arithmetic progression {a, a +d, a+ 2d,…}. (ii) How many integer solutions are there to a1+a2+a3+a4+a5 = 28 with ak > k for each k, 1? (6 marks) 7 Question 5: a) Solve the recurrence relation n(n 1) bn = bn 1 + n2 + (4 Marks) 2 b) Consider the number of subsets of {1, 2, 3, …, n} which do not contain two consecutive integers. Denote this number by an. i) What are the values of a1, a2, a3 and a4? ii) Derive a recurrence relation of an and solve it. (6 Marks) Question 6: Prove that (a) Let G be a simple graph on p vertices, p ≥ 3, satisfying the condition that d(u)+ d(v) ≥ p for any two non-adjacent vertices u and v in G. Then G is Hamiltonian. (b) A connected graph G with two or more vertices is edge traceable if and only if it has exactly two vertices of odd degree. (10 marks) Question 7: a) Check whether the graph in Figure 5 is Eulerian. b) Check whether the graph in Figure 6 is Hamiltonian a a f b g e b f g h e c d C d Figure 5 Figure 6 c) Consider the following weighted complete graph. 8 V1 23 51 36 V5 5 v2 30 15 19 78 30 v3 v4 42 Figure 7 Start with the Hamiltonian cycle {v1, v2, v3, v4, v5, v1}. Apply the 1-exchange algorithm get a Hamiltonian cycle of lesser weight. (10 Marks) Question 8: a) A palindrome is a word that reads the same whether read from right to left or from the left to right, the word ROTOR, for example. Let a n be the number of words of length n, not necessarily meaningful, which are palindromes. We consider a single letter as a palindrome. i) What are a1 and a 2 ? ii) Set up a recurrence for a n . iii) Check that an 26 1 2 26 (1) 1 2 26 n n is the solution to the recurrence. (6 Marks) b) Show that a tree has at least 2 vertices of degree 1. (4 Marks) 9 Course Code : MCS-034 Course Title : Software Engineering Assignment Number : MCA(3)/034/Assign/09 Maximum Marks : 100 Weightage : 25% Last Dates for Submission : 30th April, 2009 (For January Session) 31st October, 2009 (For July Session) This assignment has only one question for 80 marks. 20 marks are for viva voce. You may use illustrations and diagrams to enhance the explanations. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation. Question 1: Suppose that you need to develop a Pay Roll Processing System for an organization whose employee strength is 1000. Every employee gets pay which is computed based on their designation, experience and qualifications. Now, perform the following activities for the Pay Roll Processing System. Make assumptions, wherever necessary. (a) Which SDLC model will you choose? Justify your answer. (10 marks) (b) List the functional and non-functional requirements. (6 marks) (c) Propose a schedule for the project completion. Draw Gantt and Pert charts. (16 marks) (d) Estimate cost of the project. (16 marks) (e) Develop complete SRS. (16 marks) (f) Develop test plan document. (16 marks) 10 Course Code : MCS-035 Course Title : Accountancy and Financial Management Assignment Number : MCA(3)/035/Assign/09 Maximum Marks : 100 Weightage : 25% Last Dates for Submission : 30th April, 2009 (For January Session) 31st October, 2009 (For July Session) This assignment has nine questions. Answer all questions. 20 marks are for viva voce. You may use illustrations and diagrams to enhance the explanations. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation. Question 1: From the following Trial Balance of K. Kundu as on 31.03.2008, prepare Trading Account and Profit and Loss Account for the year ended 31.3.2008 and a Balance Sheet as on that date after making necessary adjustments: (15 Marks) Trial Balance Rs. Rs. K.Kundu‟s Drawings 12,000 K. Kundu‟s Capital 60,000 Furniture & Fixtures 4,000 Returns Outward 2,000 Plant & Machinery 30,000 Sales 1,30,000 Opening Stock 20,000 Creditors 12,000 Purchases 80,000 Loan at 6% p.a. taken from 10,000 M. Mehta on 1.10.2007 Salaries and Wages 22,400 Discount 600 Debtors 20,400 Returns Inward 5,000 Postage & Telegrams 1,500 Rent, Rates & Taxes 3,600 Bad Debts written-off 400 Trade Expenses 200 Interest on loan from M. Mehta 150 Insurance 800 Travelling Expenses 500 Sundry Expenses 3,050 Cash in Hand 10,300 Total 2,14,600 2,14,600 Adjustment: (1) Closing stock: Cost Price Rs. 21,000, Market Price Rs. 25,000. (2) Of the debtors Rs. 400 are bad and should be written-off. Create a reserve for bad debts at 5% on Sundry Debtors and a reserve for discount Debtors at 2½%. (3) Salaries Rs. 800 for March 2008 were not paid. (4) Interest on Capital is to be calculated at 6% p.a. and on drawings Rs. 330. (5) Prepaid Insurance amounted to Rs. 100. (6) Depreciate Furniture & Fixture by 5% and Plant and Machinery by 10%. (7) Make a reserve for discount on creditors @ 2%. 11 Question 2: A company is considering which of two mutually exclusive projects it should undertake. The Finance Director thinks that the project with the higher NPV should be chosen whereas the Managing Director thinks that the one with the higher IRR should be undertaken especially as both projects have the same initial outlay and length of life. The company anticipates a cost of capital of 10% and the net after-tax cash flows of the projects are as follows: (10 Marks) (Rs. ‘000) Year 0 1 2 3 4 5 Cash flows: Project X (200) 35 80 90 75 20 Project Y (200) 218 10 10 4 3 Required: (a) Calculate the NPV and IRR of each project. (b) State, with reasons, which project you would recommend. (c) Explain the inconsistency in the ranking of the two projects. The discount factors are as follows: Year 0 1 2 3 4 5 Discount (10%) 1 0.91 0.83 0.75 0.68 0.62 Factors: (20%) 1 0.83 0.69 0.58 0.48 0.41 Question 3: P Ltd. uses three types of materials A, B and C for production of X, the final product. The relevant monthly data for the components are as given below: (10 Marks) (Units) Materials A B C Normal usage 200 150 180 Minimum usage 100 100 90 Maximum usage 300 250 270 Reorder quantity 750 900 720 Reorder period (months) 2 to 3 3 to 4 2 to 3 Calculate for each component: (i) Reorder level, (ii) Maximum level, (iii) Minimum level, and (iv) Average stock level. Question 4: What is „Economic order quantity? How does it help in maintaining optimum level of inventory? (5 Marks) Question 5: Sakthi Traders has a contribution/sales ratio of 20% and average book debts of Rs. 10 lakhs which it collects in an average collection period 24 days. The company eorganized its „Credit Administration‟ deptt, recently and introduced a cash incentive of 5% to speed up collection of outstandings. The incentive is payable to customers making payment within 10 days. When the company reviewed the position after a 12 few months it was found that the average collection period had actually fallen to 20 days only and the average book debts had increased to Rs. 10.50 lakhs mainly as a result of some increase in sales. It was also noticed that only about half the total sales availed of the cash discount. The company‟s cost of raising additional funds is 20%. Do you recommend continuance of the cash incentive scheme? Show workings. Assume one year = 360 days. (10 Marks) Question 6: A company sells 40,000 units of its product per year @ Rs. 35 per unit. The average cost per unit is Rs. 31 out of which variable cost per unit is Rs. 28. The average collection period is 60 days. Bad debts losses are 3% on sales and the collection charges amount to Rs. 15,000. The company is considering the proposal to follow stricter collection policy which would bring down the losses on account of bad debts to 1% of sales and average collection period to 45 days. It would, however, reduce the sales volume by 1000 units and increase collection expenses to Rs. 25,000. The company requires a rate of return of 20%. Would you recommend the adoption of the new credit policy? (Assume 360 days in a year for the purpose of your calculation.) (10 Marks) Question 7: What is Treasury Management? Explain the various tools of treasury management. How is it different from financial management? (5 Marks) Question 8: What is the concept of „operating cycle? Why is it important in working Capital management? Give a suitable example to illustrate the operating cycle concept. (5 Marks) Question 9: JB Ltd. has the following Profit and Loss Account for the year ended 31st March, 2007 and the Balance Sheet as on that date: (10 Marks) Profit and Loss Account for the year ended 31 st March, 2007 Particulars Rs. lakhs Particulars Rs. lakhs Opening stock 1.75 Sales: Credit 12.00 Add: Manufacturing cost 10.75 Cash 3.00 12.50 Less: Closing stock 1.50 Cost of goods sold 11.00 Gross Profit 4.00 15.00 15.00 Administrative expenses 0.35 Gross profit 4.00 Selling expenses 0.25 Other income 0.09 Depreciation 0.50 Interest 0.47 Income-tax 1.26 Net profit 1.26 Total 4.09 4.09 13 Balance Sheet as on 31st March, 2007 Liabilities Rs. lakhs Assets Rs. lakhs Equity shares of Rs. 10 each 3.50 Plant and machinery 10.00 10% Preference shares 2.00 Less: Depreciation 2.50 Reserves and surplus 2.00 Net plant and machinery 7.50 Long-term loan (12%) 1.00 Goodwill 1.40 Debentures (14%) 2.50 Stock 1.50 Creditors 0.60 Debtors 1.00 Bills Payable 0.20 Pre-paid expenses 0.25 Accrued expenses 0.20 Marketable securities 0.75 Provision for tax 0.65 Cash 0.25 Total 12.65 12.65 The market price of the share of JB Ltd. on 31 st March, 2007 is Rs. 45 (Rs. laksh) Reserves at the beginning 1.465 Net profit during the year 1.265 2.725 Preference dividends 0.200 Equity dividends 0.525 Reserves at the close of year 2.000 Calculate the following ratios – (1) Current ratio (2) Quick ratio (3) Debt-equity ratio (4) Interest coverage (5) Debtors turnover (6) Average collection period (7) Gross profit margin (8) Net profit margin (9) Earning per share (10) Return on shareholder‟s equity (11) P/E ratio and (12) Earning yield. 14 Course Code : MCSL-036 Course Title : Laboratory Course Assignment Number : MCA(3)/036/Assign/09 Maximum Marks : 100 Weightage : 25% Last Dates for Submission : 30th April, 2009 (For January Session) 31st October, 2009 (For July Session) This assignment has three sections. Answer all the questions in each section. Section 1 and Section 2 are of 13 marks each. The lab records related to these sections also carries 13 marks each. Section 3 and lab records related to section 3 carry 14 marks each. Rest 20 marks are for viva voce. You may use illustrations and diagrams to enhance the explanations. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation. SECTION 1: MCS-032 Question 1: A Departmental Store maintains inventory of various products being sold by them. The products are classified under three Categories – Fruits and Vegs; Groceries; and Cloths. All these items have different kinds of promotion schemes. For example, the items of fruits and vegs category are perishable in nature and heavy discount are given on these items in case they are in the store for more that two days. As far as Groceries are concerned discounts are given if some stock is nearing its expiry. In cloths section discounts are given during festival time. You need to help departmental store to design an online stock management, stock pricing and discount system. Visit a department store and study the system and perform the following activities for the proposed system for the departmental store. Make necessary assumption wherever needed. i. Draw at least two use case diagrams and define all the classes. (2 Marks) ii. Draw the Sequence and Collaboration Diagrams. (3 Marks) iii. Draw the Class Diagrams. (3 Marks) iv. Draw the State Transition Diagram. (3 Marks) v. Draw the Component Deployment Model. (2 Marks) SECTION 2: MCS-034 Question 1: A News Printing Agency wants to develop an Information System for keeping track of its clients. These clients give various advertisements in the Newspaper. The company offers discounts to the preferred customers and also uses this system to generate yearly business information about its employees. Perform the following activities for the proposed system. Make suitable assumptions, if any. i. Visit any such organisation or similar type organisation and develop the SRS by performing requirements study. (2 Marks) ii. Identify various processes of the system and generate the DFD‟s for the system. You may use any software to develop the DFD. (2 Marks) iii. Design the ER diagram for the company and do the database design giving all the constraints. (3 Marks) iv. Perform the detailed procedural design for any two processes (2 Marks) 15 v. Create at least four test cases for each of the procedures designed in part (iv) (2 Marks) vi. Suggest some security mechanisms for the usage of the system with various privileges. (2 Marks) SECTION 3: MCS-035 Question 1: (a) Choose any accounting software of your choice and make journal entries for the following transactions. Make suitable assumptions, if any. (10 marks) (i) Invested Rs 75,000 in various capital goods for the Business. (ii) Opened a checking bank account with Bank of Punjab with a deposit of Rs 50,000. (iii) Paid a commission of Rs. 500 to Mr Ramesh for his services. (iv) Purchased a telephone from Telephone Nigam on a payment of Rs 2000. (v) Purchased furniture form Mr Dayal for Rs. 7000. (vi) Defective chair worth Rs.500 was returned to Mr Dayal. (vii) Negotiated with Mr Dayal and paid only Rs 6000 as final settlement. (viii) Received interest from bank for one month at a rate of 12% per year compounded monthly. (ix) Paid Rs 5000 as the rent for the shop to Mr Abdul. (x) Withdrew cash of Rs. 5000 for personal expenses. (xi) Sold a keyboard to Mr. Jain for Rs. 250 in cash. (xii) Sold 5 Hard Disk to Mr. Donald on credit for Rs. 10,000. (xiii) One hard disk was returned by Mr. Donald for Rs. 2000. (xiv) Received Rs 7500 in cash from Mr. Donald in full settlement of the remaining hard disks. (xv) Paid carriage of Rs 100 on the Computer sold for Rs. 35000. (xvi) Paid postage of Rs 50 on the letters sent to customers. (xvii) Purchased a painting for the office for cash amounted to Rs. 10,000. (xviii) Purchased old computer for re-sale for Rs. 10,000. (xix) Spend Rs. 5000 to refurbish the computer. (xx) Sold the refurbished computer for Rs.17,000. (b) After passing the journal entries prepare ledgers. (4 Marks) 16

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