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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:

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
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)

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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.

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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

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
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

(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

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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

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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)

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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)

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