IGNOU MCA Semester – 3 Solved Assignments

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MASTER OF COMPUTER

APPLICATIONS

(MCA)

MCA/ASSIGN/SEMESTER-III

ASSIGNMENTS

(July – 2020 & January – 2021)

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 – 110 068

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CONTENTS

 Assignment No. Submission-SchedulePage
Course    No.
    
Code  For July-For January- 
  December SessionJune Session 
     
MCS-031MCA(3)/031/Assignment/20-2131st October, 202015th  April, 20213
      
MCS-032MCA(3)/032/Assignment/20-2131stOctober, 202015th  April, 20215
      
MCS-033MCA(3)/033/Assignment/20-2131stOctober, 202015th April, 20216
     
MCS-034MCA(3)/034/Assignment/20-2131st  October,  202015th  April, 20218
      
MCS-035MCA(3)/035/Assignment/20-2131stOctober, 202015th  April, 20219
      
MCSL-036MCA(3)/L-036/Assignment/20-2131stOctober, 202015th April, 202112
      

Important Notes

  1. Submit your assignments to the Coordinator of your Study Centre on or before the due date.
  • Assignment submission before due dates is compulsory to become eligible for appearing in corresponding Term End Examinations. For further details, please refer to MCA Programme Guide.
  • To become eligible for appearing the Term End Practical Examination for the lab courses, it is essential to fulfill the minimum attendance requirements as well as submission of assignments (on or before the due date). For further details, please refer to the MCA Programme Guide.
  • The viva voce is compulsory for the assignments. For any course, if a student submitted the assignment and not attended the viva-voce, then the assignment is treated as not successfully completed and would be marked as ZERO.

2

Course Code:MCS-031
Course Title:Design and Analysis of Algorithms
Assignment Number:MCA(III)/031/Assign/2020-21
Maximum Marks:100
Weightage:25%
Last Dates for Submission:31st October, 2020 (For July, 2020 Session)
 :15th April, 2021 (For January, 2021 Session)

There are eight 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.

Q1: Write Merge sort algorithm. Determine its complexity in Best, Average and Worst Case.

Sort the following sequence in increasing order: 35, 37, 18, 15, 40, 12; Using Merge Sort.

(10

marks)

Q2: Explain how using dynamic programming reduces the complexity of a simple algorithm?Also explain the matrix chain multiplication algorithm in this context. Derive the principle of optimality for multiplication of matrix chain. Compute the optimal multiplications required following matrices.

A1 of order 30 x 35;   A2 of order 35 x 15;   A3 of order 15 x 5                                           (10 marks)

Q3: Give a divide and conquer based algorithm (Write a pseudo-code) to perform following:

  • find the is largest element in an array of size n. Derive the running time complexity of your algorithm.
  • finding the position of an element in an array of n numbers
Estimate the number of key comparisons made by your algorithms.(10
marks) 

Q4: Write Quick Sort Algorithm. How is it Different from Randomized Quick Sort Algorithm?Prove that that Worst case of Quick Sort is Best case of Bubble Sort. Apply Quick sort Algorithm to sort the following list: Q U I C K S O R T, in alphabetical order. Find the element

whose position is unchanged in the sorted list.                                                                                                                                                     (10

marks)

Q5: Answer the following:

(10 marks)

  • Explain the meaning of Big O notation with suitable example. How does it differ from Theta and Omega notations. Arrange the following growth rates in increasing order:

O (3n), O (n2), O (1), O (n log n)

  • Explain the essential idea of Dynamic Programming. How Dynamic programming differs from Divide and conquers approach for solving problems?

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  • Define Knapsack Problem and cite one instance of the problem. Compare Knapsack Problem with fractional Knapsack problem. Give a Greedy algorithm for fractional Knapsack Problem.
  • Write pseudo code for DFS and calculate its time complexity. Explain briefly how DFS differs from BFS
  • Write Prim’s Algorithm. How Prim’s algorithm differs from Kruskal’s algorithm.

Illustrate with the help of an example

Q6: Answer the following:                                                                                                                                                     (10 marks)

  • Write a context free grammar to generate palindromes of even length Over alphabet

∑= {a, b}.

  • Write the finite automata corresponding to the regular expression (a+b)*ab.
  • Explain the Chomsky’s Classification of grammars. What is an ambiguous grammar? How do you prove that a given grammar is ambiguous? Explain with an example.
  • If L1 and L2, are context free languages then, prove that L1 U L2 is a context free language.
  • Construct a turing machine that copies agiven string over {a, b}. Further find a computation of TM for the string ‘aab’.

Q7: Differentiate between :                                                                                                                                                     (10 marks)

  • Strassen’s Algorithm & Chain Matrix Multiplication algorithm
  • Context free & Context sensitive Language
  • NP-Complete & NP Hard Problem
  • Greedy technique and Dynamic programming technique
  • Decidable & Un-decidable problems

Q8: Write note on each of the following:                                                                                                                                                     (10 marks)

  • Verte Cover Problem
  • Rice theorem
  • Post correspondence problem
  • Halting problem
  • K-colourability problem

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4

Course Code:MCS-032
Course Title:Object Oriented Analysis and Design
Assignment Number:MCA (III)/032/Assignment/2020-21
Maximum Marks:100%
Weightage:25%
Last Dates for Submission:31st October, 2020 (For July, 2020 Session)
 :15th April, 2021 (For January, 2021 Session)

There are eight questions in this assignment which carried 80 marks. Rest 20 marks are for viva-voce. Answer all the questions. Wherever required, you may write C++/java program, as part of solutions. Please go through the guidelines regarding assignments given in the Program Guide for the format of presentation.

Q1: What is OOAD? Explain advantages of OOAD over structured system analysis and design.

(10 Marks)

Q2: What isGeneralization? How is it different fromSpecialization explain with the help of

examples and UML diagrams.                                                                                                                                          (10 Marks)

Q3: What isa  class? How class is different from object? Draw an Object diagram for Online

Banking System.(10 Marks)
Q4:  (a)  Explain advantage of use case diagram with the help of an example.(5
Marks) 
(b)  Draw a sequence diagram for Online Railway Ticket Booking.(5
Marks) 
Q5: (a) What is need of concurrency control is object oriented system modeling? 
Explain with of example.(5
Marks) 
(b)What is aggregation? Explain with an example.(5
Marks) 

Q6: What isAssociation? What are its types? Explain howAssociations are implemented with

the help of an example.                                                                                                                                                     (10 Marks)

Q7: Draw a 1st and 2ndlevel DFDs for Online Banking System. Make necessary assumptions

required.

(10

Marks)

Q8: Write short note on followings (minimum in 300 words)

:

(10 Marks)

i)           UML Diagrams

ii)          States of a System

iii)         Integrity Constraints

iv)         Persistent Objects

5

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Course Code:MCS-033
Course Title:Advanced Discrete Mathematics
Assignment Number:MCA(III)/033/Assignment/2020-21
Maximum Marks:100
Weightage:25%
Last Dates for Submission:31st October, 2020 (For July, 2020 Session)
 :15th April, 2021 (For January, 2021 Session)

Answer all the questions in the assignment which carry 80 marks in total. 20 marks are for viva voce. You may use illustrations. Place go through the guidelines regarding assignments given in the Programme Guide for the format of presentation.

Q1. Is a Hamiltonian graph Eulerian ? Is a Eulerian graph Hamiltonian ? Show(5Marks)
  with the help of a suitable example.  
Q2.(a)Solve    +1+1 = 5    for n≥ 0,  0= 2 by Substitution method.(5Marks)
 (b)Solve the recurrence by using iterative approach :(5Marks)

=            −1  + 2n + 3,  0= 4.

Q3.                 Define a recurrence relation. Describe the following problems with the (10 Marks) help of examples which can be solved through Divide and Conquer

technique and Show its recurrence relation.

(i)      Binary Search

(ii)    Merge Sort

Solve these recurrence relations  with a substitution method.

Q4.To multiply two n-digit numbers, one must do normally   2digit-times-(5Marks)
 digit multiplications. Use a divide and conquer algorithm to propose an  
 algorithm when n is a power of 2.  
Q5.Find a recurrence relation and initial conditions for 4, 14, 44, 134, 404, …(5Marks)
Q6.Prove/show the followings:(16Marks)

·      the sum of the degrees of the vertices of G is twice the number of edges

·      If W is a u-v walk joining two distinct vertices u and v, then there is a path joining u and v contained in the walk using the principles of mathematical induction

·      A connected graph G is Eulerian if and only if the degree of each of its vertices is even.

·             If G  is  a  connected  planar  (p,q)-graph,  then the  number  r  of the

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   regions of G is given by r = q – p +2  
Q7. Show the followings:(8Marks)
  ·Show that for a subgraph H of a graph G, ∆(H) ≤ ∆ (G)  
  ·Show that    ,  is not Hamiltonian when m + n is odd  
Q8. Define homogeneous recurrence relation. Write the first order and second(6Marks)
  order homogeneous  recurrence relations with constant coefficients giving  
  an example for each.Solve the following recurrence relation:  
    −1 – 6    −2 = 0 for n ≥ 2 given that  0 = −1, 1= 8  
Q9.(a)Find chromatic number of bipartite graph Km, n.(4Marks)
 (b)Show that K3, 3 is non-planar.(3Marks)
 (c)Construct a 5-regular graph on 10 vertices.(3Marks)
Q10. Solve the recurrence=    −1  + 2;  0 = 3(5Marks)

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Course Code:MCS-034
Course Title:Software Engineering
Assignment Number:MCA(3)/034/Assign/2020-21
Maximum Marks:100
Weightage:25%
Last Dates for Submission:31st October, 2020 (For July, 2020 Session)
 :15th April, 2021 (For January, 2021 Session)

This assignment has 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.

Q1:

Assume that you are assigned responsibility of developing an Online Admission System (OAS)for a University.OAS will have all fields such asStudent’sname, address, Mobilenumber, email , AadhaarNumber, PAN Number, Educational Qualifications, etc. OAS will also have provision for student to upload the copies or all relevant documents. OAS should generate a provisional Enrollment number and also assign a Study Center to the student. There should be provision for generation of reports. Make necessary assumptions.

For developing OAS as specified above,

(a) Which SDLC paradigm will be selected. Justify your answer.(10
marks) 
(b) List the functional and non-functional requirements.(20
marks) 
(c) Estimate cost.(15
marks) 
(d) Estimate effort.(15
marks) 
(e) Develop SRS using IEEE format.(15
marks) 
(f)  List queries for whom Reports can be generated(5
marks) 

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8

Course Code:MCS-035
Course Title:Accountancy and Financial Management
Assignment Number:MCA(III)/035/Assignment/2020-21
Maximum Marks:100
Weightage:25%
Last Dates for Submission:31st October, 2020 (For July, 2020 Session)
 :15th April, 2021 (For January, 2021 Session)

Note: This assignment has five 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.

Q1.From the  following  Trial Balance  of  Raghu  Ram Associates,  prepare  (16 Marks)
 Trading and Profit & Loss Account for the year ended 31st December,
 2019 and a Balance Sheet as on that date:-  
       
  Dr. BalancesRs.Cr. BalancesRs. 
       
  Opening Stock22,000Sales3,70,000 
       
  Purchases1,80,000Purchase5,000 
    Return  
       
  Sales Return7,000Discount6,200 
       
  Carriage Inwards2,600Sundry27,000 
    Creditors  
       
  Carriage Outwards800Bills Payable2,800 
       
  Wages40,000Capital70,000 
       
  Salaries27,500   
       
  Plant & Machinery1,00,000   
       
  Furniture8,000   
       
  Sundry Debtors42,000   
       
  Bills Receivable2,500   
       
  Cash in Hand6,500   
       
  Travelling Expenses3,500   
       
  Lighting2,400   
       
  Rent and Taxes6,200   
       
  General Expenses8,500   
       
  Insurance1,500   
       
  Drawings20,000   
       
   4,81,000 4,81,000 
       

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Adjustments:-

  • Stock on 31st December, 2019 was valued at Rs. 25,000 (Market Value Rs. 35,000).
  • Wages outstanding for December, 2019 amounted to Rs. 5,000.
  • Salaries outstanding for December, 2019 amounted to Rs. 3000.
  • Prepaid insurance amounted to Rs. 500.
  • Provide depreciation on Plant and Machinery at 5% and on Furniture at 20%.
Q2.Following are the balance sheets of Shanti Niketan limited as on 31st  (16 Marks)
 December, 2018 and 2019.     
         
  Liabilities20182019Assets20182019 
   (Rs.)(Rs.) (Rs.)(Rs.) 
         
  Share65,00085,000Goodwill3,0002,500 
  Capital12,00014,500Buildings5200050,000 
    
  Reserves8,6009000Plant40,00041,000 
    
  P. & L A/c20,000Stock20,50018,800 
    
  Bank loan  Debtors41,00036,200 
      
  (Long-term)40,00035,000Cash100650 
    
  Creditors11,0007,500Bank1850 
    
  Bills      
  Payable      
         
   1,56,6001,51,000 1,56,6001,51,000 
         

Taking into account the following additional information, you are required to prepare funds flow statement and statement of changes in working capital.

  • Dividend paid was Rs.6,000/-
  • Rs.3,600/- was written off as depreciation on plant and Rs.2,950/- on buildings.
  • Profit on sale of plant was Rs.3,000/-

Q3.                 Describe the main ratios which you consider significant while interpreting (16 Marks) the published accounts of a Company and explain the inferences which may be drawn from them.

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Q4.                 “For most investment decisions that a firm faces, NPV is either a superior (16 Marks) decision criterion, or is at least as good as the competing techniques.” In

what investment situation is the profitability index better than the NPV?

Q5.                 “Efficient cash management will aim at maximizing the cash inflows and (16 Marks) showing cash outflows” Discuss.

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11

Course Code:MCSL-036
Course Title:Lab course for OOAD, S/E and Accountancy &
  Financial Management
Assignment Number:MCA(III)/L036/Assignment/2020-21
Maximum Marks:100
Weightage:25%
Last Dates for Submission:31st October, 2020 (For July, 2020 Session)
 :15th April, 2021 (For January, 2021 Session)

Note: The assignment has three components. Answer all the questions in each section. Assignment marks of section A, section B and section C are 13, 13 and 14 respectively. The lab records of section A, section B and section C carry 13, 13 and 14 respectively. The rest 20 marks are for Vive voce.

Section A: Object Oriented Analysis and Design

Q1.ASoftware  company  wants  to  develop  taxi  booking  app  having  the  
 following features :  
 ·Registration/login  
 ·  Real-time tracking  
 ·Navigation feature  
 ·  End of the trip option  
 ·Different stop option  
 ·Cash payment option  
 ·  Estimated time of arrival  
 ·  Features to calculate the price before boarding  
 ·  Review and rating system  
 Do the following tasks:  
 (1)Draw an use case diagram(2Marks)
 (2)Define all classes and the  class diagram(4Marks)
 (3)Draw a simple object model(4Marks)
 (4)Draw a state transition diagram(3Marks)
 Section B: MCS-34: Software Engineering  
Q2.For the cab booking app  problem discussed in a section A do the following  
 tasks:  
 (1)Develop SRS(4Marks)
 (1)Draw Data Flow Diagrams (Level 0 and  Level 1)(4Marks)
 (2)Draw an E-R diagram and its related normalized tables(5Marks)

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Section C: MCS-035: Accountancy and financial Management

Q3.Post the following transactions of a software development company  to prepare (14 Marks)
 the journal, ledger and trial balance  
      
  March 2020TransactionAmount 
      
  5th MarchStarted business with cash4,50000.00 
      
  10 MarchDeposited In the bank1,00000.00 
      
  15 MarchPurchased computers on2,00000.00 
   credit  
      
  18 MarchPurchased  s/w and1,30000.00 
   peripheral devices on credit  
      
  20 MarchPurchase Furniture for cash60,000.00 
      
  22 MarchSold s/w for cash90,000.00 
      
  25 MarchSold s/w on credit55,000.00 
      
  27 MarchPaid salary to staff60,000.00 
      
  31 MarchPaid rent40,000.00 
      

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13

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