Monday, August 20, 2012

IGNOU MCA -mcs-033 solved assignments 2012 -2013

Course Code : MCS-033

Course Code   : MCS-033
Course Title :  Advanced Discrete Mathematics
Assignment Number  :  MCA(3)/033/Assign/2012
Maximum Marks :  100
Weightage  :  25%
Last Dates for Submission : 15
October, 2012 (For July 2012 Session)
April, 2013 (For January 2013 Session)
There are FIVE questions of total 80 marks 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: (a) Using Karnaugh map, simplify
X': A'BC'D'+ ABCD+ ABCD'+ ABCD'  (5 Marks)
(b) Describe Konigsberg’s 7 bridges problem  and Euler's
solution  to  it. B                  (5 Marks)
(c) Show  that  the sum of  the degrees  of all vertices of a
graph  is twice the number of edges  in  the graph.  (5 Marks)
Question 2: (a) Let G be a non directed graph with 12 edges. If G has 5
vertices each of degree 3 and the rest   have degree less
than 3, what is the minimum number of vertices G
can have?          (5 Marks)
(b) What is Graph Cloning? Explain K-edge cloning with
an example.                                   (5 Marks)
(c) Let f(n)= 5 f(n/ 2) + 3 and f(1) = 7. Find f(2k) where k
is a positive integer. Also estimate f(n) if f is an increasing
function.        (5 Marks)
Question 3: (a) Define r-regular graph. Give an example of 3-regular
graph.                                            (5 Marks)
f is bijective function with Range of f as the
(5 Marks)6
(c) What are isomorphic graphs? Are the graphs given below isomorphic?
Explain why?      (7 Marks)
(i)                                                                 (ii)  
(d) What is connected Graph? Construct a graph with chromatic number 5.
(4 Marks)
Question 4:        
(a) Solve following recurrence relations                                   (9 Marks)            
i) =  + n,  = 2              
       using substitution method
ii) 9
iii) =
(b) Write a short note on  Tower  of  Hanoi  Problem.  How can it be
solved using recursion ? (4 Marks)
Question 5:
(a) Show that for subgraph H of a graph G                                             (4 Marks)
                            ∆ (H) ≤ ∆ (G)
(b) What is Divide and Concuer relations? Explain  with an example?       (4 Marks)
(c)  Find a power series associated with the problem  where we have to
find a number of ways to select 10 people to form and expert committee
from 6 Professors and 12 Associate Professors.  (4 Marks)
(d) Tree is a Bipartite Graph” justify the statement with an example?   (4 Marks)

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lisa kabi said...

plz post the solution

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