Kerala university Question Paper- Second semester BCA -MATHEMATICS

Kerala university Question paper 

Second semester BCA degree examination May 2011 (2007 scheme)

MATHEMATICS 

Time:3 hours                                                                           Max Marks:75

Section A

Answer any ten questions. Each question carries 3 marks.

1.      Find the truth table of P’ ^ Q

2.      Express the Boolean expression E(x,y,z) = (x’+y)’ + x’y in complete sum of products form.

3.      When you say that an argument is a fallacy?

4.      A, B ,C are three sets such that A intersection B= A intersection C. is it means that B=C ? Justify.

5.      Consider the function f(x)=x²+3x+1 and g(x)=2x-3. Find (gof)

6.      Define characteristic function.

7.      Define fuzzy set. When you say that a fuzzy set A is contained in a fuzzy set B?

8.      Prove that in a group G (a^-1)^-1=a where a in G

9.      Show that the set of natural numbers is not a group with respect to addition.

10.  Define Hamming weight of a code word

11.  Draw the graph G(V,E)

E={(V1,V4) , (V1,V6) , (V3,V4) , (V4,V4), (V3,V5) , (V6,V6)}

V= {V1, V2, V3, V4, V5, V6}

12.  What is a directed acyclic graph?

13.  Write a grammar for the language L={aⁿ bⁿ :n> = 0}

SECTION – B

Answer any 5 questions. Each question carries 6 marks.

14.  Verify that the proposition (p^q)^ (p  V q)’ is a contradiction

15.  Given X={1,2,3,4,5,6,7,8,9}. Give two different partitions of X.

16.  Let R= {(1,3), (1,4) , (3,2) , (3,3) , (3,4) be a relation on A={1,2,3,4}. Find the domain and range of R. draw the directed graph of R.

17.  Prove that the intersection of any two subgroups of a group G is also a subgroup of G

18.  Define integral domain. Give an example.

19.  Explain depth first searching strategy on graphs.

20.  Consider the graph in the figure. Determine

a.      Pendent vertices

b.      Pendent edges

c.       Odd vertices

d.      Even vertices

e.      Incident edges

f.        Adjacent vertices

21.  Describe a finite automation for the language whose grammar is

{{S} , {a,b}, S , {S àabS , Sàb }}

SECTION C

Answer any one question. Each question carries 15 marks

22.  a. test the validity of the argument

If I study then I will not fail in Mathematics.

If I do not play basketball, then I will study.

But I failed in mathematics

Therefore I played basket ball

b. Define warshall’s algorithm

c. Let A= {1,2,3,4} and R={ (1,2) , (2,3) ,(3,4),(2,1)}

Find the transitive closure by using Warshall’s algorithm

23.  a. Explain how will you solve the following equations in MATLAB

            5x = 3y -2z +10

            8y + 4z = 3x +20

            2x + 4y – 9z = 9

b. In a class of 25 students 12 have taken economics, 8 have taken economics but not political science. Find the number of students who have taken

1. economics and political science

2. political science but not economics.