Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) MCA (Master of Computer Application) 2020 March 2nd Sem 26052 Mathematical Foundations Of Computer Science Previous Question Paper
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
MCA (2014 Batch) (Sem.?2)
MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
Subject Code : MCA-201
M.Code : 26052
Time : 3 Hrs. Max. Marks : 100
INSTRUCTIONS TO CANDIDATES :
1. SECTIONS-A, B, C & D contains TWO questions each carrying TWENTY marks
each and students has to attempt any ONE question from each SECTION.
2. SECTION-E is COMPULSORY consisting of TEN questions carrying TWENTY
marks in all.
SECTION-A
1. a) Define a Hamiltonian circuit in a graph. Give an example of a graph which has a
Hamiltonian circuit and an example of a graph which does not have a Hamiltonian
circuit.
b) State and prove five-color problem.
2. A connected multigraph has an Euler circuit. Prove that each of its vertices has even
degree.
SECTION-B
3. In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken
Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had
taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all
the three subjects. Find the number of students studying (a) only Physics; (b) Physics and
Chemistry but not Mathematics; (c) Atleast one of the three subjects.
4. a) Partition the set A = {1, 2, 3, ...., 10} using the minsets generated by B1 = {1, 7, 8},
B2 = {1, 6, 9,10}, B3 = {1, 9, 10}. Also represent the minsets thus generated through
a Venn diagram.
b) Define a Relation. Discuss the properties of relations.
SECTION-C
5. Prove by the principle of mathematical induction that for all n ? ? N:
1
2
+ 2
2
+ 3
2
+ ?????..+ n
2
=
1
6
n (n+1) (2n+l)
6. Show that ( ? x) (P(x) v Q(x)) => ( ? x) P(x) v ( ?x) Q(x).
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1 | M-26052 (S14)-1644
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
MCA (2014 Batch) (Sem.?2)
MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
Subject Code : MCA-201
M.Code : 26052
Time : 3 Hrs. Max. Marks : 100
INSTRUCTIONS TO CANDIDATES :
1. SECTIONS-A, B, C & D contains TWO questions each carrying TWENTY marks
each and students has to attempt any ONE question from each SECTION.
2. SECTION-E is COMPULSORY consisting of TEN questions carrying TWENTY
marks in all.
SECTION-A
1. a) Define a Hamiltonian circuit in a graph. Give an example of a graph which has a
Hamiltonian circuit and an example of a graph which does not have a Hamiltonian
circuit.
b) State and prove five-color problem.
2. A connected multigraph has an Euler circuit. Prove that each of its vertices has even
degree.
SECTION-B
3. In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken
Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had
taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all
the three subjects. Find the number of students studying (a) only Physics; (b) Physics and
Chemistry but not Mathematics; (c) Atleast one of the three subjects.
4. a) Partition the set A = {1, 2, 3, ...., 10} using the minsets generated by B1 = {1, 7, 8},
B2 = {1, 6, 9,10}, B3 = {1, 9, 10}. Also represent the minsets thus generated through
a Venn diagram.
b) Define a Relation. Discuss the properties of relations.
SECTION-C
5. Prove by the principle of mathematical induction that for all n ? ? N:
1
2
+ 2
2
+ 3
2
+ ?????..+ n
2
=
1
6
n (n+1) (2n+l)
6. Show that ( ? x) (P(x) v Q(x)) => ( ? x) P(x) v ( ?x) Q(x).
2 | M-26052 (S14)-1644
SECTION-D
7. a) Find the inverse of the matrix :
1 1 0
1 0 1
1 2 2
b) Discuss matrix addition, scalar multiplication and multiplication of matrices by taking
suitable example.
8. Solve the following system using Gauss-Jordan elimination :
3x
1
+ x
2
+ 7x
3
+ 2x
4
= 13
2x
1
? 4x
2
+ 14x
3
? x
4
= ?10
5x
1
+ 11x
2
? 7x
3
+ 8x
4
= 59
2x
1
+ 5x
2
? 4x
3
? 3x
4
= 39
SECTION-E
9. Write briefly :
a) What is a bipartite graph and a complete bipartite graph?
b) Differentiate between directed and undirected graph.
c) What is chromatic number?
d) What is a universal set? Give an example.
e) State the DeMorgan?s laws.
f) What are the different types of quantifiers? What is the purpose of each?
g) Define Proposition.
h) What is the difference between Equivalence and Implication?
i) What is transpose of a matrix? Give an example.
j) What is an Identity matrix? Give an example.
NOTE : Disclosure of Identity by writing Mobile No. or Marking of passing request on any
paper of Answer Sheet will lead to UMC against the Student.
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This post was last modified on 22 March 2020