Download PTU MCA 2020 March 2nd Sem 72876 Mathematical Foundations Of Computer Science Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) MCA (Master of Computer Application) 2020 March 2nd Sem 72876 Mathematical Foundations Of Computer Science Previous Question Paper

1 | M-72876 (S6)-1670

Roll No. Total No. of Pages : 02
Total No. of Questions : 09
MCA (2015 & Onward) (Sem.?2)
MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
Subject Code : MCA-201
M.Code : 72876
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTIONS-A, B, C & D contains TWO questions each carrying TEN 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. What is meant by simple graph? Show that degree of a vertex in a simple graph of n-
vertices cannot exceed n-1.
2. a) What is Euler Graph? State and explain the condition for checking whether a given
graph is Eulerian or not.
b) What is meant by Chromatic Number? What are various applications of graph
colouring in graph theory?
SECTION-B
3. Prove that set of real numbers in the set [0, I] is uncountable set. Justify the proof.
4. State and prove the following concepts :
a) De-Morgan Laws
b) If a relation R on set A is reflexive, so is R
?1

SECTION-C
5. If P, Q and R are three prepositions.
Prove that (P ? (Q ? R)) ? ((P ? Q) ? (P ? R)) ?
FirstRanker.com - FirstRanker's Choice
1 | M-72876 (S6)-1670

Roll No. Total No. of Pages : 02
Total No. of Questions : 09
MCA (2015 & Onward) (Sem.?2)
MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
Subject Code : MCA-201
M.Code : 72876
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTIONS-A, B, C & D contains TWO questions each carrying TEN 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. What is meant by simple graph? Show that degree of a vertex in a simple graph of n-
vertices cannot exceed n-1.
2. a) What is Euler Graph? State and explain the condition for checking whether a given
graph is Eulerian or not.
b) What is meant by Chromatic Number? What are various applications of graph
colouring in graph theory?
SECTION-B
3. Prove that set of real numbers in the set [0, I] is uncountable set. Justify the proof.
4. State and prove the following concepts :
a) De-Morgan Laws
b) If a relation R on set A is reflexive, so is R
?1

SECTION-C
5. If P, Q and R are three prepositions.
Prove that (P ? (Q ? R)) ? ((P ? Q) ? (P ? R)) ?
2 | M-72876 (S6)-1670

6. Using Principle of Mathematical Induction, prove that :
a + (a + d) + (a + 2d) + ... + (a + (n ? 1 )d) =
2
n
(2a + (n ? l)d)
SECTION-D
7. Does scalar multiplication of two matrices commutative? (Yes/No), Also justify the result
using an appropriate example.
8. Solve the following equations using Gauss Jordan Method :
2x ? y + 3z = 9, x + y + z = 6, x ? y + z = 2
SECTION-E
9. Write briefly :
a) Define directed graph.
b) Write a short note on bipartite graph.
c) Discuss briefly the concept of Cartesian product of a set.
d) Define Partition of a set.
e) What is the application of tautology in algebra of logic?
f) Discuss the use universal quantifier by taking an example.
g) Describe the application of transpose of a matrix in Computer Science.
h) What is meant by rank of a square matrix?
i) Why matrix inversion is needed in real world Computer Applications?
j) Define equivalence relation.

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.
FirstRanker.com - FirstRanker's Choice