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

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

This post was last modified on 22 March 2020