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

Roll No.

Total No. of Questions : 09 Total No. of Pages : 02

MCA (2015 & Onward) (Sem.-2)

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MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

Subject Code : MCA-201

M.Code : 72876

Time: 3 Hrs. Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :

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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?

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SECTION-B

1. Prove that set of real numbers in the set [0, I] is uncountable set. Justify the proof.
2. 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

1. If P, Q and R are three prepositions. Prove that (P ? (Q ? R)) ? (P ? Q) ? (P ? R))

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2. Using Principle of Mathematical Induction, prove that :
   a + (a + d) + (a + 2d) + ... + (a + (n-1)d) = (n/2)(2a + (n - 1)d)

SECTION-D

1. Does scalar multiplication of two matrices commutative? (Yes/No), Also justify the result using an appropriate example.
2. Solve the following equations using Gauss Jordan Method :
   2x - y + 3z = 9, x + y + z = 6, x - y + z = 2

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SECTION-E

1. 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.
   

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   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?
   

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   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.

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