Download JNTUH MCA 1st Sem R13 2017 August 811AA Mathematical Foundations Of Computer Science Question Paper

Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 1st Sem (First Semester) Regulation-R13 2017 August 811AA Mathematical Foundations Of Computer Science Previous Question Paper

R13

Code No: 811AA















JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

MCA I Semester Examinations, August - 2017

MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

Time: 3hrs













Max.Marks:60


Note: This question paper contains two parts A and B.


Part A is compulsory which carries 20 marks. Answer all questions in Part A.



Part B consists of 5 Units. Answer any one full question from each unit. Each



question carries 8 marks and may have a, b, c as sub questions.



PART - A



















5 ? 4 Marks = 20



1.a) What do you mean by tautological implication? Give an example.

[4]

b) Explain transitive closure property.









[4]

c)

Write about binomial and multinomial theorems.







[4]

d)

What are generating functions? Give an example.





[4]

e)

Write about binary trees.













[4]



PART - B

















5 ? 8 Marks = 40

2.a)

Express P ( P Q) in terms of only.

b)

Define Universe of Discourse? Symbolize the given statement with and without
using the set of positive numbers as the Universe of Discourse. Statement:
"Given any positive integer there is a greater positive integer."



[4+4]

OR

3.

Give an over view of theory of inference for predictive calculus.

[8]


4.

S = { 1, 2, 3, 4} and A= S?S. Define a relation R on A by
(a, b) R (a', b') a+b = a' +b'.



a) Show that R is an equivalence relation.



b) Compute A/R.















[4+4]

OR

5.a)

Let (S,*) and (T,*') be Semi Groups. Show that the function f: S?T S defined
by f(s,t)= s is a Homomorphism of the Semi Group S?T onto the Semi Group
S?

b) Give an over view of lattice as an algebraic structures.





[4+4]


6.a)

Explain pigeon hole principles and its applications.

b)

Explain the principles of inclusion and exclusion.





[4+4]

OR

7.

Determine the coefficients of x2y3 and x3y2in (2x+3y)10.





[8]





8.

What are characteristic roots? Explain how characteristics roots can be used in
solving recurrence relation using examples.







[8]

OR

9.

Write short notes on how each of the following can be used in solving recurrence
relation.



a) Function of sequences



b) Coefficients of generating functions.









[4+4]


10.

Explain the following with examples:



a) Hamiltonian Graphs



b) Planar graphs and multi ?graphs.









[4+4]

OR

11.

Write Kruskal's Algorithm and explain. Find the minimum cost spanning tree for
the given graph? And calculate its minimum cost.





[8]







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