Download JNTUH MCA 1st Sem R17 2019 April-May 841AA Aprilmay Mathematical Foundations Of Computer Science Question Paper

Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 1st Sem (First Semester) Regulation-R17 2019 April-May 841AA Aprilmay Mathematical Foundations Of Computer Science Previous Question Paper


R17

Code No:841AA















JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

MCA I Semester Examinations, April/May - 2019

MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

Time: 3hrs















Max.Marks:75


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

Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B
consists of 5 Units. Answer any one full question from each unit. Each question carries
10 marks and may have a, b, c as sub questions.



PART - A



















5 ? 5 Marks = 25



1.a)

Construct the truth table (PQ) (QR) (P~R).







[5]

b)

Let G be the set of real numbers not equal to-1 and be defined by a*b=a+b+ab.
Prove that < G,* > is an abelian group.











[5]

c)

How many integers between 1 and 100 have a sum of digits of integer numbers equal to
10?



















[5]

d)

Find the particular solution for the following difference equation an+5an-1+6an-2=42.4n

























[5]

e) What do you mean by Isomorphic graph? When will you say that two graphs are

isomorphic?

















[5]

PART - B

















5 ? 10 Marks = 50

2.

Obtain the Principal Disjunctive normal form of

P[(PQ)~(~Q~P)]















[10]

OR

3.

Show that the following argument is valid. If today is Tuesday, I have a test in
Mathematics or Economics. If my Economics professor is sick, I will not have a test in
Economics. Today is Tuesday and my Economics professor is sick. Therefore I have a
test in Mathematics.















[10]


4.

Consider the group G = {1,2,4,7,8,11,13,14} under multiplication modulo 15. Construct
the multiplication table of G and verify whether G is cycle or not.



[10]

OR

5.a)

Let f: RR and g: RR, where R is the set of real numbers. Find fog and gof, where
f(x) = x2-2 and g(x) = x+4. State whether these functions are injective, surjective, and
bijective.

b)

Define Lattice and write various properties of Lattice.







[5+5]


6.

Using binomial identities evaluate the sum1.2.3+2.3.4+......+(n-2)(n-1)n.

[10]

OR

7.

Suppose there are 15 red balls and 5 white balls. Assume that the balls are
distinguishable and that a sample of 5 balls is to be selected.
a) How many samples of 5 balls are there?
b) How many samples contain all red balls?
c) How many samples contain 3 red balls and 2 white balls?

d) How many samples contain at least 4 red balls?







[10]





8.

Solve the recurrence relation an-7an-1+10an-2=0 for n2 where a0=10 and a1=41. [10]

OR

9.

Explain and illustrate various ways of solving the recurrence relation.



[10]


10.

State and explain the 4-color problem for planar graphs.





[10]

OR

11.

What is planar graph? Show that following graph is planar.





[10]




a

b













g



f

e



d

c




















---ooOoo---




















This post was last modified on 16 March 2023