Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 1st Sem (First Semester) Regulation-R15 2019 April-May 821AA Mathematical Foundations Of Computer Science Previous Question Paper
R15
Code No:821AA
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
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This post was last modified on 16 March 2023