Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 1st Sem (First Semester) Regulation-R13 2019 April-May Mathematical Foundations Of Computer Science Previous Question Paper
R13
Code No:811AA
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA I Semester Examinations, April/May - 2019
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) Give the converse, contrapositive and inverse of the following statement:
The hut will destroy if there is a cyclone.
[4]
b) Define the terms: Equivalence relation, Partially ordered relation and Totally ordered
relation. Give examples for each.
[4]
c)
How many integers between 1 and 1000 inclusive have the sum of the digits equal to 7.
[4]
d)
Solve the recurrence relation an = nan-1 for n 1, given that a0 = 1.
[4]
e) What is a Hamiltonian graph? Discuss briefly.
[4]
PART - B
5 ? 8 Marks = 40
2.a)
Show that (PS) can be derived from the premises P Q, Q R, RS using CP
rule.
b)
Obtain the PCNF of the (P(Q R)) ( P (Q R)).
[4+4]
OR
3.a)
Show that (x) (p(x) Q(x)) (x) p(x) (x) Q(x).
b)
Use truth tables to establish whether the following statement forms a tautology
or a contradiction or neither. P (Q R).
[4+4]
4.
Define equivalence classes. Let Z be the set of integers and Let R be the relation called
"congruence modulo 3" defined by R={<x,y> / xZ yZ (x-y) is divisible by
3}. Determine the equivalence classes generated by the elements of Z.
[8]
OR
5.a)
Draw the Hasse diagram for the Poset. <{2,4,5,10,12,20,25}, / >.
b)
Let R = { (b,c), (b,e), (c,e), (d,a), (c,b), (e,c)} be a relation on the set A = {a,b,c,d,e}.
Find the transitive closure of the relation R.
[4+4]
6.a)
What is the coefficient of x2y5 in (2x-9y)10?
b)
How many 6 digit numbers without repetition of digits are there such that the digits are
all non-zero and 1 and 2 do not appear consequently in either order?
[4+4]
OR
7.
State and explain Multinomial theorem with an example illustration.
[8]
8.
Solve the recurrence relation an-6an-1+9an-2 = 0 where a0=1 and a1= 6.
[8]
OR
9.
Using generating function, solve the yn+2 ? 4yn+1 + 3yn = 0, given y0 = 2, y1 = 4. [8]
10.
Explain prim's algorithms with suitable example.
[8]
OR
11.
State Graph coloring problem and describe its importance in computations.
[8]
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This post was last modified on 16 March 2023