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Writing anything except Roll Number on question paper will be deemed as an act of
indulging in unfair means and action shall be taken as per rules.
प्रश्नपत्र पर रोल नम्बर के अतिररक्त कु छ भी तलखना अनुतिि साधनों का प्रयोग माना जायेगा िथा
तनयमानुसार काययवाही की जायेगी|
Roll No._________________
End Semester Examination  Summer 2014
MCA Semester IV
MODELQUESTION PAPER
MCA415A-DISCRETE MATHEMATICS
Time: 3 Hrs
Note:
1.
MM: 80
ALL questions are compulsory in section A. The answers of these questions are limited upto
30 words each. Each question carries 2 marks.
2.
Attempt FIVE questions in all from Section B, selecting ONE question either A or B from each
question. Answer of each question shall be limited upto 250 words. Each question carries 6
marks.
3.
Attempt THREE questions in all from section C. Answer of each question shall be limited upto
500 words. Each question carries 10 marks.
SECTION A
1.
a.
Define power set of a set.
b.
There are 8 chairs in a room. In how many ways 5 student can sit on
them.
c. Obtain the disjunction normal form of the form (p→q)ᶺ(͠pᶺq)
d. Define Eulerian graph.
e.
Define spanning trees.
f.
Define rooted trees.
g.
Draw a directed graph of the set R={(1,2), (1,3), (2,3), (3,2), (2,2)}
h.
Define a partial order set.
i.
Define Floor and ceiling functions.
j.
Write inverse function of f(x)=2x-3 if f:R→R
SECTION B
2.
A. In an advertising survey conducted on 200 people, it was found that
P.T.O.
140 drink tea, 80 drink coffee, and 40 drink both. Find how many
drink neither?
OR
B. State and prove generalised pigeonhole principle.
3.
A. Form the truth table of 𝑝 ∧ 𝑞 ∨ ͠𝑟 and (𝑝 ∧ 𝑞) ∨ ͠(𝑟) and explain where
differ.
OR
B. Determine whether the followin statement is tautologies
(p→q)∨(q→p)
4.
A. If T is binary tree with n vertices and of height h; then
(h+1)≤n≤(2ℎ+1 − 1)
OR
B. Find the minimal spanning tree of the following labelled connected
graphG.
5.
A. Q.14 Prove that the relation R1 in the set NxN, where N is the set of
natural numbers, defined as follows: (a,b)R1(c,d) ⇔a+d=b+c
OR
B. If (L, ⊂,∪,∩) is a lattice then (L, ⊇,∩,∪) is also a lattice.
6.
A. Let the function f: R→R be defined by f(x)=x2+3 and g:R→R be
defined by x/(x+1). Find fog and gof.
OR
B. If G={1,2,3,4,5,6} then prove that (G, X7) is an abelian group.
SECTION C
7.
𝑛(𝑛+1)2𝑛+1)
8.
Show that P(n)=12+22+32+…………..+n2=
,
n≥1 by
6
mathematical induction.
Solve the travelling salesperson problem for the following weighted graph:
9.
Prove that A tree with n vertices, has precisely (n-1) edges.
10. Find the closure of reflexive, symmetric and transitive relation on the set
A={1,2,3} defined by R={(1,1),(1,2),(2,3),(3,3)}.
11. Show that the set of real numbers of the form m+n√2, m,n∊Z with
ordinary addition and multip[lication of numbers form a ring.
P.T.O.
Writing anything except Roll Number on question paper will be deemed as an act of
indulging in unfair means and action shall be taken as per rules.
प्रश्नपत्र पर रोल नम्बर के अतिररक्त कु छ भी तलखना अनुतिि साधनों का प्रयोग माना जायेगा िथा
तनयमानुसार काययवाही की जायेगी|
Roll No._________________
End Semester Examination  Summer 2014
MCA Semester IV
MODELQUESTION PAPER
MCA415A-DISCRETE MATHEMATICS
Time: 3 Hrs
Note:
1.
MM: 80
ALL questions are compulsory in section A. The answers of these questions are limited upto
30 words each. Each question carries 2 marks.
2.
Attempt FIVE questions in all from Section B, selecting ONE question either A or B from each
question. Answer of each question shall be limited upto 250 words. Each question carries 6
marks.
3.
Attempt THREE questions in all from section C. Answer of each question shall be limited upto
500 words. Each question carries 10 marks.
SECTION A
1.
a. Define power set of a set.
b. There are 8 chairs in a room. In how many ways 5 student can sit on
them.
c. Obtain the disjunction normal form of the form (p→q)ᶺ(͠pᶺq)
d.
Define Eulerian graph.
e.
Define spanning trees.
f.
Define rooted trees.
g.
Draw a directed graph of the set R={(1,2), (1,3), (2,3), (3,2), (2,2)}
h.
Define a partial order set.
i.
Define Floor and ceiling functions.
j.
Write inverse function of f(x)=2x-3 if f:R→R
SECTION B
2.
A. In an advertising survey conducted on 200 people, it was found that
140 drink tea, 80 drink coffee, and 40 drink both. Find how many
drink neither?
OR
B. State and prove generalised pigeonhole principle.
3.
A. Form the truth table of 𝑝 ∧ 𝑞 ∨ ͠𝑟 and (𝑝 ∧ 𝑞) ∨ ͠(𝑟) and explain where
differ.
OR
B. Determine whether the followin statement is tautologies
(p→q)∨(q→p)
A. If T is binary tree with n vertices and of height h; then
(h+1)≤n≤(2ℎ+1 − 1)
OR
B. Find the minimal spanning tree of the following labelled connected
graphG.
4.
5.
A. Q.14 Prove that the relation R1 in the set NxN, where N is the set of
natural numbers, defined as follows: (a,b)R1(c,d) ⇔a+d=b+c
OR
B. If (L, ⊂,∪,∩) is a lattice then (L, ⊇,∩,∪) is also a lattice.
6.
A. Let the function f: R→R be defined by f(x)=x2+3 and g:R→R be
defined by x/(x+1). Find fog and gof.
OR
B. If G={1,2,3,4,5,6} then prove that (G, X7) is an abelian group.
SECTION C
7.
𝑛(𝑛+1)2𝑛+1)
8.
Show that P(n)=12+22+32+…………..+n2=
,
n≥1 by
6
mathematical induction.
Solve the travelling salesperson problem for the following weighted graph:
9.
Prove that A tree with n vertices, has precisely (n-1) edges.
10. Find the closure of reflexive, symmetric and transitive relation on the set
A={1,2,3} defined by R={(1,1),(1,2),(2,3),(3,3)}.
11. Show that the set of real numbers of the form m+n√2, m,n∊Z with
ordinary addition and multip[lication of numbers form a ring.
P.T.O.