How many relations are there on a set with n elements that are symmetric and a set with n elements that are reflexive and symmetric ?
2n(n+1)/2 and 2n.3n(n–1)/2
3n(n–1)/2 and 2n(n–1)
2n(n+1)/2 and 3n(n–1)/2
2n(n+1)/2 and 2n(n–1)/2
The number of colours required to properly colour the vertices of every planer graph is
2
3
4
5
In how many ways can a president and vice president be chosen from a set of 30 candidates?
820
850
880
870
Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is ½. What is the expected number of unordered cycles of length three?
1/8
1
7
8
In a graph if e=(u, v) means
u is adjacent to v but v is not adjacent to u
e begins at u and ends at v
u is processor and v is successor
both b and c
A minimal spanning tree of a graph G is
A spanning sub graph
A tree
Minimum weights
All of above
The number of leaf nodes in a complete binary tree of depth d is
2d
2d–1+1
2d+1+1
2d+1
A partial ordered relation is transitive, reflexive and
Antisymmetric
Bisymmetric
Anti reflexive.
Asymmetric
In a graph if e=[u, v], Then u and v are called
Endpoints of e
Adjacent nodes
Neighbors
All of above
In how many ways can a hungry student choose 3 toppings for his prize from a list of 10 delicious possibilities?
100
120
110
150
A graph with n vertices will definitely have a parallel edge or self loop if the total number of edges are
greater than n–1
less than n(n–1)
greater than n(n–1)/2
less than n2/2
A vertex of a graph is called even or odd depending upon
Total number of edges in a graph is even or odd
Total number of vertices in a graph is even or odd
Its degree is even or odd
None of these
In any undirected graph the sum of degrees of all the nodes
Must be even
Are twice the number of edges
Must be odd
Need not be even
The expression a+a c is equivalent to
a
a+c
c
1
A graph with one vertex and no edges is
multigraph
digraph
isolated graph
trivial graph
Length of the walk of a graph is
The number of vertices in walk W
The number of edges in walk W
Total number of edges in a graph
Total number of vertices in a graph
The number of colours required to properly color vertices of every planar graph is
2
3
4
5
A graph with no edges is known as empty graph. Empty graph is also known as
Trivial graph
Regular graph
Bipartite graph
None of these
Which two of the following are equivalent for an undirected graph G? (i) G is a tree (ii) There is at least one path between any two distinct vertices of G (iii) G contains no cycles and has (n-1) edges (iv)G has n edges
(i) and (ii)
(i) and (iii)
(i) and (iv)
(ii) and (iii)
Choose the most appropriate definition of plane graph
A graph drawn in a plane in such a way that any pair of edges meet only at their end vertices
A graph drawn in a plane in such a way that if the vertex set of graph can be partitioned into two non - empty disjoint subset X and Y in such a way that each edge of G has one end in X and one end in Y
A simple graph which is Isomorphic to Hamiltonian graph
None of these
A continuous non intersecting curve in the plane whose origin and terminus coincide
Planer
Jordan
Hamiltonian
All of these
A graph with n vertices will definitely have a parallel edge or self loop of the total number of edges are
more than n
more than n+1
more than (n+1)/2
more than n(n-1)/2
A debating team consists of 3 boys and 2 girls. Find the number of ways they can sit in a row?
120
24
720
12
Which one of the following statements is incorrect ?
The number of regions corresponds to the cyclomatic complexity.
Cyclometric complexity for a flow graph G is V(G) = N–E+2, where E is the number of edges and N is the number of nodes in the flow graph.
Cyclometric complexity for a flow graph G is V(G) = E–N+2, where E is the number of edges & N is the number of nodes in the flow graph.
Cyclometric complexity for a flow graph G is V(G) = P + 1, where P is the number of predicate nodes contained in the flow graph G.
Which of the following pair is not congruent modulo 7?
10, 24
25, 56
-31, 11
-64, -15
The maximum degree of any vertex in a simple graph with n vertices is
n–1
n+1
2n–1
n
The complete graph with four vertices has k edges where k is
3
4
5
6
Consider a weighted undirected graph with positive edge weights and let (u, v) be an edge in the graph. It is known that the shortest path from source vertex s to u has weight 53 and shortest path from s to v has weight 65. Which statement is always true ?
Weight (u, v) <= 12
Weight (u, v) = 12
Weight (u, v) >= 12
Weight (u, v) > 12
How many onto (or surjective) functions are there from an n-element (n => 2) set to a 2-element set?
2n
2n - 1
2n - 2
2(2n – 2)
Suppose v is an isolated vertex in a graph, then the degree of v is
0
1
2
3
The number of nodes in a complete binary tree of height h (with roots at level 0) is equal to
20 + 21 + ….. 2h
20 + 21 + ….. 2h-1
20 + 21 + ….. 2h+1
21 + ….. 2h+1
Hasse diagram are drawn
Partially ordered sets
Lattices
Boolean algebra
None of these
In how many ways can 5 balls be chosen so that 2 are red and 3 are black
910
990
970
960
Circle has ____________
No vertices
Only 1 vertex
8 vertices
None of these
How many different words can be formed out of the letters of the word VARANASI?
64
120
40320
720
The proposition ~qvp is equivalent to
p?q
q?p
p?q
p?q
A graph is tree if and only if
Is planar
Contains a circuit
Is minimally
Is completely connected
If B is a Boolean Algebra, then which of the following is true
B is a finite but not complemented lattice
B is a finite, complemented and distributive lattice
B is a finite, distributive but not complemented lattice
B is not distributive lattice
Let G be a simple undirected planar graph on 10 vertices with 15 edges. If G is a connected graph, then the number of bounded faces in any embedding of G on the plane is equal to
3
4
5
6
The number of distinguishable permutations of the letters in the word BANANA are,
60
36
20
10
If R is a relation “Less Than” from A = {1,2,3,4} to B = {1,3,5} then RoR-1 is
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