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)
      _____________________________________________________________________________________
A partial ordered relation is transitive, reflexive and

Antisymmetric
Bisymmetric
Anti reflexive.
Asymmetric
      _____________________________________________________________________________________
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
      _____________________________________________________________________________________

Which of the following statements are TRUE?
(1) The problem of determining whether there exists a cycle in an undirected graph is in P.
(2) The problem of determining whether there exists a cycle in an undirected graph is in NP.
(3) If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A.


1,2 and 3
1 and 2 only
1 and 3 only
2 and 3 only
      _____________________________________________________________________________________
If n is an integer and n2 is odd ,then n is

even
odd
even or odd
prime
      _____________________________________________________________________________________
How many different words can be formed out of the letters of the word VARANASI?

64
120
40320
720
      _____________________________________________________________________________________
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)
      _____________________________________________________________________________________
The complete graph with four vertices has k edges where k is

3
4
5
6
      _____________________________________________________________________________________

Which of the following shall be a compound proposition involving the propositions p, q and r, that is true when exactly two of the p, q and r are true and is false otherwise ?


A
B
C
D
      _____________________________________________________________________________________
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
      _____________________________________________________________________________________
In any undirected graph,the sum of degrees of all nodes

Must be even
Is twice the number of edges
Must be odd
Must be even
      _____________________________________________________________________________________
The number of colours required to properly color vertices of every planar graph is

2
3
4
5
      _____________________________________________________________________________________
The trapzoidal rule for integration gives exact result when integrated is polynomial of degree

0 but not 1
1 but not 0
0 or 1
2
      _____________________________________________________________________________________
Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to

15
45
90
360
      _____________________________________________________________________________________
Consider an undirected graph G with 100 nodes. The maximum number of edges to be included in G so that the graph is not connected is

2451
4950
4851
9900
      _____________________________________________________________________________________
If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?

1/3
1/4
1/2
2/3
      _____________________________________________________________________________________
A graph G is called a ..... if it is a connected acyclic graph

Cyclic graph
Regular graph
Tree
Not a graph
      _____________________________________________________________________________________
In how many ways can a president and vice president be chosen from a set of 30 candidates?

820
850
880
870
      _____________________________________________________________________________________
Let G be a simple undirected planar graph on 10 vertices with 15edges. 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
      _____________________________________________________________________________________
Which of the following pair is not congruent modulo 7?

10, 24
25, 56
-31, 11
-64, -15
      _____________________________________________________________________________________
The number of nodes in a complete binary tree of height h (with roots at level 0) is equal to

20 + 21 + ….. 2h
2+ 21 + ….. 2h-1
20 + 21 + ….. 2h+1
21 + ….. 2h+1
      _____________________________________________________________________________________
The relation { (1,2), (1,3), (3,1), (1,1), (3,3), (3,2), (1,4), (4,2), (3,4)} is

Reflexive
Transitive
Symmetric
Asymmetric
      _____________________________________________________________________________________
The length of Hamiltonian Path in a connected graph of n vertices is

n–1
n
n+1
n/2
      _____________________________________________________________________________________
The number of leaf nodes in a complete binary tree of depth d is

2d
2d–1+1
2d+1+1
2d+1
      _____________________________________________________________________________________
Four fair coins are tossed simultaneously. The probability that latest one head  and tail turn up is

1/16
1/8
7/8
15/16
      _____________________________________________________________________________________
Find the number of relations from A = {cat, dog, rat} to B = {male , female}

64
6
32
15
      _____________________________________________________________________________________
Find the number of ways to paint 12 offices so that 3 of them will be green, 2 of them pink, 2 of them yellow and the rest ones white.

55,440
1,66,320
4.790E+08
39,91,680
      _____________________________________________________________________________________
The number of functions from an m element set to an n element set is:

mn
m + n
nm
m * n
      _____________________________________________________________________________________
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
      _____________________________________________________________________________________
Rank of the matrix Row1 [1,1 ] and Row2[0,0]  is 

4
2
1
0
      _____________________________________________________________________________________
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
      _____________________________________________________________________________________
Let N = {1, 2, 3, ….} be ordered by divisibility, which of the following subset is totally ordered,

(2, 6, 24)
(3, 5, 15)
(2, 9, 16)
(4, 15, 30)
      _____________________________________________________________________________________
Two dice are thrown simultaneously. The probability that the product of the two numbers  on the two disc is an even number, is

1/2
3/4
5/16
3/8
      _____________________________________________________________________________________
McCabe’s cyclomatic metric V(G) of a graph G with n vertices, e edges and p connected component is

e
n
e – n + 2p
e – n + p
      _____________________________________________________________________________________
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
      _____________________________________________________________________________________
An undirected graph possesses an eulerian circuit if and only if it is connected and its vertices are

all of even degree
all of odd degree
of any degree
even in number
      _____________________________________________________________________________________
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
      _____________________________________________________________________________________


A
B
C
D
      _____________________________________________________________________________________
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
      _____________________________________________________________________________________
Number of elements in the power set P(S) of the set S={(Q),1(2,3)}

2
4
8
10
      _____________________________________________________________________________________
A graph is a collection of 

Row and columns
Vertices and edges
Equations
None of these
      _____________________________________________________________________________________
Hasse diagram are drawn

Partially ordered sets
Lattices
Boolean algebra
None of these
      _____________________________________________________________________________________
Number of vertices of odd degree in a graph is

Always even
Always odd
Either even or odd
Always zero
      _____________________________________________________________________________________
Which of the following statements is/are TRUE for undirected graphs?
P: Number of odd degree vertices is even.
Q: Sum of degrees of all vertices is even.


P only
Q only
Both P and Q
Neither P nor Q
      _____________________________________________________________________________________
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
      _____________________________________________________________________________________
Cyclometric complexity of a flow graph G with n vertices and e edges is

V(G) = e+n–2
V(G) = e–n+2
V(G) = e+n+2
V(G) = e–n–2
      _____________________________________________________________________________________
The statement ( p^q) _ p is a

Contingency
Absurdity
Tautology
None of the above
      _____________________________________________________________________________________
Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to

15
30
90
360
      _____________________________________________________________________________________

Which of the following statements is/are TRUE for undirected graphs?
P: Number of odd degree vertices is even.
Q: Sum of degrees of all vertices is even.


P only
Q only
Both P and Q
Neither P nor Q
      _____________________________________________________________________________________
Bag A contains 5 white and 2 black balls .Bag B contains 2 white and 3 black balls .if any one bag is chosen and a ball is taken out of it at random ,what is the probability the ball is black?


31/70
1/2
5/12
3/5
 
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