1) Let A and B be any two arbitrary events then which one of the following is true ?
P( A intersection B) = P(A). P(B)
P(A union B) = P(A) + P(B)
P(AB) = P(A intersection B). P(B)
P(A union B) >= P(A) + P(B)
Answer = D
2) If X and Y be the sets. Then the set ( X – Y) union (Y- X) union (X intersection Y ) is equal to?
X union Y
Xc union Yc
X intersection Y
Xc intersection Yc
Answer = A
3) If G is an undirected planer graph on n vertices with e edges then ?
e<=n
e<=2n
e<=3n
None of these
Answer = B
4) Which of the following statement is false ?
G is connected and is circuitless
G is connected and has n edges
G is minimally connected graph
G is circuitless and has n-1 edges
Answer = B
5) Probability that two randomly selected cards from a set of two red and two black cards are of same color is ?
1 / 2
1 / 3
2 / 3
None of these
Answer = B
6) The number of circuits that can be created by adding an edge between any two vertices in a tree is ?
Two
Exactly one
At least two
None
Answer = B
7) In a tree between every pair of vertices there is ?
Exactly one path
A self loop
Two circuits
n number of paths
Answer = A
8) The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from some same suit is ?
8
3
9
12
Answer = C
9) Context free languages are closed under ?
union, intersection
Intersection , complement
union , kleene star
Complement , kleene star
Answer = C
10) Let R be a symmetric and transitive relation on a set A. Then ?
R is reflexive and hence a partial order
R is reflexive and hence an equivalence relation
R is not reflexive and hence not an equivalence relation
None of above
Answer = D
SET-2
1) A graph is a collection of…. ?
Row and columns
Vertices and edges
Equations
None of these
Answer = B
Explanation: A graph contains the edges and vertices
2) The degree of any vertex of graph is …. ?
The number of edges incident with vertex
Number of vertex in a graph
Number of vertices adjacent to that vertex
Number of edges in a graph
Answer = A
Explanation: The number of edges connected on a vertex v with the self loop counted twice is called the degree of vertex.
3) If for some positive integer k, degree of vertex d(v)=k for every vertex v of the graph G, then G is called… ?
K graph
K-regular graph
Empty graph
All of above
s
Answer = B
Explanation: A graph in which all vertices are of equal degree is called regular graph.
4) 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
Answer = A
Explanation: Trivial graph is the second name for empty graph.
5) 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
Answer = B
Explanation: A walk is defined as finite altering sequence of vertices and edges. No Edges appear more than once but vertex may appear more than once.
6) If the origin and terminus of a walk are same, the walk is known as… ?
Open
Closed
Path
None of these
Answer = B
Explanation: A walk which begins and ends with same vertex is called closed walk otherwise it is open.
7) A graph G is called a ….. if it is a connected acyclic graph ?
Cyclic graph
Regular graph
Tree
Not a graph
Answer = C
Explanation: No explanation for this question.
8) Eccentricity of a vertex denoted by e(v) is defined by…. ?
max { d(u,v): u belongs to v, u does not equal to v : where d(u,v) is the distance between u&v}
min { d(u,v): u belongs to v, u does not equal to v }
Both A and B
None of these
Answer = A
Explanation: The eccentricity E(v) of a vertex V in the graph is the distance from v to the vertex farthest from v in G.
9) Radius of a graph, denoted by rad(G) is defined by…. ?
max {e(v): v belongs to V }
min { e(v): v belongs to V}
max { d(u,v): u belongs to v, u does not equal to v }
min { d(u,v): u belongs to v, u does not equal to v }
Answer = A
Explanation: The diameter or radius of a graph G is largest distance between two vertices in the graph G.
10) The complete graph K, has… different spanning trees?
nn-2
n*n
nn
n2
Answer = A
Explanation: No explanation for this question.