Showing posts with label Discrete Structure. Show all posts
Showing posts with label Discrete Structure. Show all posts

Multiple Choice Questions On Discrete Structure - Set 4

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Following are the multiple choice questions on Discrete Structure based on the UGC - NET Exam syllabus  along with the Explanation. Multiple Choice Questions On Discrete Mathematics. 


1) Let A and B be any two arbitrary events then which one of the following is true ?
  1. P( A intersection B) = P(A). P(B)
  2. P(A union B) = P(A) + P(B)
  3. P(AB) = P(A intersection B). P(B)
  4. P(A union B) >= P(A) + P(B)
Show/Hide Answer
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?
  1. X union Y
  2. Xc union Yc
  3. X intersection Y
  4. Xc intersection Yc
Show/Hide Answer
Answer = A 

3) If G is an undirected planer graph on n vertices with e edges then ?
  1. e<=n
  2. e<=2n
  3. e<=3n
  4. None of these
Show/Hide Answer
Answer = B 

4) Which of the following statement is false ?
  1. G is connected and is circuitless
  2. G is connected and has n edges
  3. G is minimally connected graph
  4. G is circuitless and has n-1 edges
Show/Hide Answer
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. 1 / 2
  2. 1 / 3
  3. 2 / 3
  4. None of these
Show/Hide Answer
Answer = B 

6) The number of circuits that can be created by adding an edge between any two vertices in a tree is ?
  1. Two
  2. Exactly one
  3. At least two
  4. None
Show/Hide Answer
Answer = B 

7) In a tree between every pair of vertices there is ?
  1. Exactly one path
  2. A self loop
  3. Two circuits
  4. n number of paths
Show/Hide Answer
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 ?
  1. 8
  2. 3
  3. 9
  4. 12
Show/Hide Answer
Answer = C 

9) Context free languages are closed under ?
  1. union, intersection
  2. Intersection , complement
  3. union , kleene star
  4. Complement , kleene star
Show/Hide Answer
Answer = C 

10) Let R be a symmetric and transitive relation on a set A. Then ?
  1. R is reflexive and hence a partial order
  2. R is reflexive and hence an equivalence relation
  3. R is not reflexive and hence not an equivalence relation
  4. None of above
Show/Hide Answer
Answer = D 

Tags : Multiple choice questions on discrete structure with answers and explanation, Multiple choice questions on Discrete structure based on the UGC syllabus with answers, Objective type questions on discrete structure with answers, MCQ's on discrete structure, UGC-NET computer science preparation questions with answers, MCQ's for UGC-NET exam
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Multiple Choice Questions On Discrete Structure - Set 3

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1) A tour of G is a closed walk of graph G which includes every edge G at least once. A ..... tour of G is a tour which includes every edge of G exactly once ?
  1. Hamiltonian
  2. Planar
  3. Isomorphic
  4. Euler
Show/Hide Answer
Answer = D 
Explanation: If some closed walk in a graph contains all the edges then the walk is called Euler.
2) Which of the following is not a type of graph ?
  1. Euler
  2. Hamiltonian
  3. Tree
  4. Path
Show/Hide Answer
Answer = D 
Explanation:Path is a way from one node no another but not a graph.

3) Choose the most appropriate definition of plane graph ?
  1. A graph drawn in a plane in such a way that any pair of edges meet only at their end vertices
  2. 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.
  3. A simple graph which is Isomorphic to Hamiltonian graph
  4. None of these
Show/Hide Answer
Answer = A
Explanation: No explanation for this question.
4) A continuous non - intersecting curve in the plane whose origin and terminus coincide ?
  1. Planer
  2. Jordan
  3. Hamiltonian
  4. All of these
Show/Hide Answer
Answer = B 
Explanation: The jordan graph is the set of all vertices of minimum eccentricity that is the set of all vertices A where the greatest distance to other vertex B is minimal.
5) Polyhedral is.... ?
  1. A simple connected graph
  2. A plane graph
  3. A graph in which the degree of every vertex and every face is atleast 3
  4. All of above
Show/Hide Answer
Answer = D 
Explanation: A polyhedral graph is the undirected graph formed from the vertices and edges of a convex polyhedron

6) A path in graph G, which contains every vertex of G once and only once ?
  1. Eulartour
  2. Hamiltonian Path
  3. Eular trail
  4. Hamiltonian tour
Show/Hide Answer
Answer = B 
Explanation:A Hamiltonian circuit in a connected graph is defined as a closed walk that traverse every vertex of G exactly once except the starting vertex.

7) A minimal spanning tree of a graph G is.... ?
  1. A spanning sub graph
  2. A tree
  3. Minimum weights
  4. All of above
Show/Hide Answer
Answer = D 
Explanation: A tree is said to be spanning tree of connected graph G if it is subgraph of G and contains all the vertices of G.
8) A tree having a main node, which has no predecessor is.... ?
  1. Spanning tree
  2. Rooted tree
  3. Weighted tree
  4. None of these
Show/Hide Answer
Answer = B 
Explanation:A tree in which one vertex distinguish from all other is called rooted tree.

9) Diameter of a graph is denoted by diam(G) is defined by.... ?
  1. max (e(v) : v belongs to V)
  2. max( d(u,v) )
  3. Both A and B
  4. None of these
Show/Hide Answer
Answer = C 
Explanation: The diameter of a graph G is largest distance between two vertices in a graph G.
 
10) A vertex of a graph is called even or odd depending upon ?
  1. Total number of edges in a graph is even or odd
  2. Total number of vertices in a graph is even or odd
  3. Its degree is even or odd
  4. None of these
Show/Hide Answer
Answer = C
Explanation: The vertex of a graph is called even or odd based on its degree.
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Multiple Choice Questions On Discrete Structure - Set 2

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1) A graph is a collection of.... ?
  1. Row and columns
  2. Vertices and edges
  3. Equations
  4. None of these
Show/Hide Answer
Answer = B 
Explanation: A graph contains the edges and vertices

2)  The degree of any vertex of graph is .... ?
  1. The number of edges incident with vertex
  2. Number of vertex in a graph
  3. Number of vertices adjacent to that vertex
  4. Number of edges in a graph
Show/Hide Answer
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... ?
  1. K graph
  2. K-regular graph
  3. Empty graph
  4. All of above
Show/Hide Answers
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... ?
  1. Trivial graph
  2. Regular graph
  3. Bipartite graph
  4. None of these
Show/Hide Answer
Answer = A 
Explanation: Trivial graph is the second name for empty graph.

5) Length of the walk of a graph is .... ?
  1. The number of vertices in walk W
  2. The number of edges in walk W
  3. Total number of edges in a graph
  4. Total number of vertices in a graph
Show/Hide Answer
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... ?
  1. Open
  2. Closed
  3. Path
  4. None of these
Show/Hide Answer
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 ?
  1. Cyclic graph
  2. Regular graph
  3. Tree
  4. Not a graph
Show/Hide Answer
Answer = C 
Explanation: No explanation for this question.

8) Eccentricity of a vertex denoted by e(v) is defined by.... ?
  1. max { d(u,v): u belongs to v, u does not equal to v : where d(u,v) is the distance between u&v}
  2. min { d(u,v): u belongs to v, u does not equal to v }
  3. Both A and B
  4. None of these
Show/Hide Answer
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.... ?
  1. max {e(v): v belongs to V }
  2. min { e(v):  v belongs to V}
  3. max { d(u,v): u belongs to v, u does not equal to v }
  4. min { d(u,v): u belongs to v, u does not equal to v }
Show/Hide Answer
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?
  1. nn-2
  2. n*n
  3. nn
  4. n2
Show/Hide Answer
Answer = A 
Explanation: No explanation for this question.

                                                 
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Multiple Choice Questions On Discrete Structure - Set 1

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1) Context free Grammar is ?
  1. A Compiler
  2. A language expression
  3. A regular expression
  4. None of these
Show/Hide Answer
Answer = B
Explanation: Context free Grammar generate the context free languages. These are defined by the rule of the form A -> b Where A a non terminal and b is the string of terminals.

2) The idea of an automation with a stack as auxiliary storage... ?
  1. Finite automata
  2. Push down automata
  3. Deterministic automata
  4. None of these
Show/Hide Answer
Answer = B 
Explanation: Push down automata manipulate the stack, as a part of performing a transition.

3) A Pushdown automata is.....if there is at most one transition applicable to each configuration ?

  1. Deterministic
  2. Non Deterministic
  3. Finite
  4. Non Finite
Show/Hide Answer
Answer = A 
Explanation:If in every situation only one transition is available as continuation of computation, then the result is a deterministic push down automation (DPDA).

4) The graphical representation of the transition of finite automata is ?

  1. Finite diagram
  2. State diagram
  3. Node diagram
  4. E-R diagram
Show/Hide Answer
Answer = B 
Explanation: State diagram is called the graphical representation of Finite automata.

5) If two sets A and B have no common elements i.e (A intersection B) has no element then such sets are known as ?
  1. Intersection
  2. Union
  3. Disjoint
  4. Complement
Show/Hide Answer
Answer = C 
Explanation:If two sets have no element in common then they are called disjoint sets.
6) The domain D of the relation R is defined as the.... ?
  1. Set of all elements of ordered pair which belongs to R
  2. Set of all last elements of ordered pair which belongs to R
  3. Set of all first elements of ordered pair which belongs to R
  4. None of these
Show/Hide Answer
Answer = C 
Explanation: No explanation for this question

7) 'A language is regular if and only if it is accepted by a finite automation' ?
  1. The given statement is true
  2. The given statement is false
  3. The given statement is partially true
  4. Sometime true, sometimes false
Show/Hide Answer
Answer = A 
Explanation: A regular language is accepted by the finite automation. Every regular language is context free.

8) Which of the following does not belong to the context free grammer?
  1. Terminal symbol
  2. Non-terminal symbol
  3. Start symbol
  4. End symbol
Show/Hide Answer
Answer = D 
Explanation:Context free grammar consist of terminal symbols, non terminal symbols, set of production rules, a start symbol but does not have any End symbol.

9) A regular grammar is a..... ?
  1. Context free grammar
  2. Non context free grammar
  3. English grammar
  4. None of above
Show/Hide Answer
Answer = A 
Explanation: Regular grammar is context free grammar. Such a grammar restricts its rules to a single non terminal on the left hand side and right hand side consisting of a single terminal.

10) The context free language are closed under... ?
  1. Union
  2. Kleene star
  3. Concatenation
  4. All of above
Show/Hide Answer
Answer = D 
Explanation: Context free language is closed under union, kleene star and concatenation.
                                                                
                                              
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