R4RIN – MCQs, Mock Tests | Mathematics Mathematics MCQs Set-4

The column sum in an incidence matrix for a simple graph is __________

1. depends on number of edges
2. always greater than 2
3. equal to 2
4. equal to the number of edges

✅ Correct Answer: 3

What are the dimensions of an incidence matrix?

1. Number of edges*number of edges
2. Number of edges*number of vertices
3. Number of vertices*number of vertices
4. Number of edges * (1⁄2 * number of vertices)

✅ Correct Answer: 2

The column sum in an incidence matrix for a directed graph having no self loop is __________

1. 0
2. 1
3. 2
4. equal to the number of edges

✅ Correct Answer: 1

Time complexity to check if an edge exists between two vertices would be ___________

1. O(V*V)
2. O(V+E)
3. O(1)
4. O(E)

✅ Correct Answer: 4

If a connected Graph (G) contains n vertices what would be the rank of its incidence matrix?

1. n-1
2. values greater than n are possible
3. values less than n-1 are possible
4. insufficient Information is given

✅ Correct Answer: 1

A Graph Structured Stack is a _____________

1. Undirected Graph
2. Directed Graph
3. Directed Acyclic Graph
4. Regular Graph

✅ Correct Answer: 3

If a Graph Structured Stack contains {1,2,3,4} {1,5,3,4} {1,6,7,4} and {8,9,7,4}, what would be the source and sink vertices of the DAC?

1. Source – 1, 8 Sink – 7,4
2. Source – 1 Sink – 8,4
3. Source – 1, 8 Sink – 4
4. Source – 4, Sink – 1,8

✅ Correct Answer: 3

Graph Structured Stack finds its application in _____________

1. Bogo Sort
2. Tomita’s Algorithm
3. Todd–Coxeter algorithm
4. Heap Sort

✅ Correct Answer: 2

Which is the most appropriate data structure for reversing a word?

1. queue
2. stack
3. tree
4. graph

✅ Correct Answer: 2

What will be the word obtained if the word “abbcabb” is reversed using a stack?

1. bbabbca
2. abbcabb
3. bbacbba
4. bbacabb

✅ Correct Answer: 3

How many stacks are required for reversing a word algorithm?

1. one
2. two
3. three
4. four

✅ Correct Answer: 1

What are the set of functions that are to be executed to get the following output? cat

1. push(c, s); push(a, s); push(t, s); pop(s); pop(s); pop(s);
2. push(c,s); pop(s); push(a,s); pop(s);push(t,s);pop(s);
3. pop(c ); pop(a); pop(t);
4. push(c,s); push(a,s); pop(t);

✅ Correct Answer: 2

Binary Decision Diagram is a type of __________

1. Multigraph
2. Cyclic Graph
3. Directed Acyclic Graph
4. Directed Acyclic Word Graph

✅ Correct Answer: 3

In which of the following case does a Binary Decision Diagram is used for?

1. Representation of Boolean Functions
2. String Matching
3. Searching
4. Sorting of number

✅ Correct Answer: 1

In a Binary Decision Diagram, how many types of terminal exists?

1. 1
2. 2
3. 3
4. 4

✅ Correct Answer: 2

In a Binary Decision Diagrams 0 values by a _________ line and the 1 values are represented by a _________ line.

1. dashed, bold
2. bold, dashed
3. dotted, bold
4. dotted, dashed

✅ Correct Answer: 3

Size of an And Inverter Graph is the number of _______ gates and the number of logic levels is number of ________ gates on the __________ path from a primary input to a primary output.

1. AND, AND, average
2. AND, OR, longest
3. OR, OR, shortest
4. AND, AND, longest

✅ Correct Answer: 4

And Inverter Graph is a type of __________

1. Multigraph
2. Cyclic Graph
3. Directed Acyclic Graph
4. Directed Acyclic Word Graph

✅ Correct Answer: 3

Which of the following logical operation can’t be implemented by polynomial time graph manipulation algorithms using Binary Decision Diagrams?

1. Conjunction
2. Disjunction
3. Negation
4. Tautology Checking

✅ Correct Answer: 4

Express -15 as a 6-bit signed binary number.

1. 001111
2. 101111
3. 101110
4. 001110

✅ Correct Answer: 2

Which is the predefined method available in Java to convert decimal to binary numbers?

1. toBinaryInteger(int)
2. toBinaryValue(int)
3. toBinaryNumber(int)
4. toBinaryString(int)

✅ Correct Answer: 4

How many children does a binary tree have?

1. 2
2. any number of children
3. 0 or 1 or 2
4. 0 or 1

✅ Correct Answer: 3

What is/are the disadvantages of implementing tree using normal arrays?

1. difficulty in knowing children nodes of a node
2. difficult in finding the parent of a node
3. have to know the maximum number of nodes possible before creation of trees
4. difficult to implement

✅ Correct Answer: 3

What are the children for node ‘w’ of a complete-binary tree in an array representation?

1. 2w and 2w+1
2. 2+w and 2-w
3. w+1/2 and w/2
4. w-1/2 and w+1/2

✅ Correct Answer: 1

What is the parent for a node ‘w’ of a complete binary tree in an array representation when w is not 0?

1. floor(w-1/2)
2. ceil(w-1/2)
3. w-1/2
4. w/2

✅ Correct Answer: 1

If the tree is not a complete binary tree then what changes can be made for easy access of children of a node in the array?

1. every node stores data saying which of its children exist in the array
2. no need of any changes continue with 2w and 2w+1, if node is at i
3. keep a seperate table telling children of a node
4. use another array parallel to the array with tree

✅ Correct Answer: 1

Consider a situation of writing a binary tree into a file with memory storage efficiency in mind, is array representation of tree is good?

1. yes because we are overcoming the need of pointers and so space efficiency
2. yes because array values are indexable
3. No it is not efficient in case of sparse trees and remaning cases it is fine
4. No linked list representation of tree is only fine

✅ Correct Answer: 3

Can a tree stored in an array using either one of inorder or post order or pre order traversals be again reformed?

1. Yes just traverse through the array and form the tree
2. No we need one more traversal to form a tree
3. No in case of sparse trees
4. Yes by using both inorder and array elements

✅ Correct Answer: 2

What is the location of a parent node for any arbitary node i?

1. (i/2) position
2. (i+1)/ position
3. floor(i/2) position
4. ceil(i/2) position

✅ Correct Answer: 3

Given an array of element 5, 7, 9, 1, 3, 10, 8, 4. Which of the following are the correct sequences of elements after inserting all the elements in a min-heap?

1. 1,3,4,5,7,8,9,10
2. 1,4,3,9,8,5,7,10
3. 1,3,4,5,8,7,9,10
4. 1,3,7,4,8,5,9,10

✅ Correct Answer: 1

Topological sort can be applied to which of the following graphs?

1. Undirected Cyclic Graphs
2. Directed Cyclic Graphs
3. Undirected Acyclic Graphs
4. Directed Acyclic Graphs

✅ Correct Answer: 4

Most Efficient Time Complexity of Topological Sorting is? (V – number of vertices, E – number of edges)

1. O(V + E)
2. O(V)
3. O(E)
4. O(V*E)

✅ Correct Answer: 1

In most of the cases, topological sort starts from a node which has __________

1. Maximum Degree
2. Minimum Degree
3. Any degree
4. Zero Degree

✅ Correct Answer: 4

Which of the following is not an application of topological sorting?

1. Finding prerequisite of a task
2. Finding Deadlock in an Operating System
3. Finding Cycle in a graph
4. Ordered Statistics

✅ Correct Answer: 4

Topological sort of a Directed Acyclic graph is?

1. Always unique
2. Always Not unique
3. Sometimes unique and sometimes not unique
4. Always unique if graph has even number of vertices

✅ Correct Answer: 3

Topological sort can be implemented by?

1. Using Depth First Search
2. Using Breadth First Search
3. Using Depth and Breadth First Search
4. Using level ordered search

✅ Correct Answer: 3

Topological sort is equivalent to which of the traversals in trees?

1. Pre-order traversal
2. Post-order traversal
3. In-order traversal
4. Level-order traversal

✅ Correct Answer: 1

A man wants to go different places in the world. He has listed them down all. But there are some places where he wants to visit before some other places. What application of graph can he use to determine that?

1. Depth First Search
2. Breadth First Search
3. Topological Sorting
4. Dijkstra’s Shortest path algorithm

✅ Correct Answer: 3

When the topological sort of a graph is unique?

1. When there exists a hamiltonian path in the graph
2. In the presence of multiple nodes with indegree 0
3. In the presence of single node with indegree 0
4. In the presence of single node with outdegree 0

✅ Correct Answer: 1

Which of the following statements for a simple graph is correct?

1. Every path is a trail
2. Every trail is a path
3. Every trail is a path as well as every path is a trail
4. Path and trail have no relation

✅ Correct Answer: 1

What is the number of edges present in a complete graph having n vertices?

1. (n*(n+1))/2
2. (n*(n-1))/2
3. n
4. Information given is insufficient

✅ Correct Answer: 2

A connected planar graph having 6 vertices, 7 edges contains _____________ regions.

1. 15
2. 3
3. 1
4. 11

✅ Correct Answer: 2

If a simple graph G, contains n vertices and m edges, the number of edges in the Graph G'(Complement of G) is ___________

1. (n*n-n-2*m)/2
2. (n*n+n+2*m)/2
3. (n*n-n-2*m)/2
4. (n*n-n+2*m)/2

✅ Correct Answer: 1

Which of the following properties does a simple graph not hold?

1. Must be connected
2. Must be unweighted
3. Must have no loops or multiple edges
4. Must have no multiple edges

✅ Correct Answer: 1