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This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on Discrete Mathematics Set 7
Q1 | Find the sequence generated by 1/1−x2−x4.,assume that 1, 1, 2, 3, 5, 8,… has generating function 1/1−x−x2.
- 0, 0, 1, 1, 2, 3, 5, 8,…
- 0, 1, 2, 3, 5, 8,…
- 1, 1, 2, 2, 4, 6, 8,…
- 1, 4, 3, 5, 7,…
Q2 | There are 70 patients admitted in a hospital in which 29 are diagnosed with typhoid, 32 with malaria, and 14 with both typhoid and malaria. Find the number of patients diagnosed with typhoid or malaria or both.
- 39
- 17
- 47
- 53
Q3 | At a software company, skilled workers have been hired for a project. Out of 75 candidates, 48 of them were software engineer; 35 of them were hardware engineer; 42 of them were network engineer; 18 of them had skills in all three jobs and all of them had skills in at least one of these jobs. How many candidates were hired who were skilled in exactly 2 jobs?
- 69
- 14
- 32
- 8
Q4 | In a renowned software development company of 240 computer programmers 102 employees are proficient in Java, 86 in C#, 126 in Python, 41 in C# and Java, 37 in Java and Python, 23 in C# and Python, and just 10 programmers are proficient in all three languages. How many computer programmers are there those are not proficient in any of these three languages?
- 138
- 17
- 65
- 49
Q5 | In class, students want to join sports. 15 people will join football, 24 people will join basketball, and 7 people will join both. How many people are there in the class?
- 19
- 82
- 64
- 30
Q6 | From 1, 2, 3, …, 320 one number is selected at random. Find the probability that it is either a multiple of 7 or a multiple of 3.
- 72%
- 42.5%
- 12.8%
- 63.8%
Q7 | If each and every vertex in G has degree at most 23 then G can have a vertex colouring of
- 24
- 23 c) 176
- d
- 54
Q8 | Berge graph is similar to due to strong perfect graph theorem.
- line graph
- perfect graph
- bar graph
- triangle free graph
Q9 | A is a graph which has the same number of edges as its complement must have number of vertices congruent to 4m or 4m modulo 4(for integral values of number of edges).
- subgraph
- hamiltonian graph
- euler graph
- self complementary graph
Q10 | In a the vertex set and the edge set are finite sets.
- finite graph
- bipartite graph
- infinite graph
- connected graph
Q11 | If G is the forest with 54 vertices and 17 connected components, G has total number of edges.
- 38
- 37
- 17/54 d
- 17/53
Q12 | An undirected graph G has bit strings of length 100 in its vertices and there is an edge between vertex u and vertex v if and only if u and v differ in exactly one bit position. Determine the ratio of the chromatic number of G to the diameter of G?
- 1/2101
- 1/50 c) 1/100
- d
- 1/20
Q13 | If each and every vertex in G has degree at most 23 then G can have a vertex colouring of
- 24
- 23 c) 176
- d
- 54
Q14 | Triangle free graphs have the property of clique number is
- less than 2
- equal to 2
- greater than 3
- more than 10
Q15 | Let D be a simple graph on 10 vertices such that there is a vertex of degree 1, a vertex of degree 2, a vertex of degree 3, a vertex of degree 4, a vertex of degree 5, a vertex of degree 6, a vertex of degree 7, a vertex of degree 8 and a vertex of degree 9. What can be the degree of the last vertex?
- 4
- 0
- 2
- 5
Q16 | A bridge can not be a part of
- a simple cycle
- a tree
- a clique with size ≥ 3 whose every edge is a bridge
- a graph which contains cycles
Q17 | Any subset of edges that connects all the vertices and has minimum total weight, if all the edge weights of an undirected graph are positive is called
- subgraph
- tree
- hamiltonian cycle
- grid
Q18 | G is a simple undirected graph and some vertices of G are of odd degree. Add a node n to G and make it adjacent to each odd degree vertex of G. The resultant graph is
- complete bipartite graph
- hamiltonian cycle
- regular graph
- euler graph
Q19 | Let G be a directed graph whose vertex set is the set of numbers from 1 to 50. There is an edge from a vertex i to a vertex j if and only if either j = i + 1 or j = 3i. Calculate the minimum number of edges in a path in G from vertex 1 to vertex 50.
- 98
- 13
- 6
- 34
Q20 | What is the number of vertices in an undirected connected graph with 39 edges, 7 vertices of degree 2, 2 vertices of degree 5 and remaining of degree 6?
- 11
- 14
- 18
- 19
Q21 | is the maximum number of edges in an acyclic undirected graph with k vertices.
- k-1
- k2
- 2k+3
- k3+4
Q22 | The minimum number of edges in a connected cyclic graph on n vertices is
- n – 1
- n
- 2n+3
- n+1
Q23 | The maximum number of edges in a 8- node undirected graph without self loops is
- 45
- 61
- 28
- 17
Q24 | Let G be an arbitrary graph with v nodes and k components. If a vertex is removed from G, the number of components in the resultant graph must necessarily lie down between and
- n-1 and n+1
- v and k
- k+1 and v-k
- k-1 and v-1
Q25 | The 2n vertices of a graph G corresponds to all subsets of a set of size n, for n>=4. Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements.The number of connected components in G can be
- n+2
- 3n/2
- n2
- 2n