14MA2010 Discrete Mathematics B.Tech Question Bank : karunya.edu

Name of the College : Karunya Institute of Technology & Sciences
University : Karunya University
Degree : B.Tech
Department : Information Technology
Subject Name : Discrete Mathematics
Document Type : Question Bank
Website : karunya.edu

Download :https://www.pdfquestion.in/uploads/ka…athematics.pdf

Karunya Discrete Mathematics Question Paper

Part – A

1. List A = {1, 2, 3, 4, 5} B = {0, 3, 6}. Find (A – B).
2. Write the converse of the statement. “If I am late, then I did not take the train to work.
6. The process of visiting each vertex of a tree in some specified order is called_________.
7. For the given graph, find the degree of the vertex ‘C’.

Related : Karunya University Digital Principles & System Design B.Tech Question Bank : www.pdfquestion.in/2884.html

8. Define an Euler path in a graph.
9. Find the distance between the code words : x = 1001, y = 0100
10. Define finite state machine.
13. If the set A has n elements ,how many relations are there from A to A
15. Say whether the relation > on the set of positive integers is a partial order relation
16. True or False “The spanning tree of a graph is unique”.
17. Define Euler graph
18. Give an example of a semi group
19. Define group code

Part – B

21. Give an example of infinite sequence
22. Let A be a set with n elements .How many subjects does A have?
24. When a permutation of finite set is called even permutation?
25. Determine whether the relation R is a partial order on the set
A = Z (the set of int egers), and aRb if and only if a = 2b
26. Give the tree representation for the expression (a + b)c – d
27. Define Hamiltonian graph
28. Give an example of a semi group which has no identity element
29. Find the weight of the code word x =110101
30. Define equivalent Finite State Machines
31. What can you say about A and B if A = {1,2,3} and B = {x / x > 0 and x2 < 12}.
32. Express the specifications “the automated reply cannot be sent when the file system is full” using logical connectives.
33. Define an equivalence relation.
34. Let f be a function from Z to Z with f (x) = x2 . Is f invertible?
35. Define lattice.
36. Define weighted graph.
37. Define an Euler circuit.
38. Give an example of not a semi group.
40. Define finite state machine.
41. Give an example of empty set
43. If the set A has m elements and the set B has n , then how many relations are there from A to B
45. Say whether the relation < on the set of positive integers is a partial order relation.
46. True or False “The sum of the degrees of all vertices of a graph is equal to the total number of edges ”.
47. Define Hamiltonian path
48. The set Z(set of all integers) with the binary operation subtraction is a semi group or not
49. Define group code

Part – C

52. If A has five elements. Find the cardinality of the power set of A.
55. Define : Partial order relation.
56. Draw a binary tree with five vertices.
57. Give an example of Euler graph.
58. Define : Semi-group.
59. Define : Type-2 grammar.
60. Define group code.
61. If the cardinality of a set A is n, what is the cardinality of the power set p(A)?
64. Define an equivalence relation.
66. A tree with n vertices has ________edges.
67. Define a Hamiltonian path in a graph.
68. Find an Euler circuit in the given graph.
69. Find the distance between the code words x = 1101, y = 0110.
70. Define a moore machine
72. State the Pigeon Hole Principle.
73. Give any one partition of the set {a, b, c, d, e}.
75. State the idempotent properties of a lattice.
76. Give the logic diagram of p(x,y,z) =(xÙy) Ú z’.
77. Define degree of a vertex in a graph.
78. Give an example of a monoid.
79. Define Group code.
80. Define state transition function.
81. What is the binary representation of 53?
82. Write in symbolics : When you sing my head hurts.
83. If R = { (1,2), (1,3), (2,4), (3,3)} is a relation from A = {1, 2, 3}to B = = { 2, 3, 4} find the complement of R.
85. What is the least element of the poset of nonnegative real numbers with partial order ‘=’ ?
86. How many edges does a tree with10 vertices have?
87. What is meant by a monoid?
88. What is meant by a Hamiltonian circuit?
89. Find the distance between x = 11010010 and y = 00100111.
90. What is meant by context free grammar?
91. Choose four cards at random from a standard 52 card deck. What is the probability that four kings will be chosen?96. Give the tree representation of the expression a + (b – c) d.
97. Define : Regular graph.
98. Define chromatic number of G.
99. Find the distance between x = 110110 and y = 000101
100. Define Type 2 pharse structure grammar.
101. Write the formula with out conditional statement (P Û Q) Þ R.
102. State : Pigeonhole Principle.
103. Let R be the relation on A = {2, 3, 4, 9} defined by “x is relatively prime to y”.
Write R as the set of order pairs (x, y).
104. Determine the T – class of the polynomial function f (n) = 4n4 – 6n7 + 25n3.
105. Draw the Hasse diagram for divisibility on the set {1, 2, 3, 5, 11, &13}.
106. Determine the Root if R is a Tree R = {(a, d), (b, c), (c, a), (d, e)}.
107. Does the graph has Euler Graph? If so, give one Example :
108. The Identity Element of the Semi group (Z+, +) is _____________
109. Construct the State transition Table of the Finite State machine Whose Digraph is as shown below :
110. Find the Weight of the following words in B5 (i) 00100 (ii) 10001.
111. If A and B are two sets, define their symmetric difference.
113. Given A = {a, b,c} and R = {(a,a), (a,b)}, is R transitive?
115. Give an example of a Boolean algebra having nine elements.
116. Name one algorithm used to find minimal spanning tree.
117. What is the chromatic number of the complete graph with four vertices?
118. What is the difference between a monoid and a semi-group?
119. Which notation is commonly used to display productions for type 2 grammars?
120. Find the weights of x = 01000 and y = 11100
122. State the Pigeon Hole Principle.
123. Give any one partition of the set {a, b, c, d, e}.
125. State the idempotent properties of a lattice.
127. Define degree of a vertex in a graph.
128. Give an example of a monoid.
129. Define Group code.
130. Define state transition function.