Quiznetik

Discrete Mathematics | Set 4

1. S -> aAB, AB -> bB, B -> b, A -> aB satisfies ___________ type of grammar

Correct : C. 0,1

2. If there are more than 2 LMD for a string then it is said to be ___________.

Correct : A. Ambigious

3. A finite non-empty set of symbols is called _________.

Correct : A. alphabet

4. The specification of proper construction of a sentence is called ______.

Correct : C. syntax

5. Context free grammar is also known as _______ grammar.

Correct : C. type 2

6. A class of machine which accepts a ________ language is called finite state automata.

Correct : D. type 3

7. Accepting states are denoted by ________.

Correct : C. double circle

8. For converting NDFA to DFA we should __________ all the states which have no incoming.

Correct : D. delete

9. The set of all finite words over E is denoted by ________.

Correct : A. E+

10. Surjective function is also called ________.

Correct : A. onto

11. One to one onto function is also called __________.

Correct : A. bijective

12. The composition of function is associative but not _______.

Correct : A. commutative

13. A mapping x into itself is called __________.

Correct : A. reflexive

14. The duality law of (P^Q)vT is ________.

Correct : D. (PvQ)^F

15. A sum of the variables and their negations in a formula is called _________.

Correct : A. elementary sum

16. A premise may be introduced at any point in the derivation is called ________.

Correct : A. Rule P

17. A product of the variables and their negations in a formula is called _________.

Correct : A. elementary product

18. Min-terms of two statements are formed by introducing the connective _________.

Correct : A. Conjunction

19. Any vertex having degree one is called _______.

Correct : B. pendent vertex

20. A graph that has neither self loops nor parallel edges is called_____graph.

Correct : B. simple

21. A graph in which every vertex has same degree is called _________graph.

Correct : A. regular

22. Kn denotes _______graph.

Correct : C. complete

23. The number of vertices of odd degree in a graph is always________.

Correct : B. even

24. A path of a graph is said to be ______ if it contains all the edges of the graph.

Correct : A. eulerian

25. Traveling salesman problem is example for_______graph.

Correct : B. hamiltonian

26. If a node v is reachable from node u then the path of minimum length u to v is called _____.

Correct : C. geodesic

27. The eccentricity of a center in a tree is defined as ______ of the tree.

Correct : A. radius

28. P -> Q , Q ->R then________.

Correct : A. P -> R

29. If a normal form contains all minterms, then it is ________.

Correct : A. a tautology

30. PCNF is also called _______.

Correct : B. product of sum canonical form

31. PDNF is also called _____________

Correct : A. sum of product canonical form

32. Max-terms of two statements are formed by introducing the connective _________.

Correct : A. disjunction

33. The Subset relation on a set of sets is ________.

Correct : A. partial ordering

34. A relation R is defined on the set of integers as xRy if and only if (x+y) is even. Which of the following statement is TRUE?

Correct : C. R is an equivalence relation having two equivalence classes

35. If R = {(1, y), (1, z), (3, y)} then R power (-1)= ___________.

Correct : B. {(y, 1), (z, 1), (y, 3)}

36. Let R ={ (a,b),(c,d),(b,b)}, S = {(d,b),(c,b),(a,d)} then R composite S = ___________

Correct : D. {(c,b)}

37. Let R and S be two relations on a set of positive integers I. If R = {(a, 3a+a)},S = {(a,a+a)} then R composition R composition R = __________.

Correct : C. {(a,27a+a)}

38. The number of relations from A = {a,b,c} to B = {1,2} are __________.

Correct : D. 64

39. The minimum number of edges in a connected graph with n vertices is ___________.

Correct : B. n-1

40. The number of distinct simple graphs with up to three nodes is _________.

Correct : A. 7

41. A graph is planar if and only if it does not contain ________.

Correct : D. sub graphs homeomorphic to k5 or k3,3

42. Maximum number of edges in an n-node undirected graph without self loops is ____.

Correct : A. [n(n-a)]/2

43. Number of distinct nodes in any elementary path of length p is ________.

Correct : C. p+1

44. The total number of edges in a complete graph of n vertices is _________.

Correct : D. [n(n-a)]/2

45. A directed complete graph of n vertices contains __________.

Correct : A. one arrow between each pair of distinct vertices

46. A directed graph G = (V, E) is said to be finite if its ________.

Correct : A. set V of vertices is finite

47. A state from which a deterministic finite state automata can never come out is called a ____________.

Correct : A. trape state

48. If a compound statement is made up of three simple statements then the number of rows in the truth table is _______.

Correct : D. 8

49. Let R = {(3, 3), (6, 6), (9, 9), (12,12), (3,6), (6,3), (3, 9), (9, 3), (9, 12),(12,9)} be a relation on the set A = {3, 6, 9, 12}. The relation is _________

Correct : D. equivalence relation

50. Let R={(1,b),(3,d),(2,b)} and S={(b,4),(2,5),(d,a)} be a relation then R composition S=____.

Correct : B. {(1,4),(3,a),(2,4)}

51. If R= {(x, 2x)} and S= {(x, 4x)} then R composition S=____.

Correct : C. {(x, 8x)}

52. If R= {(x, 2x)} and S= {(x, 5x)} then R composition S=____.

Correct : D. {(x, 10x)}

53. A regular grammar contains rules of the form _____.

Correct : C. A tends to aB

54. A type-2 grammar contains the rules of the form is____.

Correct : C. A tends to aBC

55. Let R={(1, 3), (4, 2), (2, 2), (3, 3), (1, 1),(4,4)} be a relation on the set A={1, 2, 3, 4}. The relation R is ____.

Correct : C. not symmetric

56. The NAND statement is a combination of ______.

Correct : A. NOT and AND

57. The NOR statement is a combination of ________.

Correct : B. NOT and OR

58. If a relation is reflexive then in the graph of a relation there must be a loop at _____.

Correct : A. each node

59. Which of the following traversal techniques lists the nodes of binary search in ascending order?

Correct : C. in order

60. The grammar G ={{S},{0,1},P,S}} where P={S tends to 0S1 , S tends to S1} is a ________.

Correct : D. context free grammar

61. Which of the following regular expressions identifiers are true?

Correct : A. (r*)* = r

62. In a grammar or language LAMDA is used to denote _______.

Correct : A. empty word

63. The number of letters in a word is called ________.

Correct : A. length

64. If r is a regular expression then r* is a _______ expression.

Correct : A. regular

65. An example for regular grammar is _____.

Correct : C. S tends to aB

66. If all the productions have single non-terminal in the left hand side then the grammar defined is ________grammar.

Correct : A. context free

67. In Backus Naur Form the symbol:: = is used instead of _______.

Correct : B. tends to

68. Any subset L of A* is called ________ over A.

Correct : A. Language

69. Let S be a start symbol and S -> aA, A -> BA, A -> a, B -> b be the productions in a grammar then one of the string derived form the grammar is _____.

Correct : C. abba

70. If S is a start symbol and S -> AB, A -> aB, B -> b are the productions then a string generated by the grammar is _______.

Correct : C. abb

71. In FSA ,the notation for M being in state S0, reading the input symbol a, moving one cell right and reaching the state S1 is given by ________.

Correct : B. f(S0 , a) = S1

72. If "S -> aS, S -> a" are the productions in a grammar G, then the grammar is called_____.

Correct : A. regular grammar

73. The rank of the incidence matrix of any connected graph G with n vertices is ______.

Correct : C. n-1

74. The number of 1's in each row of an incidence matrix of a graph G is equal to _____.

Correct : A. the degree of the corresponding vertices

75. Each column of an incidence matrix of a graph G has exactly _______.

Correct : B. two 1's

76. An undirected graph is tripartite if and only if it has no circuits of _______ lengths

Correct : A. odd

77. A graph is bipartite if and only if its chromatic number is ________.

Correct : B. 2

78. G is strongly connected implies _________.

Correct : A. G is unilaterally connected.

79. The number of pendant vertices in a full binary tree with n vertices is ________.

Correct : C. (n+a)/2

80. The number of vertices in a full binary tree is _______.

Correct : A. odd

81. A binary tree with 2k vertices of level k has at least _______ vertices.

Correct : D. 2 power (k+1)-1

82. For a symmetric digraph, the adjacency matrix is _________.

Correct : A. symmetric

83. The diagonal entries of A A^T where A is the adjacency matrix are the _______.

Correct : A. outdegrees of the node

84. DFSA and NDFSA represent the ________ language.

Correct : A. regular

85. The chromatic number of the chess board is ______.

Correct : B. 2

86. The total number of degrees of an isolated node is _______.

Correct : A. 0

87. If G is a connected planar graph then it has a vertex of degree _______.

Correct : C. 5 or less

88. A product of the variable and their negation in a formula is called ________.

Correct : B. an elementary product

89. A formula consisting of disjunctions of min-terms is called _________.

Correct : C. PDNF

90. The less than relation < on real is __________.

Correct : D. not a partial ordering since it is not anti-symmetric and not reflexive

91. A relation R in X is said to be a ________, if it is reflexive and symmetric.

Correct : D. compatibility relation

92. The set X*X itself defines a relation in X is called a _____relation.

Correct : B. universal

93. A self complemented distributive lattice is called _______.

Correct : A. boolean algebra

94. Every finite subset of a lattice has ____________.

Correct : A. a Least Upper Bound and Greatest Lower Bound

95. A formula consisting of conjunctions of max-terms is called _________.

Correct : C. PCNF

96. The set of all divisors of 24 are ___________.

Correct : A. {1, 2, 3, 4, 6, 8, 12, 24}

97. Which of the following is Absorption Law?

Correct : B. a+(a*b)<=> a

98. In a bounded lattice, an element b belongs to L is called a complement of an element a belongs to L if ______.

Correct : C. both a and b

99. If each non-empty subset of a lattice has a least upper bound and greatest lower bound then the lattice is called ________.

Correct : A. complete

100. A __________ is a complemented distributive lattice.

Correct : D. boolean function