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440+ Discrete Mathematics Solved MCQs

These multiple-choice questions (MCQs) are designed to enhance your knowledge and understanding in the following areas: Computer Science Engineering (CSE) .

351.

A regular grammar contains rules of the form _____.

A. A tends to AB
B. AB tends to a
C. A tends to aB
D. AB tends to CD
Answer» C. A tends to aB
352.

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

A. a tends to AB
B. AaB tends to a
C. A tends to aBC
D. AB tends to CD
Answer» C. A tends to aBC
353.

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 ____.

A. transitive
B. reflexive
C. not symmetric
D. function
Answer» C. not symmetric
354.

The NAND statement is a combination of ______.

A. NOT and AND
B. NOT and OR
C. AND and OR
D. NOT or OR
Answer» A. NOT and AND
355.

The NOR statement is a combination of ________.

A. NOT and AND
B. NOT and OR
C. AND and OR
D. NOT or OR
Answer» B. NOT and OR
356.

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

A. each node
B. only first node
C. any two nodes
D. only first and last nodes
Answer» A. each node
357.

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

A. pre order
B. post order
C. in order
D. root order
Answer» C. in order
358.

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

A. recursively enumerable grammar.
B. regular grammar
C. context sensitive grammar
D. context free grammar
Answer» D. context free grammar
359.

Which of the following regular expressions identifiers are true?

A. (r*)* = r
B. (r+s)* = r* . s*
C. r*.s* = r* + s*
D. (r.s)* = r*/s*
Answer» A. (r*)* = r
360.

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

A. empty word
B. entire set
C. set of words
D. set of letters
Answer» A. empty word
361.

The number of letters in a word is called ________.

A. length
B. string
C. syntax
D. alphabet
Answer» A. length
362.

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

A. regular
B. irregular
C. isomorphic
D. homomorphic
Answer» A. regular
363.

An example for regular grammar is _____.

A. S tends to Ab
B. AB tends to SAB
C. S tends to aB
D. S tends to aBB
Answer» C. S tends to aB
364.

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

A. context free
B. context sensitive
C. regular
D. phrase structure
Answer» A. context free
365.

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

A. { }
B. tends to
C. <>
D. $
Answer» B. tends to
366.

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

A. Language
B. Syntax
C. Alphabet
D. Word
Answer» A. Language
367.

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 _____.

A. baba
B. bbaa
C. abba
D. aabb
Answer» C. abba
368.

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

A. baa
B. aba
C. abb
D. bab
Answer» C. abb
369.

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 ________.

A. f(Si , x) = Sj
B. f(S0 , a) = S1
C. f(Si , a) = Sj
D. f(S0 , x) = S1
Answer» B. f(S0 , a) = S1
370.

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

A. regular grammar
B. phrase structure grammar
C. context free grammar
D. context sensitive grammar
Answer» A. regular grammar
371.

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

A. n
B. n+1
C. n-1
D. n-2
Answer» C. n-1
372.

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

A. the degree of the corresponding vertices
B. the sum of degrees of all vertices
C. the degree of the initial vertex
D. the degree of the terminal vertex
Answer» A. the degree of the corresponding vertices
373.

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

A. one 1's
B. two 1's
C. one 2's
D. two 2's
Answer» B. two 1's
374.

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

A. odd
B. even
C. distinct
D. equal
Answer» A. odd
375.

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

A. 1
B. 2
C. odd
D. even
Answer» B. 2
376.

G is strongly connected implies _________.

A. G is unilaterally connected.
B. G is bilaterally connected
C. G is unilaterally connected
D. G has more than one component
Answer» A. G is unilaterally connected.
377.

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

A. (n-a)/2
B. (n-1)/2
C. (n+a)/2
D. n/2
Answer» C. (n+a)/2
378.

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

A. odd
B. even
C. equal
D. 0
Answer» A. odd
379.

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

A. 2 power k
B. 2 power (k-1)
C. 2 power (k-1)-1)
D. 2 power (k+1)-1
Answer» D. 2 power (k+1)-1
380.

For a symmetric digraph, the adjacency matrix is _________.

A. symmetric
B. antisymmetric
C. asymmetric
D. symmetric and asymmetric
Answer» A. symmetric
381.

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

A. outdegrees of the node
B. indegrees of the nodes
C. unit degree of the nodes
D. in & out degrees of the nodes
Answer» A. outdegrees of the node
382.

DFSA and NDFSA represent the ________ language.

A. regular
B. context free
C. context sensitive
D. phrase structure
Answer» A. regular
383.

The chromatic number of the chess board is ______.

A. 1
B. 2
C. 3
D. 4
Answer» B. 2
384.

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

A. 0
B. 1
C. 2
D. 3
Answer» A. 0
385.

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

A. 3 or less
B. 4 or less
C. 5 or less
D. 6 or less
Answer» C. 5 or less
386.

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

A. an elementary sum
B. an elementary product
C. a well-formed formula
D. an equivalence of relation formula
Answer» B. an elementary product
387.

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

A. DNF
B. CNF
C. PDNF
D. PCNF
Answer» C. PDNF
388.

The less than relation < on real is __________.

A. a partial ordering since it is asymmetric and reflexive
B. a partial ordering since it is anti-symmetric and reflexive
C. not a partial ordering since it is not asymmetric and not reflexive
D. not a partial ordering since it is not anti-symmetric and not reflexive
Answer» D. not a partial ordering since it is not anti-symmetric and not reflexive
389.

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

A. void relation
B. circular
C. partial order relation
D. compatibility relation
Answer» D. compatibility relation
390.

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

A. void
B. universal
C. partial
D. equivalence
Answer» B. universal
391.

A self complemented distributive lattice is called _______.

A. boolean algebra
B. modular lattice
C. complete lattice
D. self dual lattice
Answer» A. boolean algebra
392.

Every finite subset of a lattice has ____________.

A. a Least Upper Bound and Greatest Lower Bound
B. many Least Upper Bounds and a Greatest Lower Bound
C. many Least Upper Bounds and many Greatest Lower Bounds
D. either some Least Upper Bounds or some Greatest Lower Bounds
Answer» A. a Least Upper Bound and Greatest Lower Bound
393.

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

A. DNF
B. CNF
C. PCNF
D. PDNF
Answer» C. PCNF
394.

The set of all divisors of 24 are ___________.

A. {1, 2, 3, 4, 6, 8, 12, 24}
B. {2, 3, 4, 6, 8, 12}
C. {1, 3, 6, 12,}
D. {2, 4, 6, 8}
Answer» A. {1, 2, 3, 4, 6, 8, 12, 24}
395.

Which of the following is Absorption Law?

A. a*a <=>a
B. a+(a*b)<=> a
C. a*b <=>a*a
D. (a*b)*c <=>a*(b*c)
Answer» B. a+(a*b)<=> a
396.

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

A. a*b=0
B. a+b=1
C. both a and b
D. none
Answer» C. both a and b
397.

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

A. complete
B. associative
C. absorption
D. commutative
Answer» A. complete
398.

A __________ is a complemented distributive lattice.

A. boolean homomorphism
B. boolean algebra
C. boolean isomorphism
D. boolean function
Answer» D. boolean function
399.

Boolean expression except 0 expressed in an equivalent form is called _____.

A. canonical
B. sum
C. product
D. standard
Answer» A. canonical
400.

_________relations are useful in solving certain minimization problems of switching theory.

A. Void
B. Universal
C. Compatibility
D. Equivalence
Answer» C. Compatibility

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