MCQOPTIONS
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MCQOPTIONS
This section includes 315 Mcqs, each offering curated multiple-choice questions to sharpen your Computer Science Engineering (CSE) knowledge and support exam preparation. Choose a topic below to get started.
| 101. |
a * H is a set of            coset. |
| A. | right |
| B. | left |
| C. | sub |
| D. | semi |
| Answer» C. sub | |
| 102. |
a * H = H * a relation holds if |
| A. | h is semigroup of an abelian group |
| B. | h is monoid of a group |
| C. | h is a cyclic group |
| D. | h is subgroup of an abelian group |
| Answer» E. | |
| 103. |
Lagrange’s theorem specifies |
| A. | the order of semigroup is finite |
| B. | the order of the subgroup divides the order of the finite group |
| C. | the order of an abelian group is infinite |
| D. | the order of the semigroup is added to the order of the group |
| Answer» C. the order of an abelian group is infinite | |
| 104. |
Two groups are isomorphic if and only if                      is existed between them. |
| A. | homomorphism |
| B. | endomorphism |
| C. | isomorphism |
| D. | association |
| Answer» D. association | |
| 105. |
A normal subgroup is |
| A. | a subgroup under multiplication by the elements of the group |
| B. | an invariant under closure by the elements of that group |
| C. | a monoid with same number of elements of the original group |
| D. | an invariant equipped with conjugation by the elements of original group |
| Answer» E. | |
| 106. |
What is a circle group? |
| A. | a subgroup complex numbers having magnitude 1 of the group of nonzero complex elements |
| B. | a subgroup rational numbers having magnitude 2 of the group of real elements |
| C. | a subgroup irrational numbers having magnitude 2 of the group of nonzero complex elements |
| D. | a subgroup complex numbers having magnitude 1 of the group of whole numbers |
| Answer» B. a subgroup rational numbers having magnitude 2 of the group of real elements | |
| 107. |
Intersection of subgroups is a |
| A. | group |
| B. | subgroup |
| C. | semigroup |
| D. | cyclic group |
| Answer» C. semigroup | |
| 108. |
A group of rational numbers is an example of |
| A. | a subgroup of a group of integers |
| B. | a subgroup of a group of real numbers |
| C. | a subgroup of a group of irrational numbers |
| D. | a subgroup of a group of complex numbers |
| Answer» C. a subgroup of a group of irrational numbers | |
| 109. |
                     is not necessarily a property of a Group. |
| A. | commutativity |
| B. | existence of inverse for every element |
| C. | existence of identity |
| D. | associativity |
| Answer» B. existence of inverse for every element | |
| 110. |
{1, i, -i, -1} is |
| A. | a commutative subgroup |
| B. | a lattice |
| C. | a trivial group |
| D. | a monoid |
| Answer» D. a monoid | |
| 111. |
A cyclic group is always |
| A. | abelian group |
| B. | monoid |
| C. | semigroup |
| D. | subgroup |
| Answer» B. monoid | |
| 112. |
How many properties can be held by a group? |
| A. | 2 |
| B. | 3 |
| C. | 5 |
| D. | 4 |
| Answer» D. 4 | |
| 113. |
Matrix multiplication is a/an                    property. |
| A. | commutative |
| B. | associative |
| C. | additive |
| D. | disjunctive |
| Answer» C. additive | |
| 114. |
Let K be a group with 8 elements. Let H be a subgroup of K and H |
| A. | semigroup |
| B. | subgroup |
| C. | cyclic group |
| D. | abelian group |
| Answer» D. abelian group | |
| 115. |
A monoid is called a group if |
| A. | (a*a)=a=(a+c) |
| B. | (a*c)=(a+c) |
| C. | (a+c)=a |
| D. | (a*c)=(c*a)=e |
| Answer» E. | |
| 116. |
An algebraic structure                    is called a semigroup. |
| A. | (p, *) |
| B. | (q, +, *) |
| C. | (p, +) |
| D. | (+, *) |
| Answer» B. (q, +, *) | |
| 117. |
Condition for monoid is |
| A. | (a+e)=a |
| B. | (a*e)=(a+e) |
| C. | a=(a*(a+e) |
| D. | (a*e)=(e*a)=a |
| Answer» E. | |
| 118. |
A non empty set A is termed as an algebraic structure |
| A. | with respect to binary operation * |
| B. | with respect to ternary operation ? |
| C. | with respect to binary operation + |
| D. | with respect to unary operation – |
| Answer» B. with respect to ternary operation ? | |
| 119. |
The set of even natural numbers, {6, 8, 10, 12,..,} is closed under addition operation. Which of the following properties will it satisfy? |
| A. | closure property |
| B. | associative property |
| C. | symmetric property |
| D. | identity property |
| Answer» B. associative property | |
| 120. |
A group G, ({0}, +) under addition operation satisfies which of the following properties? |
| A. | identity, multiplicity and inverse |
| B. | closure, associativity, inverse and identity |
| C. | multiplicity, associativity and closure |
| D. | inverse and closure |
| Answer» C. multiplicity, associativity and closure | |
| 121. |
If (M, *) is a cyclic group of order 73, then number of generator of G is equal to |
| A. | 89 |
| B. | 23 |
| C. | 72 |
| D. | 17 |
| Answer» D. 17 | |
| 122. |
Let * be the binary operation on the rational number given by a*b=a+b+ab. Which of the following property does not exist for the group? |
| A. | closure property |
| B. | identity property |
| C. | symmetric property |
| D. | associative property |
| Answer» C. symmetric property | |
| 123. |
Consider the binary operations on X, a*b = a+b+4, for a, b ∈ X. It satisfies the properties of |
| A. | abelian group |
| B. | semigroup |
| C. | multiplicative group |
| D. | isomorphic group |
| Answer» B. semigroup | |
| 124. |
If group G has 65 elements and it has two subgroups namely K and L with order 14 and 30. What can be order of K intersection L? |
| A. | 10 |
| B. | 42 |
| C. | 5 |
| D. | 35 |
| Answer» D. 35 | |
| 125. |
B1: ({0, 1, 2….(n-1)}, xm) where xn stands for “multiplication-modulo-n†and B2: ({0, 1, 2….n}, xn) where xn stands for “multiplication-modulo-m†are the two statements. Both B1 and B2 are considered to be |
| A. | groups |
| B. | semigroups |
| C. | subgroups |
| D. | associative subgroup |
| Answer» C. subgroups | |
| 126. |
A relation (34 × 78) × 57 = 57 × (78 × 34) can have                      property. |
| A. | distributive |
| B. | associative |
| C. | commutative |
| D. | closure |
| Answer» C. commutative | |
| 127. |
Let (A7, ⊗7)=({1, 2, 3, 4, 5, 6}, ⊗7) is a group. It has two sub groups X and Y. X={1, 3, 6}, Y={2, 3, 5}. What is the order of union of subgroups? |
| A. | 65 |
| B. | 5 |
| C. | 32 |
| D. | 18 |
| Answer» C. 32 | |
| 128. |
If in sets A, B, C, the set B ∩ C consists of 8 elements, set A ∩ B consists of 7 elements and set C ∩ A consists of 7 elements then the minimum element in set A U B U C will be? |
| A. | 8 |
| B. | 14 |
| C. | 22 |
| D. | 15 |
| Answer» B. 14 | |
| 129. |
Let a set be A then A ∩ φ and A U φ are |
| A. | φ, φ |
| B. | φ, a |
| C. | a, φ |
| D. | none of the mentioned |
| Answer» C. a, φ | |
| 130. |
Let Universal set U is {1, 2, 3, 4, 5, 6, 7, 8}, (Complement of A) A’ is {2, 5, 6, 7}, A ∩ B is {1, 3, 4} then the set B’ will surely have of which of the element? |
| A. | 8 |
| B. | 7 |
| C. | 1 |
| D. | 3 |
| Answer» B. 7 | |
| 131. |
Let C = {1,2,3,4} and D = {1, 2, 3, 4} then which of the following hold not true in this case? |
| A. | c – d = d – c |
| B. | c u d = c ∩ d |
| C. | c ∩ d = c – d |
| D. | c – d = Φ |
| Answer» D. c – d = Φ | |
| 132. |
Which of the following statement regarding sets is false? |
| A. | a ∩ a = a |
| B. | a u a = a |
| C. | a – (b ∩ c) = (a – b) u (a –c) |
| D. | (a u b)’ = a’ u b’ |
| Answer» E. | |
| 133. |
For two sets C and D the set (C – D) ∩ D will be |
| A. | c |
| B. | d |
| C. | Φ |
| D. | none of the mentioned |
| Answer» D. none of the mentioned | |
| 134. |
Let C and D be two sets then C – D is equivalent to |
| A. | c’ ∩ d |
| B. | c‘∩ d’ |
| C. | c ∩ d’ |
| D. | none of the mentioned |
| Answer» D. none of the mentioned | |
| 135. |
If set C is {1, 2, 3, 4} and C – D = Φ then set D can be |
| A. | {1, 2, 4, 5} |
| B. | {1, 2, 3} |
| C. | {1, 2, 3, 4, 5} |
| D. | none of the mentioned |
| Answer» D. none of the mentioned | |
| 136. |
What is the grade of a planar graph consisting of 8 vertices and 15 edges? |
| A. | 30 |
| B. | 15 |
| C. | 45 d |
| D. | 106 |
| Answer» B. 15 | |
| 137. |
A Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â is a graph with no homomorphism to any proper subgraph. |
| A. | poset |
| B. | core |
| C. | walk |
| D. | trail |
| Answer» C. walk | |
| 138. |
An isomorphism of graphs G and H is a bijection f the vertex sets of G and H. Such that any two vertices u and v of G are adjacent in G if and only if |
| A. | f(u) and f(v) are contained in g but not contained in h |
| B. | f(u) and f(v) are adjacent in h |
| C. | f(u * v) = f(u) + f(v) d) f(u) = f(u)2 + f(v |
| D. | 2 |
| Answer» C. f(u * v) = f(u) + f(v) d) f(u) = f(u)2 + f(v | |
| 139. |
A graph is              if and only if it does not contain a subgraph homeomorphic to k5 or k3,3. |
| A. | bipartite graph |
| B. | planar graph |
| C. | line graph |
| D. | euler subgraph |
| Answer» C. line graph | |
| 140. |
A complete n-node graph Kn is planar if and only if |
| A. | n ≥ 6 |
| B. | n2 = n + 1 |
| C. | n ≤ 4 |
| D. | n + 3 |
| Answer» D. n + 3 | |
| 141. |
A cycle on n vertices is isomorphic to its complement. What is the value of n? |
| A. | 5 |
| B. | 32 |
| C. | 17 |
| D. | 8 |
| Answer» B. 32 | |
| 142. |
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 |
| A. | n+2 |
| B. | 3n/2 |
| C. | n2 |
| D. | 2n |
| Answer» C. n2 | |
| 143. |
Every Isomorphic graph must have                  representation. |
| A. | cyclic |
| B. | adjacency list |
| C. | tree |
| D. | adjacency matrix |
| Answer» E. | |
| 144. |
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 |
| A. | n-1 and n+1 |
| B. | v and k |
| C. | k+1 and v-k |
| D. | k-1 and v-1 |
| Answer» E. | |
| 145. |
The maximum number of edges in a 8- node undirected graph without self loops is |
| A. | 45 |
| B. | 61 |
| C. | 28 |
| D. | 17 |
| Answer» D. 17 | |
| 146. |
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. |
| A. | 98 |
| B. | 13 |
| C. | 6 |
| D. | 34 |
| Answer» D. 34 | |
| 147. |
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? |
| A. | 11 |
| B. | 14 |
| C. | 18 |
| D. | 19 |
| Answer» D. 19 | |
| 148. |
             is the maximum number of edges in an acyclic undirected graph with k vertices. |
| A. | k-1 |
| B. | k2 |
| C. | 2k+3 |
| D. | k3+4 |
| Answer» B. k2 | |
| 149. |
The minimum number of edges in a connected cyclic graph on n vertices is |
| A. | n – 1 |
| B. | n |
| C. | 2n+3 |
| D. | n+1 |
| Answer» C. 2n+3 | |
| 150. |
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 |
| A. | complete bipartite graph |
| B. | hamiltonian cycle |
| C. | regular graph |
| D. | euler graph |
| Answer» E. | |