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MCQOPTIONS
This section includes 379 Mcqs, each offering curated multiple-choice questions to sharpen your VITEEE knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
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. | |
| 52. |
An algebraic structure is called a semigroup. |
| A. | (p, *) |
| B. | (q, +, *) |
| C. | (p, +) |
| D. | (+, *) |
| Answer» B. (q, +, *) | |
| 53. |
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 ? | |
| 54. |
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 | |
| 55. |
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 | |
| 56. |
If group G has 65 elements and it has two subgroups namely K and L with order 14 and30. What can be order of K intersection L? |
| A. | 10 |
| B. | 42 |
| C. | 5 |
| D. | 35 |
| Answer» D. 35 | |
| 57. |
B1: ({0, 1, 2….(n-1)}, xm) where xn standsfor “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 | |
| 58. |
A relation (34 × 78) × 57 = 57 × (78 × 34)can have property. |
| A. | distributive |
| B. | associative |
| C. | commutative |
| D. | closure |
| Answer» C. commutative | |
| 59. |
Let (A7, ⊗7)=({1, 2, 3, 4, 5, 6}, ⊗7) is agroup. 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 | |
| 60. |
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 | |
| 61. |
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 | |
| 62. |
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 | |
| 63. |
Let C = {1,2,3,4} and D = {1, 2, 3, 4} thenwhich 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 | |
| 64. |
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 | |
| 65. |
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 | |
| 66. |
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 | |
| 67. |
A is a graph with no homomorphism to any proper subgraph. |
| A. | poset |
| B. | core |
| C. | walk |
| D. | trail |
| Answer» C. walk | |
| 68. |
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 | |
| 69. |
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 | |
| 70. |
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 | |
| 71. |
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 | |
| 72. |
Every Isomorphic graph must have representation. |
| A. | cyclic |
| B. | adjacency list |
| C. | tree |
| D. | adjacency matrix |
| Answer» E. | |
| 73. |
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 | |
| 74. |
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. | |
| 75. |
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 | |
| 76. |
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 | |
| 77. |
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. | |
| 78. |
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 |
| A. | subgraph |
| B. | tree |
| C. | hamiltonian cycle |
| D. | grid |
| Answer» C. hamiltonian cycle | |
| 79. |
A bridge can not be a part of |
| A. | a simple cycle |
| B. | a tree |
| C. | a clique with size ≥ 3 whose every edge is a bridge |
| D. | a graph which contains cycles |
| Answer» B. a tree | |
| 80. |
Triangle free graphs have the property of clique number is |
| A. | less than 2 |
| B. | equal to 2 |
| C. | greater than 3 |
| D. | more than 10 |
| Answer» E. | |
| 81. |
If G is the forest with 54 vertices and 17 connected components, G has total number of edges. |
| A. | 38 |
| B. | 37 |
| C. | 17/54 d |
| D. | 17/53 |
| Answer» C. 17/54 d | |
| 82. |
In a the vertex set and the edge set are finite sets. |
| A. | finite graph |
| B. | bipartite graph |
| C. | infinite graph |
| D. | connected graph |
| Answer» C. infinite graph | |
| 83. |
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). |
| A. | subgraph |
| B. | hamiltonian graph |
| C. | euler graph |
| D. | self complementary graph |
| Answer» E. | |
| 84. |
If each and every vertex in G has degree at most 23 then G can have a vertex colouring of |
| A. | 24 |
| B. | 23 c) 176 |
| C. | d |
| D. | 54 |
| Answer» E. | |
| 85. |
Berge graph is similar to due to strong perfect graph theorem. |
| A. | line graph |
| B. | perfect graph |
| C. | bar graph |
| D. | triangle free graph |
| Answer» C. bar graph | |
| 86. |
Find the sequence generated by 1/1−x2−x4.,assume that 1, 1, 2, 3, 5, 8,… has generating function 1/1−x−x2. |
| A. | 0, 0, 1, 1, 2, 3, 5, 8,… |
| B. | 0, 1, 2, 3, 5, 8,… |
| C. | 1, 1, 2, 2, 4, 6, 8,… |
| D. | 1, 4, 3, 5, 7,… |
| Answer» B. 0, 1, 2, 3, 5, 8,… | |
| 87. |
What will be the sequence generated by the generating function 4x/(1-x)2? |
| A. | 12, 16, 20, 24,… |
| B. | 1, 3, 5, 7, 9,… |
| C. | 0, 4, 8, 12, 16, 20,… |
| D. | 0, 1, 1, 3, 5, 8, 13,… |
| Answer» D. 0, 1, 1, 3, 5, 8, 13,… | |
| 88. |
What is the sequence depicted by the generating series 4 + 15x2 + 10x3 + 25x5 + 16x6+⋯? |
| A. | 10, 4, 0, 16, 25, … |
| B. | 0, 4, 15, 10, 16, 25,… |
| C. | 4, 0, 15, 10, 25, 16,… |
| D. | 4, 10, 15, 25,… |
| Answer» D. 4, 10, 15, 25,… | |
| 89. |
Determine the value of a2 for the recurrence relation an = 17an-1 + 30n with a0=3. |
| A. | 4387 |
| B. | 5484 |
| C. | 238 |
| D. | 1437 |
| Answer» E. | |
| 90. |
Determine the solution for the recurrence relation an = 6an-1−8an-2 provided initial conditions a0=3 and a1=5. |
| A. | an = 4 * 2n – 3n |
| B. | an = 3 * 7n – 5*3n |
| C. | an = 5 * 7n |
| D. | an = 3! * 5n |
| Answer» C. an = 5 * 7n | |
| 91. |
What is the solution to the recurrence relation an=5an-1+6an-2? |
| A. | 2n2 |
| B. | 6n |
| C. | (3/2)n |
| D. | n!*3 |
| Answer» C. (3/2)n | |
| 92. |
Find the value of a4 for the recurrence relation an=2an-1+3, with a0=6. |
| A. | 320 |
| B. | 221 |
| C. | 141 |
| D. | 65 |
| Answer» D. 65 | |
| 93. |
Find the number of factors of the product 58 * 75 * 23 which are perfect squares. |
| A. | 47 |
| B. | 30 |
| C. | 65 |
| D. | 19 |
| Answer» C. 65 | |
| 94. |
How many ways are there to divide 4 Indian countries and 4 China countries into 4groups of 2 each such that at least one group must have only Indian countries? |
| A. | 6 |
| B. | 45 |
| C. | 12 |
| D. | 76 |
| Answer» B. 45 | |
| 95. |
If a, b, c, d and e are five natural numbers, then find the number of ordered sets(a, b, c, d,e) possible such that a+b+c+d+e=75. |
| A. | 65c5 |
| B. | 58c6 |
| C. | 72c7 |
| D. | 74c4 |
| Answer» E. | |
| 96. |
The number of diagonals can be drawn in a hexagon is |
| A. | 9 |
| B. | 32 |
| C. | 16 |
| D. | 21 |
| Answer» B. 32 | |
| 97. |
In a get-together party, every person present shakes the hand of every other person. If there were 90 handshakes in all, how manypersons were present at the party? |
| A. | 15 |
| B. | 14 |
| C. | 16 |
| D. | 17 |
| Answer» C. 16 | |
| 98. |
During a month with 30 days, a cricket team plays at least one game a day, but no more than 45 games. There must be a period of some number of consecutive days during which the team must play exactly number of games. |
| A. | 17 |
| B. | 46 c) 124 |
| C. | d |
| D. | 24 |
| Answer» E. | |
| 99. |
When four coins are tossed simultaneously, in number of the outcomes at most two of the coins will turn up as heads. |
| A. | 17 |
| B. | 28 |
| C. | 11 |
| D. | 43 |
| Answer» D. 43 | |
| 100. |
In a multiple-choice question paper of 15 questions, the answers can be A, B, C or D. The number of different ways of answering the question paper are |
| A. | 65536 x 47 |
| B. | 194536 x 45 |
| C. | 23650 x 49 |
| D. | 11287435 |
| Answer» B. 194536 x 45 | |