MCQOPTIONS
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MCQOPTIONS
This section includes 99 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
In Modern particle physics there must exist ______________ |
| A. | group theory |
| B. | graph theory |
| C. | lattice structure |
| D. | invariant semigroup |
| Answer» B. graph theory | |
| 2. |
There exists _______ between group homology and group cohomology of a finite group. |
| A. | homomorphism |
| B. | isomorphism |
| C. | automorphism |
| D. | semilattice structure |
| Answer» B. isomorphism | |
| 3. |
If any group is a manifold what is the dimension of that group? |
| A. | same as manifold |
| B. | same as vector space |
| C. | infinite |
| D. | finite |
| Answer» B. same as vector space | |
| 4. |
In basic ring theory, any ring R1 may be embedded in its own ________ |
| A. | semilattice |
| B. | endomorphism ring |
| C. | homomorphic ring |
| D. | subgroup |
| Answer» C. homomorphic ring | |
| 5. |
A Latin square graph is a representation of a _______ |
| A. | quasi group |
| B. | homomorphic group |
| C. | semigroup |
| D. | subgroup |
| Answer» B. homomorphic group | |
| 6. |
For any graph say G, Cayley graph is ______________ |
| A. | canonial |
| B. | not canonical |
| C. | isomorphic |
| D. | homomorphic |
| Answer» C. isomorphic | |
| 7. |
Which of the following is the set of m×m invertible matrices? |
| A. | a permutation group of degree m² |
| B. | a general linear group of degree m |
| C. | a sublattice group of degree m |
| D. | a isomorphic graph of m nodes |
| Answer» C. a sublattice group of degree m | |
| 8. |
In invariant algebra, some generators of group G1 that goes either into itself or zero under ______ with any other element of the algebra. |
| A. | commutation |
| B. | permutation |
| C. | combination |
| D. | lattice |
| Answer» B. permutation | |
| 9. |
Which of the following can be embedded in an algebraically closed group? |
| A. | infinite group |
| B. | stargraph |
| C. | a countable group |
| D. | a semilattice |
| Answer» D. a semilattice | |
| 10. |
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. | 17/53 |
| Answer» C. 17/54 | |
| 11. |
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 | |
| 12. |
In a 7-node directed cyclic graph, the number of Hamiltonian cycle is to be ______ |
| A. | 728 |
| B. | 450 |
| C. | 360 |
| D. | 260 |
| Answer» D. 260 | |
| 13. |
An undirected graph G has bit strings of length 100 in its vertices and there is an edge between vertex u and vertex v if and only if u and v differ in exactly one bit position. Determine the ratio of the chromatic number of G to the diameter of G? |
| A. | 1/2¹⁰¹ |
| B. | 1/50 |
| C. | 1/100 |
| D. | 1/20 |
| Answer» C. 1/100 | |
| 14. |
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 |
| D. | 54 |
| Answer» B. 23 | |
| 15. |
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 | |
| 16. |
The number of edges in a regular graph of degree 46 and 8 vertices is ____________ |
| A. | 347 |
| B. | 230 |
| C. | 184 |
| D. | 186 |
| Answer» D. 186 | |
| 17. |
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. | |
| 18. |
All closed walks are of ______ length in a bipartite graph. |
| A. | infinite |
| B. | even |
| C. | odd |
| D. | odd prime |
| Answer» C. odd | |
| 19. |
Let D be a simple graph on 10 vertices such that there is a vertex of degree 1, a vertex of degree 2, a vertex of degree 3, a vertex of degree 4, a vertex of degree 5, a vertex of degree 6, a vertex of degree 7, a vertex of degree 8 and a vertex of degree 9. What can be the degree of the last vertex? |
| A. | 4 |
| B. | 0 |
| C. | 2 |
| D. | 5 |
| Answer» D. 5 | |
| 20. |
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. | |
| 21. |
If a partial order is drawn as a Hasse diagram in which no two edges cross, its covering graph is called ______ |
| A. | upward planar |
| B. | downward planar |
| C. | lattice |
| D. | biconnected components |
| Answer» B. downward planar | |
| 22. |
Bipartite graphs are used in ________ |
| A. | modern coding theory |
| B. | colouring graphs |
| C. | neural networks |
| D. | chemical bonds |
| Answer» B. colouring graphs | |
| 23. |
The partition V = V₁ ∪ V₂ in a bipartite graph G₁ is called ________ |
| A. | bipartition of G₁ |
| B. | 2-vertex set of G₁ |
| C. | sub bipartite graphs |
| D. | disjoint vertex set |
| Answer» C. sub bipartite graphs | |
| 24. |
The maximum number of edges in a bipartite graph on 14 vertices is ___________ |
| A. | 56 |
| B. | 14 |
| C. | 49 |
| D. | 87 |
| Answer» D. 87 | |
| 25. |
The spectrum of a graph is _______ if and only if it is _______ graph. |
| A. | symmetry, bipartite |
| B. | transitive, bipartite |
| C. | cyclic, Euler |
| D. | reflexive, planar |
| Answer» B. transitive, bipartite | |
| 26. |
Every complete bipartite graph must not be _______ |
| A. | planar graph |
| B. | line graph |
| C. | complete graph |
| D. | subgraph |
| Answer» D. subgraph | |
| 27. |
The time complexity to test whether a graph is bipartite or not is said to be _______ using depth first search. |
| A. | O(n³) |
| B. | linear time |
| C. | O(1) |
| D. | O(nlogn) |
| Answer» C. O(1) | |
| 28. |
What is the maximum number of edges in a bipartite graph on 14 vertices? |
| A. | 78 |
| B. | 15 |
| C. | 214 |
| D. | 49 |
| Answer» E. | |
| 29. |
In a ______ the degree of each and every vertex is equal. |
| A. | regular graph |
| B. | point graph |
| C. | star graph |
| D. | euler graph |
| Answer» D. euler graph | |
| 30. |
In a complete bipartite graph, the intersection of two sub graphs is ______ |
| A. | 1 |
| B. | |
| C. | 2¹⁰ |
| D. | 412 |
| Answer» C. 2¹⁰ | |
| 31. |
A ________ has a greatest element and a least element which satisfy 0<=a<=1 for every a in the lattice(say, L). |
| A. | semilattice |
| B. | join semilattice |
| C. | meet semilattice |
| D. | bounded lattice |
| Answer» E. | |
| 32. |
A free semilattice has the _______ property. |
| A. | intersection |
| B. | commutative and associative |
| C. | identity |
| D. | universal |
| Answer» E. | |
| 33. |
In the poset (Z⁺, |) (where Z⁺ is the set of all positive integers and | is the divides relation) are the integers 9 and 351 comparable? |
| A. | comparable |
| B. | not comparable |
| C. | comparable but not determined |
| D. | determined but not comparable |
| Answer» B. not comparable | |
| 34. |
A sublattice(say, S) of a lattice(say, L) is a convex sublattice of L if _________ |
| A. | x>=z, where x in S implies z in S, for every element x, y in L |
| B. | x=y and y<=z, where x, y in S implies z in S, for every element x, y, z in L |
| C. | x<=y<=z, where x, y in S implies z in S, for every element x, y, z in L |
| D. | x=y and y>=z, where x, y in S implies z in S, for every element x, y, z in L |
| Answer» D. x=y and y>=z, where x, y in S implies z in S, for every element x, y, z in L | |
| 35. |
Every poset that is a complete semilattice must always be a _______ |
| A. | sublattice |
| B. | complete lattice |
| C. | free lattice |
| D. | partial lattice |
| Answer» C. free lattice | |
| 36. |
A Poset in which every pair of elements has both a least upper bound and a greatest lower bound is termed as _______ |
| A. | sublattice |
| B. | lattice |
| C. | trail |
| D. | walk |
| Answer» C. trail | |
| 37. |
Suppose P₁ is a partially ordered class and a cut of P₁ is pair (D, T) of nonempty subclasses of P₁ satisfies which of the following properties? |
| A. | D∩T=Ø |
| B. | D∪T=P₁ |
| C. | xyz∈T |
| D. | z∈T and zx∈D |
| Answer» B. D∪T=P₁ | |
| 38. |
If every two elements of a poset are comparable then the poset is called ________ |
| A. | sub ordered poset |
| B. | totally ordered poset |
| C. | sub lattice |
| D. | semigroup |
| Answer» C. sub lattice | |
| 39. |
Let G be the graph defined as the Hasse diagram for the ⊆ relation on the set S{1, 2,…, 18}. How many edges are there in G? |
| A. | 43722 |
| B. | 2359296 |
| C. | 6487535 |
| D. | 131963 |
| Answer» C. 6487535 | |
| 40. |
For a connected planar simple graph G=(V, E) with e=|E|=16 and v=|V|=9, then find the number of regions that are created when drawing a planar representation of the graph? |
| A. | 321 |
| B. | 9 |
| C. | 1024 |
| D. | 596 |
| Answer» C. 1024 | |
| 41. |
______ and _______ are the two binary operations defined for lattices. |
| A. | Join, meet |
| B. | Addition, subtraction |
| C. | Union, intersection |
| D. | Multiplication, modulo division |
| Answer» B. Addition, subtraction | |
| 42. |
Determine the density of a planar graph with 34 edges and 13 nodes. |
| A. | 22/21 |
| B. | 12/23 |
| C. | 328 |
| D. | 576 |
| Answer» B. 12/23 | |
| 43. |
If the number of vertices of a chromatic polynomial PG is 56, what is the degree of PG? |
| A. | 344 |
| B. | 73 |
| C. | 265 |
| D. | 56 |
| Answer» E. | |
| 44. |
A non-planar graph can have ____________ |
| A. | complete graph |
| B. | subgraph |
| C. | line graph |
| D. | bar graph |
| Answer» C. line graph | |
| 45. |
A direct product of a group G possess which of the following characteristics? |
| A. | a multiplication of subgroups of G |
| B. | a factorization via subgroups of G |
| C. | a superset of subgroups of G |
| D. | a maximal power set of subgroups |
| Answer» C. a superset of subgroups of G | |
| 46. |
Suppose G be a connected planar graph of order n≥5 and size m. If the length of the smallest cycle in G is 5, then which of the following is true? |
| A. | (m+n)⁴>=mn |
| B. | m≤5/3(n−2) |
| C. | (m²+n)/3 |
| D. | n>=(6/5)(n+1) |
| Answer» C. (m²+n)/3 | |
| 47. |
What is the number of edges of the greatest planar subgraph of K₃,₂ where m,n≤3? |
| A. | 18 |
| B. | 6 |
| C. | 128 |
| D. | 702 |
| Answer» C. 128 | |
| 48. |
If a graph G is k-colorable and k |
| A. | n-colorable |
| B. | n² nodes |
| C. | (k+n)-colorable |
| D. | (k³+n³+1) nodes |
| Answer» B. n² nodes | |
| 49. |
The relation ≤ is a partial order if it is ___________ |
| A. | reflexive, antisymmetric and transitive |
| B. | reflexive, symmetric |
| C. | asymmetric, transitive |
| D. | irreflexive and transitive |
| Answer» B. reflexive, symmetric | |
| 50. |
If Cₙ is the nth cyclic graph, where n>3 and n is odd. Determine the value of X(Cₙ). |
| A. | 32572 |
| B. | 16631 |
| C. | 3 |
| D. | 310 |
| Answer» D. 310 | |