MCQOPTIONS
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MCQOPTIONS
This section includes 91 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
An isomorphism of a group onto itself is called ____________ |
| A. | homomorphism |
| B. | heteromorphism |
| C. | epimorphism |
| D. | automorphism |
| Answer» E. | |
| 52. |
A finite group G of order 219 is __________ |
| A. | a semigroup |
| B. | a subgroup |
| C. | a commutative inverse |
| D. | a cyclic group |
| Answer» E. | |
| 53. |
__________ 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 | |
| 54. |
Suppose P(h) is a group of permutations and identity permutation(id) belongs to P(c). If ϕ(c)=c then which of the following is true? |
| A. | ϕ∈P(h) |
| B. | ϕ⁻¹∈P(h) |
| C. | ϕ⁻²∈P(h) |
| D. | None of the mentioned |
| Answer» C. ϕ⁻²∈P(h) | |
| 55. |
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 | |
| 56. |
Suppose (2, 5, 8, 4) and (3, 6) are the two permutation groups that form cycles. What type of permutation is this? |
| A. | odd |
| B. | even |
| C. | acyclic |
| D. | prime |
| Answer» C. acyclic | |
| 57. |
An identity element of a group has ______ element. |
| A. | associative |
| B. | commutative |
| C. | inverse |
| D. | homomorphic |
| Answer» D. homomorphic | |
| 58. |
__________ matrices do not have multiplicative inverses. |
| A. | non-singular |
| B. | singular |
| C. | triangular |
| D. | inverse |
| Answer» C. triangular | |
| 59. |
If A, B, and C are invertible matrices, the expression (AB⁻¹)⁻¹(CA⁻¹)⁻¹C2 evaluates to ____________ |
| A. | BC |
| B. | C⁻¹BC |
| C. | AB⁻¹ |
| D. | C⁻¹B |
| Answer» B. C⁻¹BC | |
| 60. |
The set of odd and even positive integers closed under multiplication is ________ |
| A. | a free semigroup of (M, ×) |
| B. | a subsemigroup of (M, ×) |
| C. | a semigroup of (M, ×) |
| D. | a subgroup of (M, ×) |
| Answer» C. a semigroup of (M, ×) | |
| 61. |
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 | |
| 62. |
How many different non-isomorphic Abelian groups of order 8 are there? |
| A. | 5 |
| B. | 4 |
| C. | 2 |
| D. | 3 |
| Answer» D. 3 | |
| 63. |
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 | |
| 64. |
Two groups are isomorphic if and only if __________ is existed between them. |
| A. | homomorphism |
| B. | endomorphism |
| C. | isomorphism |
| D. | association |
| Answer» D. association | |
| 65. |
The elements of a vector space form a/an ____________ under vector addition. |
| A. | abelian group |
| B. | commutative group |
| C. | associative group |
| D. | semigroup |
| Answer» B. commutative group | |
| 66. |
The set of rational numbers form an abelian group under _________ |
| A. | Association |
| B. | Closure |
| C. | Multiplication |
| D. | Addition |
| Answer» D. Addition | |
| 67. |
The Number of Elements Satisfying g7=e in a finite Group F is ______ |
| A. | even |
| B. | not a number |
| C. | odd |
| D. | rational |
| Answer» D. rational | |
| 68. |
If x * y = x + y + xy then (G, *) is _____________ |
| A. | Monoid |
| B. | Abelian group |
| C. | Commutative semigroup |
| D. | Cyclic group |
| Answer» D. Cyclic group | |
| 69. |
If 54th row of a 67th row matrix is linearly independent with each other then find the rank of the matrix. |
| A. | 61 |
| B. | 54 |
| C. | 187 |
| D. | 32 |
| Answer» C. 187 | |
| 70. |
A relation (34 × 78) × 57 = 57 × (78 × 34) can have __________ property. |
| A. | distributive |
| B. | associative |
| C. | commutative |
| D. | closure |
| Answer» C. commutative | |
| 71. |
__________ are called group postulates. |
| A. | Group lemmas |
| B. | Group theories |
| C. | Group axioms |
| D. | Group |
| Answer» D. Group | |
| 72. |
Invariant permutations of two functions can form __________ |
| A. | groups |
| B. | lattices |
| C. | graphs |
| D. | rings |
| Answer» B. lattices | |
| 73. |
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 | |
| 74. |
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 | |
| 75. |
Let M be an 4×4 matrix with real entries such that Mᵏ=0, for some k≥1. Find the determinant value of (I+M), where, I be the 4 x 4 identity matrix. |
| A. | 72 |
| B. | 1 |
| C. | 4 |
| D. | 36 |
| Answer» C. 4 | |
| 76. |
If we take a collection of {∅, {2}, {3}, {5}} ordered by inclusion. Which of the following is true? |
| A. | isomorphic graph |
| B. | poset |
| C. | lattice |
| D. | partially ordered set |
| Answer» C. lattice | |
| 77. |
Which of the following is not an abelian group? |
| A. | semigroup |
| B. | dihedral group |
| C. | trihedral group |
| D. | polynomial group |
| Answer» C. trihedral group | |
| 78. |
Intersection of subgroups is a ___________ |
| A. | group |
| B. | subgroup |
| C. | semigroup |
| D. | cyclic group |
| Answer» C. semigroup | |
| 79. |
A group G of order 20 is __________ |
| A. | solvable |
| B. | unsolvable |
| C. | 1 |
| D. | not determined |
| Answer» B. unsolvable | |
| 80. |
An element a in a monoid is called an idempotent if ______________ |
| A. | a⁻¹=a*a⁻¹ |
| B. | a*a²=a |
| C. | a²=a*a=a |
| D. | a³=a*a |
| Answer» D. a³=a*a | |
| 81. |
___________ are the symmetry groups used in the Standard model. |
| A. | lie groups |
| B. | subgroups |
| C. | cyclic groups |
| D. | poincare groups |
| Answer» B. subgroups | |
| 82. |
Matrix multiplication is a/an _________ property. |
| A. | Commutative |
| B. | Associative |
| C. | Additive |
| D. | Disjunctive |
| Answer» C. Additive | |
| 83. |
A group (M,*) is said to be abelian if ___________ |
| A. | (x+y)=(y+x) |
| B. | (x*y)=(y*x) |
| C. | (x+y)=x |
| D. | (y*x)=(x+y) |
| Answer» C. (x+y)=x | |
| 84. |
A cyclic group is always _________ |
| A. | abelian group |
| B. | monoid |
| C. | semigroup |
| D. | subgroup |
| Answer» B. monoid | |
| 85. |
How many properties can be held by a group? |
| A. | 2 |
| B. | 3 |
| C. | 5 |
| D. | 4 |
| Answer» D. 4 | |
| 86. |
{1, i, -i, -1} is __________ |
| A. | semigroup |
| B. | subgroup |
| C. | cyclic group |
| D. | abelian group |
| Answer» D. abelian group | |
| 87. |
An algebraic structure _________ is called a semigroup. |
| A. | (P, *) |
| B. | (Q, +, *) |
| C. | (P, +) |
| D. | (+, *) |
| Answer» B. (Q, +, *) | |
| 88. |
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 ? | |
| 89. |
A cyclic group can be generated by a/an ________ element. |
| A. | singular |
| B. | non-singular |
| C. | inverse |
| D. | multiplicative |
| Answer» B. non-singular | |
| 90. |
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. | |
| 91. |
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. | |