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Welcome to the Group Theory MCQs Page

Dive deep into the fascinating world of Group Theory with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Group Theory, a crucial aspect of Discrete Mathematics. In this section, you will encounter a diverse range of MCQs that cover various aspects of Group Theory, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within Discrete Mathematics.

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Check out the MCQs below to embark on an enriching journey through Group Theory. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Discrete Mathematics.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Group Theory. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Group Theory MCQs | Page 3 of 9

Explore more Topics under Discrete Mathematics

Q21.
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

Discuss
Answer: (b).5
Q22.
A relation (34 × 78) × 57 = 57 × (78 × 34) can have __________ property.

a.

distributive

b.

associative

c.

commutative

d.

closure

Discuss
Answer: (b).associative
Q23.
B₁: ({0, 1, 2….(n-1)}, xₘ) where xₘ 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

Discuss
Answer: (b).semigroups
Q24.
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

Discuss
Answer: (c).5
Q25.
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

Discuss
Answer: (a).abelian group
Q26.
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

Discuss
Answer: (b).identity property
Q27.
Let G be a finite group with two sub groups M & N such that |M|=56 and |N|=123. Determine the value of |M⋂N|.

a.

1

b.

56

c.

14

d.

78

Discuss
Answer: (a).1
Q28.
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

Discuss
Answer: (b).closure, associativity, inverse and identity
Q29.
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

Discuss
Answer: (c).72
Q30.
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

Discuss
Answer: (a).closure property
Page 3 of 9

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