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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 9 of 9

Explore more Topics under Discrete Mathematics

Q81.
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

Discuss
Answer: (b).poset
Q82.
_______ characterizes the properties of distributive lattices.

a.

Congruence Extension Property

b.

Algebraic extension property

c.

Poset

d.

Semigroup

Discuss
Answer: (b).Algebraic extension property
Q83.
Suppose that H be an X-set and suppose that a∼b and |Xₐ|=|Xᵦ|, the which of the following is true?

a.

Xₐ is powerset of Xᵦ

b.

Xₐ is isomorphic to Xᵦ

c.

Xₐ is homomorphic to Xᵦ

d.

Xᵦ is the subset of Xₐ

Discuss
Answer: (b).Xₐ is isomorphic to Xᵦ
Q84.
If the 4 sides of a square are to be colored by colors. How many different colourings with 50 colours are there if two arrangements that can be obtained from each other by rotation are identical?

a.

773762

b.

363563

c.

4536822

d.

1563150

Discuss
Answer: (d).1563150
Q85.
Let H be a finite group. The order of Sylow p-subgroup of H for every prime factor p with multiplicity 9 is?

a.

p+6

b.

p⁹

c.

pᵖ

d.

3!*p²

Discuss
Answer: (b).p⁹
Q86.
How many indistinguishable necklaces can be made from beads of 4 colors with exactly 9 beads of each color where each necklace is of length 16?

a.

76967234

b.

5652209

c.

14414400

d.

8686214

Discuss
Answer: (c).14414400
Q87.
Invariant permutations of two functions can form __________

a.

groups

b.

lattices

c.

graphs

d.

rings

Discuss
Answer: (a).groups
Q88.
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

Discuss
Answer: (b).ϕ⁻¹∈P(h)
Q89.
An isomorphism of Boolean algebra is defined as _______

a.

order isomorphism

b.

unordered isomorphism

c.

order homomorphism

d.

hyper-morphism

Discuss
Answer: (a).order isomorphism
Page 9 of 9

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