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.

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 8 of 9

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Q71.

Suppose Kₘ={P∈Sₘ|, |P| is odd prime}. Determine the set for which m≥3 Kₘ a subgroup of Sₘ.

{3, 5, 7, 11, 13, …}

{-14, -8, -3, 0, 3, 8, 14}

{2, 4, 6, 8, 10, 12}

{12, 25, 56, 78, 134,…}

Discuss

Answer: (a).{3, 5, 7, 11, 13, …}

Q72.

The dihedral group having order 6 can have degree _____________

326

208

Discuss

Answer: (a).3

Q73.

Let (z, *) is a group with x*y=x+y-2 then inverse of x is ___________

-(x+4)

(x²+6)

(x+y)/5

(3y+4x²)

Discuss

Answer: (a).-(x+4)

Q74.

Let X be a n-square matrix such that Y = X + 8I. Which of the following property will exist?

idempotent

Y transpose is nilpotent

X nilpotent

Y inverse

Discuss

Answer: (b).Y transpose is nilpotent

Q75.

Suppose, M is a lower triangular matrix with all diagonal entries zero. The resultant matrix of M+I will be ___________

idempotent

singular

nilpotent

inverse

Discuss

Answer: (b).singular

Q76.

If Y⁹⁸ (a raised to the power of 5) = 0 and Y is a 97-square matrix. Determine the value of Y⁹⁷.

I+Y

-Y+3

Y²

Discuss

Answer: (c).0

Q77.

If 54th row of a 67th row matrix is linearly independent with each other then find the rank of the matrix.

187

Discuss

Answer: (b).54

Q78.

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.

Discuss

Answer: (b).1

Q79.

Suppose (2, 5, 8, 4) and (3, 6) are the two permutation groups that form cycles. What type of permutation is this?

odd

even

acyclic

prime

Discuss

Answer: (b).even

Q80.

Which of the following is not an abelian group?

semigroup

dihedral group

trihedral group

polynomial group

Discuss

Answer: (b).dihedral group

Page 8 of 9

Welcome to the Group Theory MCQs Page

Group Theory MCQs | Page 8 of 9

Explore more Topics under Discrete Mathematics

Logics and Proofs

Sets and Functions

Sequences,Sums and Matrices

Algorithms

Number Theory and Cryptography

Induction and Recursion

Counting Theory

Discrete Probability

Relations

Graphs and Graphs Properties

Tree Properties

Boolean Algebra and Modeling Computations

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