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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 1 of 9

Explore more Topics under Discrete Mathematics

Q1.
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 –

Discuss
Answer: (a).with respect to binary operation *
Q2.
An algebraic structure _________ is called a semigroup.

a.

(P, *)

b.

(Q, +, *)

c.

(P, +)

d.

(+, *)

Discuss
Answer: (a).(P, *)
Q3.
Condition for monoid is __________

a.

(a+e)=a

b.

(a*e)=(a+e)

c.

a=(a*(a+e)

d.

(a*e)=(e*a)=a

Discuss
Answer: (d).(a*e)=(e*a)=a
Q4.
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

Discuss
Answer: (d).(a*c)=(c*a)=e
Q5.
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)

Discuss
Answer: (b).(x*y)=(y*x)
Q6.
Matrix multiplication is a/an _________ property.

a.

Commutative

b.

Associative

c.

Additive

d.

Disjunctive

Discuss
Answer: (b).Associative
Q7.
A cyclic group can be generated by a/an ________ element.

a.

singular

b.

non-singular

c.

inverse

d.

multiplicative

Discuss
Answer: (a).singular
Q8.
How many properties can be held by a group?

a.

2

b.

3

c.

5

d.

4

Discuss
Answer: (c).5
Q9.
A cyclic group is always _________

a.

abelian group

b.

monoid

c.

semigroup

d.

subgroup

Discuss
Answer: (a).abelian group
Q10.
{1, i, -i, -1} is __________

a.

semigroup

b.

subgroup

c.

cyclic group

d.

abelian group

Discuss
Answer: (c).cyclic group
Page 1 of 9

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