# Group Theory Mcqs With Solution

## Group Theory Mcqs With Solution

Some important group Theory Mcqs With Solution are awailble on this post . These multiple choice of group Theory with solution are most important from the examination point of view.

Also view Complex Numbers MCQS

Bold Options are correct option of the following group Theory Mcqs

1. Which of the following is not a binary operation on R?

A. +

B. .

C. ×

D. ÷

2. An element b ∈ G is inverse of a ∈ G if:

A. ab = ba

B. ab = ab2

C. ba = a^2b

D. ab = ba = e

3. An element x of a group G is said to be … if x^2 = x.

A. Nilpotent

B. Involutory

C. Idempotent

D. Square

4. The only idempotent element in a group is:

A. Inverse

B. Identity

C. Both A and B

D. None of these

5. Which of the following is a group under multiplication?

A. Z

B. Q

C. R

D. Q − {0}

6. A group is abelian if its Cayley’s table is … about its main diagonal.

A. Symmetric

B. Skew symmetric

C. Hermitian

D. Skew Hermitian

7. The set of all the nth roots of unity, Cn ={e2kπin , k = 0, 1, …, n n 1} is a group under:

B. Subtraction

C. Multiplication

D. Division

8. In the group of Quaternions {±I, ±i, ±j, ±k}, which of the following is not true?

A. jk = i

B. ik =-j

C. j^2=-i

D. None of these

9. In the group Z5, the inverse of 3 is:

A. 1

B. 2

C. 3

D. 4

10. Which of the following holds in a group.

A. Cancellation

B. Associative

C. Both A and B

D. None of these