# 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:

A. Addition

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