MCQs of Group Theory

MCQs of Group Theory

1. This is an abelian group { – 3 n : n ε Z } under?
A. division
B. subtraction
C. addition
D. multiplication

Answer - Click Here:
C

2. What is the inverse of – ι If G = { 1, -1, ι, – ι } is group under multiplication?
A. −1
B. ι
C. 1
D. None of Above

Answer - Click Here:
B

3. The monoid is a?
A. a non-abelian group
B. groupoid
C. A group
D. a commutative group

Answer - Click Here:
A

4. (ba)-1 =_____ If a, b are elements of a group G?
A. b-1 a
B. a-1 b
C. b-1 a-1
D. a-1 b-1

Answer - Click Here:
D

5. What is an inverse of – i in the multiplicative group if {1, – 1, i , – i} is?
A. -1
B. 1
C. i
D. None of these

Answer - Click Here:
C

6. What is the value of (a- 1 b)- 1 is in the group (G, .)?
A. b- 1a
B. ab-1
C. ba-1
D. a-1b

Answer - Click Here:
A

7. What is the inverse of an if (Z,*) is a group with a*b = a+b+1 ∀ a, b ∈Z?
A. -2
B. 0
C. -a-2
D. a-2

Answer - Click Here:
C

8. Which sentence is true?
A. Set of all matrices forms a group under multiplication
B. Set of all rational negative numbers forms a group under multiplication
C. Set of all non-singular matrices forms a group under multiplication
D. Both (b) and (c)

Answer - Click Here:
C

9. Which statement is false?
A. The set of rational integers is an abelian group under addition
B. The set of rational numbers form an abelian group under multiplication
C. The set of rational numbers is an abelian group under addition
D. None of these

Answer - Click Here:
B

10. What is the identity element In the group G = {2, 4, 6, 8) under multiplication modulo 10?
A. 5
B. 9
C. 6
D. 12

Answer - Click Here:
C