MTH405 Quiz 1

MTH405

QUIZ 1 UPDATED 22 MAY 2023

Q1. The order of the group {1, ω, ω^2} is:

1. 4
2. 3
3. 2
4. 5

Correct option: c) 2

Q2. (R, +) is not a subgroup of (C, +). Is this statement true or false?

1. False
2. True

Correct option: b) True

Q3. (Z, +) is a subgroup of (Q, +). Is this statement true or false?

1. False
2. True

Correct option: b) True

Q4. Let the order of a group be 27. Which of the following CANNOT be the order of a subgroup of G?

1. 1
2. 3
3. 9
4. 7

Correct option: d) 7

Q5. Which of the following is NOT a rational number?

1. 3
2. 22/7
3. π
4. 0

Correct option: c) π

Q6. If a, b are elements of group G, then (a^(-1)b)^(-1) is equal to:

1. a^(-1)b^(-1)
2. a^(-1)b
3. ba^(-1)
4. b^(-1)a

Correct option: d) b^(-1)a

Q7. If G = {1, -1, i, -i} is a group under multiplication, then the inverse of i is:

1. i
2. -i
3. -1
4. 1

Correct option: b) -i

Q8. If X has 5 elements, then the total number of permutations on X is:

1. 5
2. 5+1
3. 5!
4. 5^2

Correct option: c) 5!