The following are multiple choice questions (with answers) about  abstract algebra.

Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
A. 0
B. 1
C. 2
D. 3
Answer: B

Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
A. True, True
B. False, False
C. True, False
D. False, True
Answer: B

Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
A. True, True
B. False, False
C. True, False
D. False, True
Answer: C

Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
A. True, True
B. False, False
C. True, False
D. False, True
Answer: A

Find the characteristic of the ring 2Z.
A. 0
B. 3
C. 12
D. 30
Answer: A

Find the degree for the given field extension Q(sqrt(2), sqrt(3)) over Q.
A. 0
B. 4
C. 2
D. 6
Answer: