81. The number of elements in alternating group An is:
A. n
B. n^2
C. n!
D. n!/2
82. The order of a cyclic permutation of length m is:
A. m
B. m 2
C. m!
D. m! 2
85. A ring R is an abelian group under:
A. Addition
B. Subtraction
C. Multiplication
D. Division
86. Which of the following is a ring under usual addition and multiplication?
A. Z
B. Q
C. R
D. All of these
87. If (R, +, ·) is a ring with additive identity 0, then for all a, b ∈ R, we have:
A. a0 = 0a = 0
B. a(−b) = (−a)b = −ab
C. (−a)(−b) = ab
D. All of these
88. The multiplicative identity (if it exists) is called:
A. Unit
B. Unity
C. Identity
D. None of these
89. An element of a ring whose multiplicative inverse exists, is called:
A. Unit
B. Unity
C. Identity
D. None of these
90. Let R be a ring with unity. If every nonzero element of R is unit, then R is called:
A. Division ring
B. Skew field
C. Integral domain
D. Both A and B
91. A commutative division ring is called:
A. Integral Domain
B. Skew field
C. Field
D. Commutative ring
92. Which of the following is(are) field(s)?
A. Q
B. R
C. C
D. All of these
93. Zn is a field if and only if n is:
A. Prime
B. Composite
C. Even
D. Odd
