Group Theory Mcqs With Solution
70. A cycle of length 2 is called a :
A. Permutation
B. Transposition
C. Cycle
D. Matrix
71. Every cyclic permutation can be expressed as a … of transposition.
A. Sum
B. Difference
C. Product
D. Quotient
72. A permutation α in Sn is said to be … permutation if it can be written as a product of an even number of transposition.
A. Even
B. Odd
C. Composite
D. Cyclic
73. Every transposition is an … permutation.
A. Even
B. Odd
C. Composite
D. Cyclic
74. A cycle of even length is an … permutation.
A. Even
B. Odd
C. Composite
D. Cyclic
75. The product of two even permutations is … permutation.
A. Even
B. Odd
C. Composite
D. Cyclic
76. The product of two odd permutations is … permutation.
A. Even
B. Odd
C. Composite
D. Cyclic
77. The product of an even and an odd permutations is … permutation.
A. Even
B. Odd
C. Composite
D. Cyclic
78. If α is an odd permutation and τ is a transposition, then ατ is … permutation.
A. Even
B. Odd
C. Both A and B
D. None of these
79. For n ≥ 2, the number of even permutations in Sn is … the number of odd permutations in Sn.
A. Equal to
B. Not equal to
C. Greater than
D. Lesser than
80. The set of even permutations in Sn is denoted by:
A. An
B. En
C. S n 2
D. None of these