121). In the group {1, 2, ..., 1,6} under the operation multiplication modulo 17, the order of 3 is
| A). 4 |
| B). 8 |
| C). 12 |
| D). 16 |
|
122). The orders of 2 and 3 in \((Z_{8},\oplus)\) are respectively.
| A). 8 and 4 |
| B). 4 and 8 |
| C). 8 and 8 |
| D). 8 and 16 |
|
123). Let G be a group of prime order then
| A). G has no subgroups |
| B). G has no proper subgroups |
| C). G has more than 2 subgroups |
| D). G is non abelian |
|
124). In a quotient group \( \Large \frac{G}{N} \) , N is
| A). any subgroup of G |
| B). a cyclic subgroup of G |
| C). a normal subgroup of G |
| D). aiproper abelian subgroup of G |
|
125). The Cayley table is| * | e | a | b | c | | e | e | a | b | c | | a | a | e | c | b | | b | b | c | e | a | | c | c | b | a | e |
represents
| A). a non-abelian group |
| B). an abelian group |
| C). not a group |
| D). cyclic group |
|
126). Let G be a group of order 2p where p is a prime. Then G has
| A). a normal subgroup of order |
| B). a subgroup of order p + 1 |
| C). a cyclic group of order p - l |
| D). none of these |
|
127). Let G be a group of order 2p where p is a prime. Then G has
| A). a normal subgroup of order |
| B). a subgroup of order p + 1 |
| C). a cyclic group of order p - l |
| D). none of these |
|
128). \( \Large \alpha = \) \( \Large \begin{pmatrix}1&2&3&4\\3&4&1&2\end{pmatrix} \) then \( \Large \alpha ^{-1} \)
| A). \( \Large \begin{pmatrix}1&2&3&4\\2&3&4&1\end{pmatrix} \) |
| B). \( \Large \begin{pmatrix}1&2&3&4\\3&4&1&2\end{pmatrix} \) |
| C). \( \Large \begin{pmatrix}1&2&3&4\\4&2&1&3\end{pmatrix} \) |
| D). \( \Large \begin{pmatrix}1&2&3&4\\2&3&1&4\end{pmatrix} \) |
|
129). \( \Large O(S_{5})= \)
| A). 5 |
| B). 10 |
| C). 25 |
| D). 120 |
|
130). Express \( \Large \begin{pmatrix}1&2&3&4&5&6\\1&6&5&3&4&2\end{pmatrix} \) as a product of disjoint cycles.
| A). (1) (2 3) (4 5 6) |
| B). (1) (2 6) (3 5 4) |
| C). (1 2 3) (4 5 6) |
| D). (1 2) (3 4) (5 6) |
|
