131). Exoress\( \Large \begin{pmatrix}1&2&3&4&5&6&7\\1&3&2&674&5&7\end{pmatrix} \) as a product of transpositions.
| A). (1 2) (3 4) (5 6) (7) |
| B). (1 2 3) (3 4) (5 7) (6 1) |
| C). (1 2) (2 1) (2 3) (4 6) (4 5) (7 1) (1 7) |
| D). none of these |
|
132). The permutation \( \Large \begin{pmatrix}1&2&3&4&5&6&7&8\\3&1&4&7&2&5&8&6\end{pmatrix} \) is
| A). even |
| B). odd |
| C). zero permutation |
| D). identity |
|
133). Exoress as a product of disjoint cycle (1 2 3 4) (3 4 5)
| A). (1 2 4) (3 5) |
| B). (1 2) (3 4 5) |
| C). (1 3) (2 4 5) |
| D). (1 2 3 4) (5) |
|
134). Express\( \Large \begin{pmatrix}1&2&3&4&5\\4&2&5&1&3\end{pmatrix} \) as disjoint cycles
| A). (1 4 3) (2 5) |
| B). (1 2) (3 4 5) |
| C). (1 4) (3 5) |
| D). none of these |
|
135). Let \( \Large S^{5} \) be the permutation with order 5. Then the order of the alternating group \( \Large A^{5} \) is
| A). 10 |
| B). 25 |
| C). 60 |
| D). 120 |
|
136). Which of the following is non-obelian?
| A). \( \Large S_{1} \) |
| B). \( \Large S_{2} \) |
| C). \( \Large S_{3} \) |
| D). \( \Large A_{3} \) |
|
137). The Kernal of the homomorphism f : (Z, +) \( \Large \rightarrow \) (R*, .) defined by f(x)
| A). {1} |
| B). {0} |
| C). Z |
| D). {1,-1} |
|
138). The Kernel of a homomorphism f : G\( \Large \rightarrow \)G' is
| A). a subgroup of G' |
| B). a normal sub group of G' |
| C). a normalsub group of G |
| D). {e} |
|
139). The Kernal of the homomorphism f: (R*, .)\( \Large \rightarrow \)(R*, .) defined by f(x) = | x | is
| A). {1} |
| B). {-1} |
| C). {0} |
| D). {1,-1} |
|
140). Let G be an abelian group and 0(a) = i, 0(b) = j for a, b\(\in\)G. Let gcd (i, j) = 1 then 0(ab) =
| A). i + j |
| B). ij |
| C). 1 |
| D). \(i^{j}\) |
|
