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Test Instructions:-
Test NameLecturer Mathematics
SubjectMath Test 8
Test TypeMCQs Mathematics
Total Questions25
Total Time20 Minutes
Total Marks100

You have 20 minutes to pass to the quiz.

Lecturer Mathematics Online Test No. 8

1 / 25

A mapping Ø: G → G' is called homomorphism if for a, b ∈ G:

A). Ø (ab) = Ø (a) + Ø (b)

B). Ø (ab) = Ø (a) Ø (b)

C). Ø (ab) = Ø (a) - Ø  (b)

D). Ø (ab) = Ø (a) Ø (b)-1

2 / 25

A monomorphism is a homomorphism which is also:

3 / 25

In S4 group of permutation, number of even permutation is:

4 / 25

Which of the following group with binary operation of ordinary addition is torsion free.

5 / 25

Let X has n elements. The set Sn of all permutations on X is a group w. r. to mappings:

6 / 25

If a group is neither periodic nor torsion free, then G is:

7 / 25

If a homomorphism is also subjective the it is called:

8 / 25

Let D4 = {<a, b>; a4 = b2 = (ab)2 = 1} be a dihedral group of order 8. Then which of the following is a subgroup of D4.

A). {<a, b>; (ab)2 = 1}

B). {<a, b>; a4 = b2 = 1}

C). {<a3, b>; (a3b)2 = 1}

D). {<a, b>; b2 = 1}

9 / 25

A bijective homomorphism is called:

10 / 25

A permutation of degree n can be expressed as a product of:

11 / 25

The An, set of all even permutations of Sn is a subgroup of Sn. Then order of An is:

A). n !

B). n!/3

C). n !/3

D). n + 1/2

12 / 25

A transposition is a cycle of length:

13 / 25

Which of the following is a subgroup of S3 = {a, a2, b, ab, a2b, e}.

A). {e, a, a2}

B). {e, b}

C). {e, a2, b}

D). All of These


14 / 25

Let X = {1, 2, 3}. Then S3 has ..................... elements:

15 / 25

Let E be a group of even integers under binary operation of addition. Then which of the following isomorphic to E:

16 / 25

A group in which every element except the identity has infinite order is called:

17 / 25

A group all of whose elements are of finite order is called:

18 / 25

In Sn number of odd permutation is:

A). n !

B). n!/3

C). n !/3

D). n + 1/2

19 / 25

The relation of isomorphism between group is:

20 / 25

Product of two cyclic permutations is:

21 / 25

Which of the following is Abelian:

A). S2

B). S3

C). S4

D). S5

22 / 25

The group Sn is called:

23 / 25

The only idempotent element in a group is:

24 / 25

Which of the following is a representation of S3:

A). {< a, b > | a3 = b2 = (ab)2 = e}

B). {< a, b > | a2 = b2 = e }

C). {< a > | a2 = e}

D). {< a, b > | a2 = b2 = (ab)2 = e}

25 / 25

A group G is Abelian. Then:

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