Mathematics MCQs for PPSC FPSC KKPSC BPSC SPSC NTS Test 9

Lecturer Mathematics MCQs / , , , , , , , , , , , , , , ,

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Test Instructions:-
Test Name Lecturer Mathematics
Subject Math Test 9
Test Type MCQs Mathematics
Total Questions 25
Total Time 20 Minutes
Total Marks 100
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You have 20 minutes to pass to the quiz.

Lecturer Mathematics Online Test No. 9

1 / 25

Which of the following is a Klein’s four group:

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

B). <a, b ; a2 = b2 = 1>

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

D). <a, b; a4 = b2 (ab)2 = 1>

2 / 25

For any set of points S in a plane, the set of all distance preserving injective mappings of a plane which leave the points of S invariant is called:

3 / 25

Let G & H be two cyclic group of order m and n respectively. If G & H are isomorphic then:

4 / 25

Let G be a cyclic group. Then which of the following is also cyclic:

5 / 25

Which of the following is a representation of group of quaternions { ± I, ± I,± j, ± k}.

A). <a, b; a4 = (ab)2 = b2 = 1>

B). <a, b; a4 =1, a2 = b2 = (ab)2 = e>

C). <a, b; a4 = b2 = (ab)4 >

D).  None

6 / 25

In a dihedral group of order 8, D4 = <a, b; a4 = b2 = (ab)2 = 1>, the number of distinct right cosets of subgroup H = < a: a4 = 1 > are:

7 / 25

Let G = <a, b: a3 = b2 = (ab)2 = 1 > Then G is:

A). V4

B). S3

C). D8

D). S4

8 / 25

The symmetries of square of form a:

A). Klein’s four group, V4

B). Dihedral group of order 8, D4 (Optic group)

C). Group of quaternian

D).  Permutation group of order 3, S3

9 / 25

For dihedral group of order 2n, Dn, which of the following is true:

A). D2 = V4

B). D3 = S3

C). (a) & (b)

D).  None of these

10 / 25

Let G = < a, b; a-1 b2 a = b3, b-1 a2 b = a3> Then G is:

A). S3

B). D8

C). Identity group

D). C4

 

11 / 25

The smallest non-cyclic group is:

A). V4

B). S3

C). D4

D). None

12 / 25

The symmetries of a n-polygon form a:

A). Dihedral group of order 2n, Dn

B). Permutation group of order n, Sn

C). cyclic group of order n, Cn

D). None of these

13 / 25

Which of the following is a representation of C4 = {1, -1, i, -i}:

A). <x: x4 = 1>

B). <a, b : a2 = b2 = (ab)2 = 1>

C). <a, b : a3 = b2 = (ab)2 = 1}

D). <a, b; a4: b2 = 1>

14 / 25

Let H and K be two subgroup of G. Let index of H = n & index of K = m, then index of (H ∩ K) =

15 / 25

In S3 = < a, b | a3 = b2 = (ab)2 = 1 > . The number of distinct right cosets of subgroup {e, a, a2} are:

16 / 25

Ø: R+ → R is an isomorphism. Then ∀ x ∈ R+ which of the following is true:

A). Ø (x) = x

B). Ø (x) = x2 + 1

C). Ø (x) = log (x)

D). Ø (x) = tan (x)

17 / 25

Any group G can be embedded in a group of bijective mappings of certain set is a statement of:

18 / 25

The symmetries of a rectangle form a:

A). Kleins four group, V4

B). Dihedral group of order 8, D4

C). Optic group

D). Permutation group of order 3, S3

19 / 25

R+ is a group of non-zero positive real number under multiplication. Then which of the following group under addition is isomorphic to R+.

20 / 25

Let G be a cyclic group. Then which of the following can be order of G.

21 / 25

For dihedral group of order 2n, Dn, if n = 2, D2 =

A). Klein’s four group

B). S4

C). C4

D). None

22 / 25

The symmetries of an equilateral triangle form a:

A). Klein’s four group, V4

B). Dihedral group of order 8, D4

C). Optic group

D). Permutation group of order 3, S3

23 / 25

The homomorphic image Ø (G) of a group G is:

24 / 25

The smallest non-abelian group is:

A). V4

B). S3

C). D4

D). None

25 / 25

Let H and K be two left (right) cosets of a subgroup of a group. Then which of the following is true:

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