Mathematics MCQs for PPSC FPSC KKPSC BPSC SPSC NTS Test 9

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

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

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

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

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>

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

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:

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)

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

The smallest non-cyclic group is:

A). V₄

B). S₃

C). D₄

D). None

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

The smallest non-abelian group is:

A). V₄

B). S₃

C). D₄

D). None

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

A). Klein’s four group

B). S₄

C). C₄

D). None

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

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

A). D₂ = V₄

B). D₃ = S₃

C). (a) & (b)

D).  None of these

The symmetries of a n-polygon form a:

A). Dihedral group of order 2n, D_n

B). Permutation group of order n, S_n

C). cyclic group of order n, C_n

D). None of these

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

A). V₄

B). S₃

C). D₈

D). S₄

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

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

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

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

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

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:

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>

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