Algebra MCQs Test 03 - PAKMATH Primary categor

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1. If $\Psi: A\rightarrow B$ be a function and for $a \in A,b \in B\,\ ,\Psi(a)\neq \Psi (b)\,\ for \,\ a \neq b$ then function is known as

1-1

Onto

Constant

Identity

2. An endomorphism $\phi :G\rightarrow G$ is said to be automorphism if $\phi$ is

Bijective

1-1

Identity

onto

3. Let H and G be the two groups and H⊆G then

$N_G(X) = H$

$hH=H=Hh$

$N_G(X) \supseteq H$

None of these

4. Every group of order prime is

Simple group

Abelian Group

Normal group

Mixed group

Subgroup G generated by all commutators [u, v] such that u,v∈G then it is known as

Commutator subgroup

Abelian

Normal Subgroup

Commutator and Normal Subgroup

6. Let H be a subgroup of G and for fixed element of G then we define $K=hgh^{-1}=\left \{ghg^{-1}: h\in H \right \}$ then K is

Center

Trivial

Conjugate subgroup of H

Normal

7. Every group of order square of prime number is known as

Normal group

Abelian Group

Both Cyclic and Abelian

cyclic group

8. If H is a normal subgroup of G then

gH=Hg

H≠G

HG=H

H=G

9. A homomorphic image of cyclic group is

Abelian

Isomorphic

Non Cyclic

Cyclic

10. Let (Z,+) and (E,+) be the groups of integers and even numbers with mappings F:Z→E s.t f(x)=2x for all x∈ Z then function f is known as

None of these

Homomorphism

Monomorphism

Epimorphism

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