ALGEBRA MCQs Test 01

3000+ Mathematics all subject MCQs with their Answeers

Algebra mcqs tests 01 consist of 10 most important multiple choice questions. Prepare these questions for better results and also you can prepare definitions of algebra.

Algebra MCQs Test 01

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1. A relation is called anti-symmetric if $\dpi{120} \small (a, b) \in R \,\,\ and \,\,\ (b, a) \in R$ implies

$\dpi{120} \small a=b^{-1}$

a≠b

a=b

2. $\dpi{120} \small \forall \,\,\, a \in A$ The R is a reflexive relation $\dpi{120} \small \bigleftrightarow$ $\dpi{120} \small \Leftrightarrow$

a=a

$\dpi{120} \small (a , a) \in R$

$\dpi{120} \small (a, a) \notin R$

$\dpi{120} \small a \in R$

3. Relation R is symmetric if $\dpi{120} \small a, b\in A \,\,\, and \,\,\,\ (a, b) \in R$ then

a≠b

A= ab

a=b

$\dpi{120} \small (b , a) \in R$

4. for a fixed point $\dpi{120} \small c \in R \,\ and \,\ \phi_c=(x,c)$ is known as

Constant function

1-function

None of these

Identity function

5. Relation on R is transitive if $\dpi{120} \small (a, b) \in R,(b, c) \in R$ then

a=c

$\dpi{120} \small (a, c) \notin R$

$\dpi{120} \small (a, c) \in R$

$\dpi{120} \small a \in R$

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1. If X and Y are two sets, then X∩(XUY)’=0

X∩Y

2. Let An be the set of all even permutations of Sn is a subgroup of Sn. Then order of An is

n!/3

n+1/2

n!/2

3. Let G be a finite group. Let H be a subgroup of G . Then which of the following divides the order of G

All of these

order of H

index of H

order of G

4. The set of cube roots of unity is a subgroup of

C-{0}

R†

5. Any group G van be embedded in a group of bijective mappings of certain sets is a statement of

Lagrang’s theorem

Isomorphism theorem

Cauchy’s theorem

Cayley’s theorem

6. Let $D_4=\left \{ <a,b>;a^4=b^2=(ab)^2=1) \right \}$ be a dihedral group of order 8. Then which of the following is a subgroup of D4

$\left \{ <a^3,b>;(a^3b)^2=1) \right \}$

$\left \{ <a,b>;a^4=b^2=1) \right \}$

$\left \{ <a,b>;b^2=1 \right \}$

$\left \{ <a,b>;(ab)^2=1) \right \}$

7. Which of the following is abelian

$S_4$

$S_2$

$S_5$

$S_3$

8. Let G be a cyclic group of order 24. Then order of $a^9$ is

9. The symmetries of rectangle form a

Kleins four group D4

optic Group

Permutation group of order 3, S3

Dihedral group of order 8

10. The union of all positive even and all positive odd integers is

Z†

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Algebra MCQs Test 07

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1. Let G be a cyclic group of order 10. The number of subgroups of G is

2. In a group of even order there at least ______ elements of order 2.

None

3. In S4 group of permutation, number of even permutation is

4. The group Sn is called

symmetric group of degree n

None of these

polynomial group of degree n

dihidral group of degree n

5. If a group is neither periodic nor torsion free then G is

infinite group

symmetric Group

mixed group

Free group

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

all of these

subgroup of G

center of G

homomorphic of G

7. If n(U)= 700, n(A)=200, n(B)=300 and n(A∩B)=100 then n(A’∩B’)=?

400

300

240

600

8. $\Phi : R^{+}\rightarrow R$ is an isomorphism. then for all $x \in R^{+}$ which of the following is true.

$\Phi(x)=tan(x)$

$\Phi(x)=x^2+1$

$\Phi(x)=log(x)$

$\Phi(x)=x$

9. Suppose that n(A)=3 and n(B)=6 then what can be minimum number of elements

10. Which of the following is cyclic group

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Algebra MCQs Test 06

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1. Number of non-empty subsets of the set {1,2,3,4}

2. which of the following is even permutation

$\bigl(\begin{smallmatrix} 1 & 2 & 3 & 4\\ 2 & 1 & 4 & 3 \end{smallmatrix}\bigr)$

$\bigl(\begin{smallmatrix} 1 & 2 & 3 & 4\\ 2 & 3 & 1 & 4 \end{smallmatrix}\bigr)$

None

$\bigl(\begin{smallmatrix} 1 & 2 & 3 & 4\\ 2 & 4 & 1 & 3 \end{smallmatrix}\bigr)$

3. The group in which every element except the identity element has infinite order is called

a-periodic

all of these

locally infinite

torsion free

4. Let G be an infinite cyclic group . Then the number of generators of G are

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

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

1000000007

107

all of these

7. Let G be a group and a,b ∈ G then order of $a^{-1}$ =

$bab^{-1}$

$b^{-1}$

8. Let X has n elements. The Set Sn of all permutations of X is a group w.r.t to mappings

multilpication

inverse

addition

composition

9. If X and Y are two sets s.t n(x)=17, n(Y)=23 and n(X∪Y)=38 then n(X∩Y)=?

10. Let G be a cyclic group of order 17. The number of subgroups of G are

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1. Two conjugate subgroups are

Isomorphic

Centralizer

normal

Homomorphic

2. The intersection of any collection of normal subgroups of a group is

Equivalent

Abelian

Normal

Not Abelian

3. The set A(G) of all automorphism ofa group is

None of these

Normal group

Not Group

Group

4. Automorphism and inner automorphism of a group G are

none of these

conjugate

normal

abelian

5. Any two conjugate subgroups have same

order

center

none of these

order and center

6. Every group of order $P^6$ where P is a prime number is

cyclic

normal

conjugate

abelian

7. Equivalence relation between subgroups of a group is a relation

Isomorphic and congugacy

congugacy

Isomorphic

Homomorphic

8. Group obtained by the direct product of sylow- p group is

center

commutator

abelian

normal

9. Every subgroup of an abelian group is

Conjugate

Normal

Equivalent

center

10. Aytomorphism group of a finite group is

infinite

finite

abelian

normal

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Algebra MCQs Test 04

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1. The center of a finite P- group is

Normal

Non.Trivial

Trivial

Conjugate

2. Every permutation of degree n can be written as a product of

Non cyclic permutationa

Permutations

Group

cyclic permutations

3. Every permutation can be written as

Difference of transpositions

addition of transpositions

product of transpositions

both a and b

4. A homomorphic image of a cyclic group is

Isomorphic

Abelian

Cyclic

Non cyclic

5. Any two cyclic group of same order are

meromorphic

None of these

Isomorphic

Homomorphic

6. If there is a function f:W→A then aet A is said to be

Countable

infinite

finite

None of these

7. A homomorphism P: G ⇒G which is bijective is known as

Isomorphism

Monomorphism

Endomorphism

Epimorphism

8. Every subgroup of a cyclic group is

Non cyclic

Abelian

Cyclic

Abelian and Cyclic

9. The homomorphic image Φ(G) of a group G under homomorphic Φ is itself a

Group

None of these

Not Group

Abelian Group

10. Any group G be embeded in a groyp of a certain set of

Surjective mappings

aidentity mappings

Bijective mappings

Injective mappings

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Algebra MCQs Test 03

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

1-1

Bijective

onto

Identity

2. A homomorphic image of cyclic group is

Non Cyclic

Isomorphic

Cyclic

Abelian

3. Every group of order prime is

Abelian Group

Normal group

Mixed group

Simple group

4. If H is a normal subgroup of G then

H≠G

HG=H

H=G

gH=Hg

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

cyclic group

Normal group

Both Cyclic and Abelian

Abelian Group

6. 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

Homomorphism

Epimorphism

Monomorphism

None of these

7. 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

Identity

1-1

Constant

Onto

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

$hH=H=Hh$

$N_G(X) \supseteq H$

None of these

$N_G(X) = H$

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

10. 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

Conjugate subgroup of H

Center

Normal

Trivial

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1. If $\small H_1 \,\ and \,\ H_2$ be the subgroups of a group G then $\small H_1\cup H_2$ is a subgroup of G if and only if

$\small H_1\cap H_2=\Phi$

$\small H_1=H_2$

$\small H_1\neq H_2$

$\small H_1\subseteq H_2,H_2\subseteq H_1$

2. If $\small u,v \in G$ and for some $\small x \in G$ then v is known as conjugate of u if

$\small v=u^{-1}x$

$\small v=ux$

$\small v=ux^{-1}$

$\small v=xux^{-1}$

3. The Set $\small C_n=[e^{2\pi ki/n} : k={0,1,2,3,...}]$ is a cyclic group of order

4. Let A and B subgroups of a group such that A is normal G then normal suproup of B is

$A\cup B$

$A-B$

$A'\cup B'$

$A\cap B$

5. Every group whose order is a prime number is necessary

aBELIAN

Non-Abelian

Cyclic

Non-Cyclic

6. Every group in which each non identity element is of order 2 is

Cyclic

Conjugate

Abelian

Normal

7. Let H be a normal subgroup of G then Quotient Group G/H is represented as

$\left \{ a+H: a\in G \right \}$

$\left \{ aH: a\in G \right \}$

$aH^{-1}$

$aHa^{-1}$

8. Two Conjugate elements have

Same Order

No Order

Different Order

None

9. The set which is neither finite nor countable is known as

finite

Finite and Uncountable

infinite

Uncountable

10. In a group G if there are n integers such that $\small a^n=e$ then order of a group is

Infinte

Finite

Zero

abelian

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WATU 27]

PAKMATH Knowledge Learning Point

ALGEBRA MCQs Test 01

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