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

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

a=c

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

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

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

a=b

A= ab

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

a≠b

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

1-function

Identity function

Constant function

None of these

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

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

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

a=a

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

5. 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

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

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

Lagrang’s theorem

Cayley’s theorem

Cauchy’s theorem

Isomorphism theorem

3. Which of the following is abelian

$S_2$

$S_3$

$S_5$

$S_4$

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

n!/3

n!/2

n+1/2

5. 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

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

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

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

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

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

order of G

order of H

All of these

index of H

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

Z†

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

R†

C-{0}

9. The symmetries of rectangle form a

Dihedral group of order 8

Kleins four group D4

optic Group

Permutation group of order 3, S3

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

X∩Y

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Algebra MCQs Test 07

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

None

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

240

600

300

400

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

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

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

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

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

$\Phi(x)=x$

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

6. Which of the following is cyclic group

7. The group Sn is called

symmetric group of degree n

polynomial group of degree n

None of these

dihidral group of degree n

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

center of G

all of these

homomorphic of G

subgroup of G

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

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

Free group

symmetric Group

infinite group

mixed group

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Algebra MCQs Test 06

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1. which of the following is even permutation

None

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

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

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

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

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

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

$bab^{-1}$

$b^{-1}$

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

locally infinite

torsion free

all of these

a-periodic

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

1000000007

all of these

107

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

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

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

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

composition

inverse

multilpication

addition

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1. Any two conjugate subgroups have same

none of these

center

order and center

order

2. Automorphism and inner automorphism of a group G are

abelian

conjugate

normal

none of these

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

Equivalent

Abelian

Not Abelian

Normal

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

None of these

Group

Normal group

Not Group

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

Isomorphic and congugacy

Isomorphic

congugacy

Homomorphic

6. Two conjugate subgroups are

Centralizer

Homomorphic

Isomorphic

normal

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

abelian

conjugate

normal

cyclic

8. Aytomorphism group of a finite group is

normal

infinite

abelian

finite

9. Every subgroup of an abelian group is

Normal

Equivalent

Conjugate

center

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

center

abelian

normal

commutator

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Algebra MCQs Test 04

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

Abelian Group

Not Group

None of these

Group

2. Every permutation can be written as

Difference of transpositions

addition of transpositions

both a and b

product of transpositions

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

Group

cyclic permutations

Permutations

Non cyclic permutationa

4. A homomorphic image of a cyclic group is

Cyclic

Non cyclic

Abelian

Isomorphic

5. Any two cyclic group of same order are

Isomorphic

meromorphic

Homomorphic

None of these

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

Epimorphism

Isomorphism

Endomorphism

Monomorphism

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

aidentity mappings

Bijective mappings

Surjective mappings

Injective mappings

8. The center of a finite P- group is

Non.Trivial

Conjugate

Normal

Trivial

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

finite

Countable

None of these

infinite

10. Every subgroup of a cyclic group is

Cyclic

Non cyclic

Abelian

Abelian and Cyclic

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Algebra MCQs Test 03

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1. Every group of order prime is

Mixed group

Abelian Group

Simple group

Normal group

2. 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

Normal

Center

Conjugate subgroup of H

Trivial

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

1-1

onto

Bijective

Identity

4. 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

Monomorphism

Epimorphism

None of these

5. A homomorphic image of cyclic group is

Cyclic

Abelian

Non Cyclic

Isomorphic

6. If H is a normal subgroup of G then

H≠G

HG=H

H=G

gH=Hg

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

Abelian

Commutator subgroup

Commutator and Normal Subgroup

Normal Subgroup

8. 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

Onto

1-1

Identity

Constant

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

Both Cyclic and Abelian

Abelian Group

Normal group

cyclic group

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

None of these

$N_G(X) = H$

$hH=H=Hh$

$N_G(X) \supseteq H$

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

Zero

Finite

abelian

Infinte

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

Finite and Uncountable

finite

Uncountable

infinite

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

$aHa^{-1}$

$aH^{-1}$

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

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

4. Two Conjugate elements have

Same Order

None

Different Order

No Order

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

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

$A'\cup B'$

$A-B$

$A\cup B$

$A\cap B$

7. 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

$\small H_1\neq H_2$

$\small H_1=H_2$

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

$\small H_1\cap H_2=\Phi$

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

$\small v=ux$

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

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

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

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

Conjugate

Cyclic

Abelian

Normal

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

Non-Abelian

Non-Cyclic

Cyclic

aBELIAN

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WATU 27]

PAKMATH Knowledge Learning Point

ALGEBRA MCQs Test 01

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