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

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

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

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

a=c

2. 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

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

a=a

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

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

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

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

A= ab

a=b

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

a≠b

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

1-function

Constant function

Identity function

None of these

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

X∩Y

2. The symmetries of rectangle form a

Permutation group of order 3, S3

Dihedral group of order 8

Kleins four group D4

optic Group

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

Z†

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

n!/2

n!/3

n+1/2

5. Which of the following is abelian

$S_4$

$S_3$

$S_5$

$S_2$

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

Lagrang’s theorem

Isomorphism theorem

Cayley’s theorem

Cauchy’s theorem

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

C-{0}

R†

8. 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

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

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

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

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

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

10. 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 G

index of H

order of H

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Algebra MCQs Test 07

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

homomorphic of G

center of G

subgroup of G

all of these

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

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

infinite group

Free group

symmetric Group

mixed group

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

300

600

400

240

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

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

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

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

$\Phi(x)=x$

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

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

None

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

9. The group Sn is called

polynomial group of degree n

None of these

symmetric group of degree n

dihidral group of degree n

10. Which of the following is cyclic group

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Algebra MCQs Test 06

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

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

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

inverse

addition

multilpication

composition

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

107

all of these

1000000007

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

$b^{-1}$

$bab^{-1}$

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

all of these

locally infinite

a-periodic

torsion free

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

9. which of the following is even permutation

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

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

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

None

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

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

Not Abelian

Equivalent

Abelian

Normal

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

abelian

conjugate

cyclic

normal

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

center

commutator

abelian

normal

4. Every subgroup of an abelian group is

Equivalent

Conjugate

Normal

center

5. Two conjugate subgroups are

Centralizer

Isomorphic

Homomorphic

normal

6. Automorphism and inner automorphism of a group G are

conjugate

none of these

normal

abelian

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

Group

Normal group

None of these

Not Group

8. Aytomorphism group of a finite group is

normal

finite

abelian

infinite

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

Homomorphic

Isomorphic

Isomorphic and congugacy

congugacy

10. Any two conjugate subgroups have same

order and center

center

order

none of these

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Algebra MCQs Test 04

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1. Every permutation can be written as

addition of transpositions

Difference of transpositions

product of transpositions

both a and b

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

Endomorphism

Isomorphism

Monomorphism

Epimorphism

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

cyclic permutations

Group

Non cyclic permutationa

Permutations

4. Any two cyclic group of same order are

meromorphic

None of these

Isomorphic

Homomorphic

5. The center of a finite P- group is

Non.Trivial

Normal

Trivial

Conjugate

6. A homomorphic image of a cyclic group is

Non cyclic

Isomorphic

Cyclic

Abelian

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

finite

None of these

Countable

infinite

8. Every subgroup of a cyclic group is

Abelian and Cyclic

Cyclic

Abelian

Non cyclic

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

aidentity mappings

Surjective mappings

Injective mappings

Bijective mappings

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

None of these

Not Group

Abelian Group

Group

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Algebra MCQs Test 03

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

$N_G(X) \supseteq H$

$N_G(X) = H$

None of these

$hH=H=Hh$

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

Identity

1-1

Bijective

onto

3. 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

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

Commutator subgroup

Commutator and Normal Subgroup

Normal Subgroup

Abelian

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

None of these

Epimorphism

Monomorphism

Homomorphism

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

1-1

Constant

Identity

Onto

8. A homomorphic image of cyclic group is

Non Cyclic

Abelian

Cyclic

Isomorphic

9. Every group of order prime is

Normal group

Abelian Group

Simple group

Mixed group

10. If H is a normal subgroup of G then

H≠G

gH=Hg

HG=H

H=G

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

Cyclic

Conjugate

Abelian

Normal

2. Two Conjugate elements have

No Order

None

Same Order

Different Order

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

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

Cyclic

Non-Abelian

Non-Cyclic

aBELIAN

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

$A'\cup B'$

$A\cup B$

$A-B$

$A\cap B$

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

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

$aH^{-1}$

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

$aHa^{-1}$

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

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

$\small H_1\neq H_2$

$\small H_1=H_2$

$\small H_1\cap H_2=\Phi$

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

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

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

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

$\small v=ux$

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

Uncountable

finite

infinite

Finite and Uncountable

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

abelian

Infinte

Finite

Zero

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WATU 27]

PAKMATH Knowledge Learning Point

ALGEBRA MCQs Test 01

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