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

Please enter your email:

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

a≠b

a=b

A= ab

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

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

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

a=c

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

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

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

1-function

None of these

Constant function

Identity function

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

a=b

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

a≠b

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

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

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

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

a=a

Loading …

Please enter your email:

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

R†

C-{0}

2. 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

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

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

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

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

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

n!/2

n+1/2

n!/3

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

Lagrang’s theorem

Cauchy’s theorem

Isomorphism theorem

Cayley’s theorem

5. Which of the following is abelian

$S_5$

$S_4$

$S_2$

$S_3$

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

X∩Y

7. 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 H

index of H

order of G

All of these

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

Permutation group of order 3, S3

optic Group

Dihedral group of order 8

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

Z†

Loading …

Algebra MCQs Test 07

Please enter your email:

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

240

300

400

600

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

None

3. Which of the following is cyclic group

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

$\Phi(x)=x$

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

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

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

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

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

7. The group Sn is called

polynomial group of degree n

None of these

dihidral group of degree n

symmetric group of degree n

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

subgroup of G

homomorphic of G

center of G

all of these

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

Free group

symmetric Group

infinite group

mixed group

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

Loading …

Algebra MCQs Test 06

Please enter your email:

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

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

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

107

1000000007

all of these

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

7. 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

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

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

10. which of the following is even permutation

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

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

None

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

Loading …

Please enter your email:

1. Any two conjugate subgroups have same

center

order and center

order

none of these

2. Two conjugate subgroups are

Isomorphic

Centralizer

Homomorphic

normal

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

normal

commutator

center

abelian

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

Isomorphic

Isomorphic and congugacy

Homomorphic

congugacy

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

Not Abelian

Equivalent

Normal

Abelian

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

Group

Not Group

Normal group

None of these

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

conjugate

normal

cyclic

abelian

8. Aytomorphism group of a finite group is

infinite

abelian

normal

finite

9. Automorphism and inner automorphism of a group G are

conjugate

none of these

abelian

normal

10. Every subgroup of an abelian group is

Normal

center

Equivalent

Conjugate

Loading …

Algebra MCQs Test 04

Please enter your email:

1. A homomorphic image of a cyclic group is

Isomorphic

Non cyclic

Cyclic

Abelian

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

Group

Abelian Group

Not Group

None of these

3. Every permutation can be written as

Difference of transpositions

product of transpositions

both a and b

addition of transpositions

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

finite

None of these

Countable

infinite

5. The center of a finite P- group is

Trivial

Normal

Conjugate

Non.Trivial

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

Endomorphism

Isomorphism

Epimorphism

Monomorphism

7. Every subgroup of a cyclic group is

Cyclic

Abelian

Abelian and Cyclic

Non cyclic

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

Bijective mappings

Injective mappings

Surjective mappings

aidentity mappings

9. Any two cyclic group of same order are

None of these

Isomorphic

Homomorphic

meromorphic

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

cyclic permutations

Non cyclic permutationa

Permutations

Group

Loading …

Algebra MCQs Test 03

Please enter your email:

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

Abelian

Normal Subgroup

Commutator subgroup

Commutator and Normal Subgroup

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

Center

Conjugate subgroup of H

Trivial

Normal

3. 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

Epimorphism

None of these

Homomorphism

Monomorphism

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

1-1

Bijective

Identity

onto

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

$hH=H=Hh$

$N_G(X) \supseteq H$

None of these

$N_G(X) = H$

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

Abelian Group

Normal group

cyclic group

Both Cyclic and Abelian

7. Every group of order prime is

Simple group

Abelian Group

Normal group

Mixed group

8. A homomorphic image of cyclic group is

Cyclic

Abelian

Non Cyclic

Isomorphic

9. 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

Constant

1-1

Onto

10. If H is a normal subgroup of G then

HG=H

H≠G

gH=Hg

H=G

Loading …

Please enter your email:

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

$A\cup B$

$A'\cup B'$

$A\cap B$

$A-B$

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

Non-Cyclic

aBELIAN

Non-Abelian

Cyclic

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

Finite and Uncountable

Uncountable

finite

infinite

4. 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

$\small H_1\neq H_2$

$\small H_1=H_2$

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

$\small H_1\cap H_2=\Phi$

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

6. Two Conjugate elements have

No Order

Same Order

None

Different Order

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

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

$\small v=ux$

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

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

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

Cyclic

Conjugate

Abelian

Normal

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

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

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

$aHa^{-1}$

$aH^{-1}$

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

Finite

abelian

Zero

Infinte

Loading …

WATU 27]

PAKMATH Knowledge Learning Point

ALGEBRA MCQs Test 01

2 comments

Leave a Reply Cancel reply