# 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

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

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

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

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

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

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

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

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

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

5. Which of the following is abelian

6. Let An be the set of all even permutations of Sis a subgroup of Sn. Then order of Ais

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

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

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

10. The symmetries of rectangle form a

Algebra MCQs Test 07

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

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

3. Which of the following is cyclic group

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

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

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

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

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

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

10. The group Sn is called

Algebra MCQs Test 06

1. which of the following is even permutation

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

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

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

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

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 . Then which of the following cab be order of G.

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

1. Any two conjugate subgroups have same

2. Two conjugate subgroups are

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

4. Aytomorphism group of a finite group is

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

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

7. Every subgroup of an abelian group is

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

9. Automorphism and inner automorphism of a group G are

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

Algebra MCQs Test 04

1. Every subgroup of a cyclic group is

2. Any two cyclic group of same order are

3. A homomorphic image of a cyclic group is

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

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

6. The center of a finite P- group is

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

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

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

10. Every permutation can be written as

Algebra MCQs Test 03

1. Every group of order prime is

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

3. If H is a normal subgroup of G then

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

5.

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

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

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

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

9. A homomorphic image of cyclic group is

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

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

2. Two Conjugate elements have

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

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

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

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

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

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

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

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

WATU 27]