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# 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 R is symmetric if  then

2. A relation is called anti-symmetric if  implies

3.  The R is a reflexive relation

4. for a fixed point  is known as

5. Relation on R is transitive if  then

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

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

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

4. The symmetries of rectangle form a

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

6. Let G be a cyclic group of order 24. Then order of  is

7. Which of the following is abelian

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

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

10. Let  be a dihedral group of order 8. Then which of the following is a subgroup of D4

Algebra MCQs Test 07

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

2. Which of the following is cyclic group

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

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

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

6.  is an isomorphism. then for all  which of the following is true.

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

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

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

10. The group Sn is called

Algebra MCQs Test 06

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

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

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

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

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

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

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

8. which of the following is even permutation

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

10. Let G be a group and a,b ∈ G then order of  =

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

2. Aytomorphism group of a finite group is

3. Any two conjugate subgroups have same

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

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

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

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

8. Every subgroup of an abelian group is

9. Two conjugate subgroups are

10. Automorphism and inner automorphism of a group G are

Algebra MCQs Test 04

1. A homomorphic image of a cyclic group is

2. Every permutation can be written as

3. The center of a finite P- group is

4. Any two cyclic group of same order are

5. Every subgroup of a cyclic group is

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

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

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

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

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

Algebra MCQs Test 03

1. If  be a function and for  then function is known as

2. 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

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

4. Every group of order prime is

5. Let H be a subgroup of G and for fixed element of G then we define  then K is

6.

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

7. An endomorphism  is said to be automorphism if  is

8. A homomorphic image of cyclic group is

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

10. If H is a normal subgroup of G then

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

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

3. Two Conjugate elements have

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

5. If  and for some   then v is known as conjugate of u if

6. In a group G if there are n integers such that  then order of a group is

7. The  Set  is a cyclic group of order

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

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

10. If  be the subgroups of a group G then  is a subgroup of G if and only if

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1. 2. 