ALGEBRA MCQs Test 02

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

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

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

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

5. The  Set  is a cyclic group of order

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

7. Two Conjugate elements have

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

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

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

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

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

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

7. The symmetries of rectangle form a

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

9. Which of the following is abelian

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

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

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

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

4. Which of the following is cyclic group

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

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

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

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

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

10. The group Sn is called

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

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

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

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

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

6. which of the following is even permutation

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

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

3. Every subgroup of an abelian group is

4. Two conjugate subgroups are

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

6. Aytomorphism group of a finite group is

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

8. Automorphism and inner automorphism of a group G are

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

10. Any two conjugate subgroups have same

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

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

3. Any two cyclic group of same order are

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

5. A homomorphic image of a cyclic group is

6. Every subgroup of a cyclic group is

7. The center of a finite P- group is

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

9. Every permutation can be written as

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

1. If H is a normal subgroup of G then

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

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

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

5. A homomorphic image of cyclic group is

6.

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

7. Every group of order prime is

8. 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

9. An endomorphism  is said to be automorphism if  is

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

1. which binary operation is not defined in the set of natural number

2. The symmetries of square form a

3. The number of subgroups of a group is

4. Let G be a group of order 36 and let a belongs to G . The order of a is

5. If aN={ax|x∈ N} then 3N∩5N=

6. A group G is abelian then

7. In 

8. A mapping  is called homorphism if a, b belongs to G

9. Let H,K be the two subgroups of a group G. Then set HK={hk|h∈H ^ k∈ K} is a subgroup of G if

10. Which of the following is the representation of