ALGEBRA MCQs Test 02

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

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

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

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

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

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

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

8. Two Conjugate elements have

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

10. The  Set  is a cyclic group of order

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

2. Which of the following is abelian

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

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

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

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

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

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

9. The symmetries of rectangle form a

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

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

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

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

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

5. The group Sn is called

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

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

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

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

10. Which of the following is cyclic group

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 group and a,b ∈ G then order of  =

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

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

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

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

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

2. Every subgroup of an abelian group is

3. Automorphism and inner automorphism of a group G are

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

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

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

7. Any two conjugate subgroups have same

8. Two conjugate subgroups are

9. Aytomorphism group of a finite group is

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

1. Every subgroup of a cyclic group is

2. Any two cyclic group of same order are

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

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

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

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. A homomorphic image of a cyclic group is

9. Every permutation can be written as

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

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.

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

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

6. Every group of order prime is

7. 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

8. A homomorphic image of cyclic group is

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

10. An endomorphism  is said to be automorphism if  is

1. Which of the following is the representation of 

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

3. The symmetries of square form a

4. The number of subgroups of a group is

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

6. If aN={ax|x∈ N} then 3N∩5N=

7. A group G is abelian then

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

9. In 

10. 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