ALGEBRA MCQs Test 02

1. Two Conjugate elements have

2. The  Set  is a cyclic group of order

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

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

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

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

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

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

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

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

1. The symmetries of rectangle form a

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

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

4. Which of the following is abelian

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

6. Let An be the set of all even permutations of Sn is a subgroup of Sn. Then order of An 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. If X and Y are two sets, then X∩(XUY)’=0

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

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

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

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

6. The group Sn is called

7. Which of the following is cyclic group

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

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

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

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

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

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

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

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

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. which of the following is even permutation

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

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. Automorphism and inner automorphism of a group G are

2. Every subgroup of an abelian group is

3. Two conjugate subgroups are

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

5. Any two conjugate subgroups have same

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

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

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

9. Aytomorphism group of a finite group is

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

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

2. Every permutation can be written as

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

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

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

6. A homomorphic image of a cyclic group is

7. Any two cyclic group of same order are

8. Every subgroup of a cyclic group is

9. The center of a finite P- group is

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

1. A homomorphic image of cyclic group is

2. An endomorphism  is said to be automorphism if  is

3. Every group of order prime is

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

5.

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

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

7. If H is a normal subgroup of G then

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

9. 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

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

1. Which of the following is the representation of 

2. If aN={ax|x∈ N} then 3N∩5N=

3. A group G is abelian then

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

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

6. The number of subgroups of a group is

7. The symmetries of square form a

8. 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

9. In 

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