ALGEBRA MCQs Test 02

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

2. Two Conjugate elements have

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

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

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

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

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

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

9. The  Set  is a cyclic group of order

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

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

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

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

6. The symmetries of rectangle form a

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

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

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

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

1. Which of the following is cyclic group

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

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

4. The group Sn is called

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

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

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

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

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

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

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

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

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

4. which of the following is even permutation

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

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

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

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

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

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

1. Aytomorphism group of a finite group is

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

3. Any two conjugate subgroups have same

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

5. Two conjugate subgroups are

6. Automorphism and inner automorphism of a group G are

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

8. Every subgroup of an abelian group is

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

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

1. Any two cyclic group of same order are

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

3. Every permutation can be written as

4. Every subgroup of a cyclic group is

5. The center of a finite P- group is

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

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

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

9. A homomorphic image of a cyclic group is

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

1. If H is a normal subgroup of G then

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

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

4. 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

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

6. A homomorphic image of cyclic group is

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

8. Every group of order prime is

9. An endomorphism  is said to be automorphism if  is

10.

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

1. The symmetries of square form a

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

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

4. 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

5. In 

6. The number of subgroups of a group is

7. A group G is abelian then

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

9. If aN={ax|x∈ N} then 3N∩5N=

10. Which of the following is the representation of