ALGEBRA MCQs Test 02

1. The  Set  is a cyclic group of order

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

5. Two Conjugate elements have

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

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

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

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

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

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

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

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

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

8. Which of the following is abelian

9. The symmetries of rectangle form a

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

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

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

3. Which of the following is cyclic group

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

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

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

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

8. The group Sn is called

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

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

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

6. which of the following is even permutation

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

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

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

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

1. Any two conjugate subgroups have same

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

3. Aytomorphism group of a finite group is

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

5. Automorphism and inner automorphism of a group G are

6. Two conjugate subgroups are

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

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

9. Every subgroup of an abelian group is

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

1. The center of a finite P- group is

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

3. Any two cyclic group of same order are

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

5. Every permutation can be written as

6. Every subgroup of a cyclic group is

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

8. A homomorphic image of a cyclic group is

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

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. 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. An endomorphism  is said to be automorphism if  is

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

5. Every group of order prime is

6. A homomorphic image of cyclic group is

7.

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

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

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

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

1. In 

2. The symmetries of square form a

3. A group G is abelian then

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

6. Which of the following is the representation of 

7. The number of subgroups of a group is

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

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

10. If aN={ax|x∈ N} then 3N∩5N=