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ALGEBRA MCQs Test 02

3000+ Mathematics all subject MCQs with their Answeers

algebra mcqs for nts  tests 02 consist of 10 most important algebra multiple choice questions. Prepare these questions for better results in nts test and also you can prepare definitions of algebra.

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

2. The  Set $\small&space;C_n=[e^{2\pi&space;ki/n}&space;:&space;k={0,1,2,3,...}]$ is a cyclic group of order

3. In a group G if there are n integers such that $\small&space;a^n=e$ then order of a group is

4. Two Conjugate elements have

5. If $\small&space;u,v&space;\in&space;G$ and for some $\small&space;x&space;\in&space;G$  then v is known as conjugate of u if

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

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

8. If $\small&space;H_1&space;\,\&space;and&space;\,\&space;H_2$ be the subgroups of a group G then $\small&space;H_1\cup&space;H_2$ is a subgroup of G if and only if

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

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

1. Let G be a cyclic group of order 24. Then order of $a^9$ is

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

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

4. Which of the following is abelian

5. Let An be the set of all even permutations of Sis a subgroup of Sn. Then order of Ais

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

7. Let $D_4=\left&space;\{&space;;a^4=b^2=(ab)^2=1)&space;\right&space;\}$ be a dihedral group of order 8. Then which of the following is a subgroup of D4

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

9. The symmetries of rectangle form a

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

Algebra MCQs Test 07

1. Which of the following is cyclic group

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

3. $\Phi&space;:&space;R^{+}\rightarrow&space;R$ is an isomorphism. then for all $x&space;\in&space;R^{+}$ which of the following is true.

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

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

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

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

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

9. The group Sn is called

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

Algebra MCQs Test 06

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

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

3. Let G be a group and a,b ∈ G then order of $a^{-1}$ =

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

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

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

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

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

1. Every group of order $P^6$ where P is a prime number  is

2. Automorphism and inner automorphism of a group G are

3. Every subgroup of an abelian group is

4. Two conjugate subgroups are

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

6. Aytomorphism group of a finite group is

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

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

9. Any two conjugate subgroups have same

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

Algebra MCQs Test 04

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

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

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

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

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

6. Every subgroup of a cyclic group is

7. A homomorphic image of a cyclic group is

8. Every permutation can be written as

9. The center of a finite P- group is

10. Any two cyclic group of same order are

Algebra MCQs Test 03

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

2. Every group of order prime is

3. Let H be a subgroup of G and for fixed element of G then we define $K=hgh^{-1}=\left&space;\{ghg^{-1}:&space;h\in&space;H&space;\right&space;\}$ then K is

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. An endomorphism $\phi&space;:G\rightarrow&space;G$ is said to be automorphism if $\phi$ is

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

7. If $\Psi:&space;A\rightarrow&space;B$ be a function and for $a&space;\in&space;A,b&space;\in&space;B\,\&space;,\Psi(a)\neq&space;\Psi&space;(b)\,\&space;for&space;\,\&space;a&space;\neq&space;b$ then function is known as

8. If H is a normal subgroup of G then

9.

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

10. A homomorphic image of cyclic group is

1. If aN={ax|x∈ N} then 3N∩5N=

2. A group G is abelian then

3. Which of the following is the representation of $C_4=&space;\left&space;\{1,-1,i,-i&space;\right&space;\}$

4. A mapping $\Phi&space;:&space;G&space;\rightarrow&space;\rightarrow&space;G'$ is called homorphism if a, b belongs to G

5. In $S_3,a=\begin{pmatrix}&space;1&space;&&space;2&space;&&space;3\\&space;2&&space;3&space;&&space;1&space;\end{pmatrix}&space;,then&space;\,\&space;a^{-1}=$

6. The number of subgroups of a group is

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

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

9. The symmetries of square form a

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

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