ALGEBRA MCQs Test 02

3000+ Mathematics all subject MCQs with their Answeers

lgebra mcqs for nts  tests 02 consist of 10 most important algebra multiple choice questions. Prepare these questions for better results in nts test

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.

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1. If \small u,v \in G and for some \small x \in G  then v is known as conjugate of u if 

 
 
 
 

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

 
 
 
 

3. Two Conjugate elements have

 
 
 
 

4. In a group G if there are n integers such that \small a^n=e then order of a group is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

7. If \small H_1 \,\ and \,\ H_2 be the subgroups of a group G then \small H_1\cup H_2 is a subgroup of G if and only if

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

3. The symmetries of rectangle form a

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

9. Which of the following is abelian

 
 
 
 

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

 
 
 
 

Algebra MCQs Test 07

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1. \Phi : R^{+}\rightarrow R is an isomorphism. then for all x \in R^{+} which of the following is true.

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

7. The group Sn is called

 
 
 
 

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

 
 
 
 

9. Which of the following is cyclic group

 
 
 
 

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

 
 
 
 

Algebra MCQs Test 06

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

 
 
 
 

2. which of the following is even permutation

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

4. Automorphism and inner automorphism of a group G are

 
 
 
 

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

 
 
 
 

6. Any two conjugate subgroups have same

 
 
 
 

7. Every subgroup of an abelian group is

 
 
 
 

8. Aytomorphism group of a finite group is

 
 
 
 

9. Two conjugate subgroups are

 
 
 
 

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

 
 
 
 

Algebra MCQs Test 04

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

 
 
 
 

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

 
 
 
 

3. Every permutation can be written as

 
 
 
 

4. A homomorphic image of a cyclic group is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

7. Any two cyclic group of same order are

 
 
 
 

8. Every subgroup of a cyclic group is

 
 
 
 

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

 
 
 
 

10. The center of a finite P- group is

 
 
 
 

Algebra MCQs Test 03

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1. 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

 
 
 
 

2. A homomorphic image of cyclic group is

 
 
 
 

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

 
 
 
 

4.

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

 
 
 
 

5. An endomorphism \phi :G\rightarrow G is said to be automorphism if \phi is

 
 
 
 

6. Every group of order prime is

 
 
 
 

7. If H is a normal subgroup of G then

 
 
 
 

8. If \Psi: A\rightarrow B be a function and for a \in A,b \in B\,\ ,\Psi(a)\neq \Psi (b)\,\ for \,\ a \neq b then function is known as

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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1. The symmetries of square form a

 
 
 
 

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

 
 
 
 

3. A mapping \Phi : G \rightarrow \rightarrow G' is called homorphism if a, b belongs to G

 
 
 
 

4. The number of subgroups of a group is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

7. A group G is abelian then

 
 
 
 

8. Which of the following is the representation of C_4= \left \{1,-1,i,-i \right \}

 
 
 
 

9. In S_3,a=\begin{pmatrix} 1 & 2 & 3\\ 2& 3 & 1 \end{pmatrix} ,then \,\ a^{-1}=

 
 
 
 

10. If aN={ax|x∈ N} then 3N∩5N=

 
 
 
 

 

WATU 15]

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