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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. Two Conjugate elements have

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

6. 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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

2. Which of the following is abelian

 
 
 
 

3. 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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

9. The symmetries of rectangle form a

 
 
 
 

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

 
 
 
 

Algebra MCQs Test 07

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

 
 
 
 

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

 
 
 
 

3. The group Sn is called

 
 
 
 

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

 
 
 
 

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

 
 
 
 

6. Which of the following is cyclic group

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

Algebra MCQs Test 06

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1. which of the following is even permutation

 
 
 
 

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 cyclic group of order 17. The number of subgroups of G are

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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1. Two conjugate subgroups are

 
 
 
 

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

 
 
 
 

3. Automorphism and inner automorphism of a group G are

 
 
 
 

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

 
 
 
 

5. Any two conjugate subgroups have same

 
 
 
 

6. Aytomorphism group of a finite group is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

9. Every subgroup of an abelian group is

 
 
 
 

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

 
 
 
 

Algebra MCQs Test 04

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1. Every permutation can be written as

 
 
 
 

2. The center of a finite P- group is

 
 
 
 

3. Every subgroup of a cyclic group is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

6. Any two cyclic group of same order are

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

10. A homomorphic image of a cyclic group is

 
 
 
 

Algebra MCQs Test 03

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1.

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

 
 
 
 

2. 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

 
 
 
 

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

 
 
 
 

4. A homomorphic image of cyclic group is

 
 
 
 

5. 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

 
 
 
 

6. 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

 
 
 
 

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

 
 
 
 

8. If H is a normal subgroup of G then

 
 
 
 

9. Every group of order prime is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

3. The number of subgroups of a group is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

6. If aN={ax|x∈ N} then 3N∩5N=

 
 
 
 

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

 
 
 
 

8. The symmetries of square form a

 
 
 
 

9. A group G is abelian then

 
 
 
 

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

 
 
 
 

 

WATU 15]

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