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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

5. 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

 
 
 
 

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

 
 
 
 

7. Two Conjugate elements have

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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1. Which of the following is abelian

 
 
 
 

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

 
 
 
 

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. The symmetries of rectangle form a

 
 
 
 

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

 
 
 
 

9. 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

 
 
 
 

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

 
 
 
 

Algebra MCQs Test 07

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

4. The group Sn is called

 
 
 
 

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

 
 
 
 

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

 
 
 
 

7. Which of the following is cyclic group

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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. which of the following is even permutation

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

2. Automorphism and inner automorphism of a group G are

 
 
 
 

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

 
 
 
 

4. Every subgroup of an abelian group is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

8. Aytomorphism group of a finite group is

 
 
 
 

9. Any two conjugate subgroups have same

 
 
 
 

10. Two conjugate subgroups are

 
 
 
 

Algebra MCQs Test 04

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

 
 
 
 

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

 
 
 
 

3. Every permutation can be written as

 
 
 
 

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

 
 
 
 

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

 
 
 
 

6. A homomorphic image of a cyclic group is

 
 
 
 

7. The center of a finite P- group is

 
 
 
 

8. Every subgroup of a cyclic group is

 
 
 
 

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

 
 
 
 

10. Any two cyclic group of same order are

 
 
 
 

Algebra MCQs Test 03

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1. 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

 
 
 
 

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

 
 
 
 

3.

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

 
 
 
 

4. If H is a normal subgroup of G then

 
 
 
 

5. A homomorphic image of cyclic group 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. 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

 
 
 
 

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

 
 
 
 

9. Every group of order prime is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

4. The symmetries of square form a

 
 
 
 

5. The number of subgroups of a group is

 
 
 
 

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

 
 
 
 

7. If aN={ax|x∈ N} then 3N∩5N=

 
 
 
 

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

 
 
 
 

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

 
 
 
 

10. A group G is abelian then

 
 
 
 

 

WATU 15]

2 comments

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