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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. 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

 
 
 
 

2. Two Conjugate elements have

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

4. The symmetries of rectangle form a

 
 
 
 

5. Which of the following is abelian

 
 
 
 

6. 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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

Algebra MCQs Test 07

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

4. The group Sn is called

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

10. Which of the following is cyclic group

 
 
 
 

Algebra MCQs Test 06

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

9. which of the following is even permutation

 
 
 
 

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

 
 
 
 

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1. Automorphism and inner automorphism of a group G are

 
 
 
 

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

 
 
 
 

3. Every subgroup of an abelian group is

 
 
 
 

4. Any two conjugate subgroups have same

 
 
 
 

5. Two conjugate subgroups are

 
 
 
 

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

 
 
 
 

7. Aytomorphism group of a finite group is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

Algebra MCQs Test 04

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

 
 
 
 

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

 
 
 
 

3. Every permutation can be written as

 
 
 
 

4. The center of a finite P- group is

 
 
 
 

5. A homomorphic image of a cyclic group is

 
 
 
 

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

 
 
 
 

7. Any two cyclic group of same order are

 
 
 
 

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

 
 
 
 

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

 
 
 
 

10. Every subgroup of a cyclic 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. Let H and G be the two groups and H⊆G then

 
 
 
 

3.

Subgroup G generated by all commutators [u, v] such that u,v∈G then it 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. Every group of order prime is

 
 
 
 

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 square of prime number is known as

 
 
 
 

10. 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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

4. The symmetries of square form a

 
 
 
 

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. The number of subgroups of a group is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

9. A group G is abelian then

 
 
 
 

10. If aN={ax|x∈ N} then 3N∩5N=

 
 
 
 

 

WATU 15]

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