ALGEBRA MCQs Test 02

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

8. Two Conjugate elements have

 
 
 
 

9. 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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

3. Let An be the set of all even permutations of Sn is a subgroup of Sn. Then order of An is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

8. Which of the following is abelian

 
 
 
 

9. The symmetries of rectangle form a

 
 
 
 

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

 
 
 
 

Algebra MCQs Test 07

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

 
 
 
 

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

 
 
 
 

3. Which of the following is cyclic group

 
 
 
 

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

 
 
 
 

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

 
 
 
 

6. The group Sn is called

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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. which of the following is even permutation

 
 
 
 

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

 
 
 
 

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1. Any two conjugate subgroups have same

 
 
 
 

2. Two conjugate subgroups are

 
 
 
 

3. Automorphism and inner automorphism of a group G are

 
 
 
 

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

 
 
 
 

5. Every subgroup of an abelian group is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

Algebra MCQs Test 04

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1. Every subgroup of a cyclic group is

 
 
 
 

2. Any two cyclic group of same order are

 
 
 
 

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

 
 
 
 

4. The center of a finite P- group is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

7. Every permutation can be written as

 
 
 
 

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

 
 
 
 

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

 
 
 
 

10. A homomorphic image of a cyclic group is

 
 
 
 

Algebra MCQs Test 03

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1. A homomorphic image of cyclic group is

 
 
 
 

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

 
 
 
 

3. If H is a normal subgroup of G then

 
 
 
 

4. 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

 
 
 
 

5. 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

 
 
 
 

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

 
 
 
 

7. Every group of order prime is

 
 
 
 

8.

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

4. A group G is abelian then

 
 
 
 

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

 
 
 
 

6. The number of subgroups of a group is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

9. The symmetries of square form a

 
 
 
 

10. If aN={ax|x∈ N} then 3N∩5N=

 
 
 
 

 

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