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ALGEBRA MCQs Test 01

3000+ Mathematics all subject MCQs with their Answeers

algebra mcqs 01

Algebra mcqs tests 01 consist of 10 most important multiple choice questions. Prepare these questions for better results and also you can prepare definitions of algebra.

Algebra MCQs Test 01

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1. A relation is called anti-symmetric if \dpi{120} \small (a, b) \in R \,\,\ and \,\,\ (b, a) \in R implies

 
 
 
 

2. Relation R is symmetric if \dpi{120} \small a, b\in A \,\,\, and \,\,\,\ (a, b) \in R then

 
 
 
 

3. for a fixed point \dpi{120} \small c \in R \,\ and \,\ \phi_c=(x,c) is known as

 
 
 
 

4. Relation on R is transitive if \dpi{120} \small (a, b) \in R,(b, c) \in R then

 
 
 
 

5. \dpi{120} \small \forall \,\,\, a \in A The R is a reflexive relation \dpi{120} \small \bigleftrightarow\dpi{120} \small \Leftrightarrow

 
 
 
 

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1. 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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

5. Which of the following is abelian

 
 
 
 

6. The symmetries of rectangle form a

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

Algebra MCQs Test 07

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1. Which of the following is cyclic group

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

10. The group Sn is called

 
 
 
 

Algebra MCQs Test 06

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

 
 
 
 

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

 
 
 
 

3. which of the following is even permutation

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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1. Every subgroup of an abelian group is

 
 
 
 

2. Two conjugate subgroups are

 
 
 
 

3. Automorphism and inner automorphism of a group G are

 
 
 
 

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

 
 
 
 

5. Aytomorphism group of a finite group is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

10. Any two conjugate subgroups have same

 
 
 
 

Algebra MCQs Test 04

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

 
 
 
 

2. Any two cyclic group of same order are

 
 
 
 

3. Every subgroup of a cyclic group is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

7. Every permutation can be written as

 
 
 
 

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

 
 
 
 

3. A homomorphic image of cyclic group is

 
 
 
 

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. Every group of order prime is

 
 
 
 

6. 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

 
 
 
 

7.

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

 
 
 
 

8. If H is a normal subgroup of G then

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

10. Two Conjugate elements have

 
 
 
 

 

WATU 27]

2 comments

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