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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

5. for a fixed point \dpi{120} \small c \in R \,\ and \,\ \phi_c=(x,c) is known 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. If X and Y are two sets, then X∩(XUY)’=0

 
 
 
 

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

 
 
 
 

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

 
 
 
 

10. 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

 
 
 
 

Algebra MCQs Test 07

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1. The group Sn is called

 
 
 
 

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

 
 
 
 

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

 
 
 
 

4. Which of the following is cyclic group

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

4. Two conjugate subgroups are

 
 
 
 

5. Any two conjugate subgroups have same

 
 
 
 

6. Aytomorphism group of a finite group is

 
 
 
 

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

 
 
 
 

8. Automorphism and inner automorphism of a group G are

 
 
 
 

9. Every subgroup of an abelian 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. Any two cyclic group of same order are

 
 
 
 

2. Every permutation can be written as

 
 
 
 

3. The center of a finite P- group is

 
 
 
 

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

 
 
 
 

5. Every subgroup of a cyclic group is

 
 
 
 

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

 
 
 
 

7. A homomorphic image of a cyclic group is

 
 
 
 

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 permutation of degree n can be written as a product of

 
 
 
 

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

 
 
 
 

5. 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

 
 
 
 

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. Every group of order prime is

 
 
 
 

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

 
 
 
 

9. If H is a normal subgroup of G then

 
 
 
 

10. A homomorphic image of cyclic group is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

5. Two Conjugate elements have

 
 
 
 

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

 
 
 
 

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

 
 
 
 

 

WATU 27]

2 comments

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