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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

2. 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

 
 
 
 

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. Which of the following is abelian

 
 
 
 

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

 
 
 
 

7. The symmetries of rectangle form a

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

Algebra MCQs Test 07

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

6. The group Sn is called

 
 
 
 

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

 
 
 
 

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

 
 
 
 

9. Which of the following is cyclic group

 
 
 
 

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

 
 
 
 

Algebra MCQs Test 06

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

5. which of the following is even permutation

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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. Two conjugate subgroups are

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

5. Aytomorphism group of a finite group is

 
 
 
 

6. Automorphism and inner automorphism of a group G are

 
 
 
 

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

 
 
 
 

8. Every subgroup of an abelian group is

 
 
 
 

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

 
 
 
 

10. Any two conjugate subgroups have same

 
 
 
 

Algebra MCQs Test 04

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

 
 
 
 

2. The center of a finite P- group is

 
 
 
 

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

 
 
 
 

4. Every subgroup of a cyclic group is

 
 
 
 

5. A homomorphic image of a cyclic group is

 
 
 
 

6. Every permutation can be written as

 
 
 
 

7. Any two cyclic group of same order are

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

Algebra MCQs Test 03

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1. Every group of order prime is

 
 
 
 

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

 
 
 
 

3. 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

 
 
 
 

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

 
 
 
 

5.

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

 
 
 
 

6. A homomorphic image of cyclic group is

 
 
 
 

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

 
 
 
 

9. 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

 
 
 
 

10. If H is a normal subgroup of G then

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

6. Two Conjugate elements have

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

10. 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

 
 
 
 

 

WATU 27]

2 comments

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