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Engineering Maths - Set Theory and Algebra - Algebra Online Exam Quiz

Important questions about Engineering Maths - Set Theory and Algebra - Algebra. Engineering Maths - Set Theory and Algebra - Algebra MCQ questions with answers. Engineering Maths - Set Theory and Algebra - Algebra exam questions and answers for students and interviews.

1. The set of all real numbers under the usual multiplication operation is not a group since

Options

A : multiplication is not a binary operation

B : multiplication is not associative

C : identity element does not exist

D : zero has no inverse

2. If (G, .) is a group such that (ab)- 1 = a-1b-1, ∀ a, b ∈ G, then G is a/an

Options

A : commutative semi group

B : abelian group

C : non-abelian group

D : None of these

3. If (G, .) is a group such that a2 = e, ∀a ∈ G, then G is

Options

A : semi group

B : abelian group

C : non-abelian group

D : none of these

4. The inverse of - i in the multiplicative group, {1, - 1, i , - i} is

Options

A : 1

B : -1

C : i

D : -i

5. The set of integers Z with the binary operation "*" defined as a*b =a +b+ 1 for a, b ∈ Z, is a group. The identity element of this group is

Options

A : 0

B : 1

C : -1

D : 12

7. If (G, .) is a group, such that (ab) 2 = a 2 b 2 ∀ a, b ∈ G, then G is a/an

Options

A : commutative semi group

B : abelian group

C : non-abelian group

D : none of these

8. (Z,*) is a group with a*b = a+b+1 ∀ a, b ∈Z. The inverse of a is

Options

A : 0

B : -2

C : a-2

D : -a-2

9. Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an

Options

A : subgroup

B : finite abelian group

C : infinite, non abelian group

D : ininite, abelian

10. Let A be the set of all non-singular matrices over real numbers and let * be the matrix multiplication operator. Then

Options

A : A is closed under * but is not a semi group

B : is a semi group but not a monoid

C : is a monoid but not a group

D : is a group but not an abelian group

11. If a, b are positive integers, define a * b = a where ab = a (modulo 7), with this * operation, then inverse of 3 in group G (1, 2, 3, 4, 5, 6) is

Options

A : 3

B : 1

C : 5

D : 4

12. Which of the following is TRUE ?

Options

A : Set of all rational negative numbers forms a group under multiplication

B : Set of all non-singular matrices forms a group under multiplication

C : Set of all matrices forms a group under multiplication

D : Both (b) and (c)

13. The set of all nth roots of unity under multiplication of complex numbers form a/an

Options

A : semi group with identity

B : commutative semigroups with identity

C : group

D : abelian group

14. Which of the following statements is FALSE ?

Options

A : The set of rational numbers is an abelian group under addition

B : The set of rational integers is an abelian group under addition

C : The set of rational numbers form an abelian group under multiplication

D : None of these

15. In the group G = {2, 4, 6, 8) under multiplication modulo 10, the identity element is

Options

A : 6

B : 8

C : 4

D : 2

17. Let (Z, *) be an algebraic structure, where Z is the set of integers and the operation * is defined by n * m = maximum (n, m). Which of the following statements is TRUE for (Z, *) ?

Options

A : (Z, *) is a monoid

B : (Z, *) is an abelian group

C : (Z, *) is a group

D : None of these

18. Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G ?

Options

A : g = g -1 for every g ∈ G

B : g = g 2 for every g ∈ G

C : (g o h) 2 = g 2 o h 2 for every g,h ∈ G

D : G is of finite order

19. If the binary operation * is deined on a set of ordered pairs of real numbers as (a, b) * (c, d) = (ad + bc, bd) and is associative, then (1, 2) * (3, 5) * (3, 4) equals

Options

A : (74,40)

B : (32,40)

C : (23,11)

D : (7,11)

20. If A = (1, 2, 3, 4). Let ~= {(1, 2), (1, 3), (4, 2)}. Then ~ is

Options

A : not anti-symmetric

B : transitive

C : reflexive

D : symmetric

21. Which of the following statements is false ?

Options

A : If R is reflexive, then R ∩ R -1 ≠ φ

B : R ∩ R -1 ≠ φ   =>R  is anti-symmetric.

C : If R, R' are equivalence relations in a set A, then R ∩ R' is also an equivalence relation in A.

D : If R, R' are reflexive relations in A, then R - R' is reflexive

22. If R = {(1, 2),(2, 3),(3, 3)} be a relation defined on A= {1, 2, 3} then R . R (= R2) is

Options

A : R itself

B : {(1, 2),(1, 3),(3, 3)}

C : {(1, 3),(2, 3),(3, 3)}

D : {(2, 1),(1, 3),(2, 3)}

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