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Free download in PDF Group Theory Multiple Choice Questions and Answers for competitive exams. These short objective type questions with answers are very important for Board exams as well as competitive exams. These short solved questions or quizzes are provided by Gkseries.
1
A non empty set A is termed as an algebraic structure ________
A
with respect to binary operation *
B
with respect to ternary operation ?
C
with respect to binary operation +
D
with respect to unary operation –
View Answer
Answer: with respect to binary operation *
2
Condition for monoid is __________
A
(a+e)=a
B
(a*e)=(a+e)
C
a=(a*(a+e)
D
(a*e)=(e*a)=a
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3
A group (M,*) is said to be abelian if ___________
A
(x+y)=(y+x)
B
(x*y)=(y*x)
C
(x+y)=x
D
(y*x)=(x+y)
View Answer
4
Matrix multiplication is a/an ____ property.
A
Commutative
B
Associative
C
Additive
D
Disjunctive
View Answer
5
How many properties can be held by a group?
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6
{1, i, -i, -1} is _____
A
semigroup
B
subgroup
C
cyclic group
D
abelian group
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7
The set of all real numbers under the usual multiplication operation is not a group since
A
multiplication is not a binary operation
B
multiplication is not associative
C
identity element does not exist
D
zero has no inverse
View Answer
Answer: zero has no inverse
8
The inverse of - i in the multiplicative group, {1, - 1, i , - i} is
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9
If (G, .) is a group, such that (ab)2 = a2 b2 ∀ a, b ∈ G, then G is a/an
A
commutative semi group
B
abelian group
C
non-abelian group
D
none of these
View Answer
10
If A = (1, 2, 3, 4). Let ~= {(1, 2), (1, 3), (4, 2)}. Then ~ is
A
not anti-symmetric
B
transitive
C
reflexive
D
symmetric
View Answer
11
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
A
(74,40)
B
(32,40)
C
(23,11)
D
(7,11)
View Answer
12
Match the following
A. Groups I. Associativity
B. Semi groups II. Identity
C. Monoids III. Commutative
D. Abelian Groups IV Left inverse
Codes. A B C D
A
IV I II III
B
III I IV II
C
II III I IV
D
I II III IV
View Answer
13
An algebraic structure ____ is called a semigroup.
A
(P, *)
B
(Q, +, *)
C
(P, +)
D
(+, *)
View Answer
14
A monoid is called a group if _______
A
(a*a)=a=(a+c)
B
(a*c)=(a+c)
C
(a+c)=a
D
(a*c)=(c*a)=e
View Answer
15
A cyclic group can be generated by a/an _____ element.
A
singular
B
non-singular
C
inverse
D
multiplicative
View Answer
16
A cyclic group is always _________
A
abelian group
B
monoid
C
semigroup
D
subgroup
View Answer
17
If (G, .) is a group such that (ab)- 1 = a-1b-1, ∀ a, b ∈ G, then G is a/an
A
commutative semi group
B
abelian group
C
non-abelian group
D
None of these
View Answer
18
If (G, .) is a group such that a2 = e, ∀a ∈ G, then G is
A
semi group
B
abelian group
C
non-abelian group
D
none of these
View Answer
19
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
View Answer
20
In the group (G, .), the value of (a- 1 b)- 1 is
A
ab-1
B
b- 1a
C
a-1b
D
ba-1
View Answer
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