Miscellaneous Test

Result

Miscellaneous Test - 53

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

G = {e, a, b, c} is an abelian group with e as identity element. The order of the other elements are

A
2, 2, 2

B
3, 3, 3

C
2, 2, 4

D
2, 3, 4

Solution
Question 2
4 / -1

A

B

C

D

Solution
Question 3
4 / -1

On the set of all natural numbers N, which one of the following * is a binary operation

A

B

C

D

Solution
Question 4
4 / -1

If the binary operation * is defined 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) =

A
(74, 40)

B
(32, 40)

C
(23, 11)

D
(*7, 11)

Solution
Question 5
4 / -1

A group (G,*) has 10 elements. The minimum number of elements of G, which are their own inverse is

A
2

B
1

C
9

D
0
Question 6
4 / -1

Let G denote the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication

A
G is a subgroup

B
G is a finite abelian group

C
G is an infinite, non-abelian group

D
G is infinite, abelian
Question 7
4 / -1

Z_n = {0, 1, 2,... (n – 1)} fails to be a group under multiplication modulo n because

A
Closure property fails

B
Closure holds but not associativity

C
There is not identity

D
There is no inverse for an element of the set

Solution
Question 8
4 / -1

A
0

B
2

C
3

D
5

Solution
Question 9
4 / -1

The remainder obtained when 5¹²⁴ is divided by 124

A
5

B
0

C
2

D
1

Solution
Question 10
4 / -1

The set of fourth roots of unity forms a group

A
Of order 4 under addition

B
Of order 4 under division

C
Of order 4 under multiplication

D
None of the above