JEE Questions for Maths Miscellaneous Quiz 10

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0%
2)
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0%

Every group of order 7 is

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Not abelian
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Not cyclic
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Cyclic
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None of these

The number of generators of an infinite cyclic group is

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1
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3
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2
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Infinite

The total number of generators of a finite cyclic group of order 28 is

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10
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8
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12
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14

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0%
2)
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Does not exist

Identify the false statement

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In a group of even order, there exists an element other than identity which is its own inverse
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2)
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Cube roots of unity form an Abelian group
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2
0%
1
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4
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3

The set of all 2 x 2 matrices over the real numbers is not a group under matrix multiplication because

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Associative law is not satisfied
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inverse axiom is not satisfied
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Closure property is not satisfied
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identity element does not exist

The number of improper subgroups of G = [1, –1, i, –i] w.r.t multiplication is

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2
0%
3
0%
4
0%
1

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9
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5
0%
7
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3

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2
0%
1
0%
4
0%
3

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0%
2)
0%
0%

Which one of the following is false

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(N, +) is a semi-group
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(N, .) is a monoid
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(Z, .) is a group
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The set of all even integers is a group under usual addition is a group

If a * b denote the bigger among a and b and a. b = (a * b) + 3, then 4.7 is equal to

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4
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31
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10
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8

Which of the following is true

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The set of all fourth roots of Unity is a multiplication group
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The set of all cube roots of unity is an additive group
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(ab)–1 = a–1b–1 for all a, b in any group G
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If (ab)2 = a2b2 for all a, b in any group G, then the group G is non-abelian

The set of all integers multiples of 5 is a group of

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The set of all rational numbers under multiplication
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The set of all integers under multiplication
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The set of all non-zero rational numbers under multiplication
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The set of all integers under addition

If Q₁ is the set of all rational numbers other than 1 with the binary operation * defined by a * b = a + b – ab for all a, b in Q₁, then the identity in Q w.r.t * is

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1
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0
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–1
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2

In the group G = {1, 3,7, 9} under multiplication modulo 10, the inverse of 7 is

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7
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3
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9
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1

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0%
2)
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0%
None of these

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

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2, 2, 2
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3, 3, 3
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2, 2, 4
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2, 3, 4

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0%
2)
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0%

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

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0%
2)
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0%

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,* (3,* (3,=