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CBSE Questions for Class 11 Commerce Applied Mathematics Relations Quiz 16 - MCQExams.com
CBSE
Class 11 Commerce Applied Mathematics
Relations
Quiz 16
Let
R
:
N
→
N
be defined by
R
=
{
(
a
,
b
)
:
a
,
b
∈
N
and
a
=
b
2
}
then, which of the following is true?
Report Question
0%
(
a
,
a
)
∈
R
,
∀
a
∈
N
0%
(
a
,
b
)
∈
R
,
⇒
(
b
,
a
)
∈
R
0%
(
a
,
b
)
∈
R
,
(
b
,
c
)
∈
R
⇒
(
a
,
c
)
∈
R
0%
None of the above
Let
A
be set of first ten natural numbers and
R
be a relation on
A
defined by (x , y)
∈
R
⇒
x + 2y = 10 , then domain of
R
is
Report Question
0%
{
1
,
2
,
3
,
.
.
.
.
.
.
.
.
.
.
.
.
,
10
}
0%
{
2
,
4
,
6
,
8
}
0%
{
1
,
2
,
3
,
4
}
0%
{
2
,
4
,
6
,
8
,
10
}
Explanation
A
=
{
1
,
2
,
3
,
⋯
⋯
,
10
}
R
=
{
(
x
,
y
)
:
x
+
2
y
=
10
,
x
,
y
∈
A
}
∴
y
=
10
−
x
2
R
=
{
(
2
,
4
)
,
(
4
,
3
)
,
(
6
,
2
)
,
(
8
,
1
)
}
∴
Domain of
R
is
{
2
,
4
,
6
,
8
}
Correct option is (B).
If
h
=
{
(
(
x
,
y
)
,
(
x
−
y
,
x
+
y
)
)
/
x
,
y
ϵ
N
}
is a relation on NxN, then domain of h
Report Question
0%
$$\left\{ (x,y):\quad x
0%
{
(
x
,
y
)
:
x
≤
y
,
x
,
y
ϵ
N
}
0%
{
(
x
,
y
)
:
x
>
y
,
x
,
y
ϵ
N
}
0%
{
(
x
,
y
)
:
x
≥
y
,
x
,
y
ϵ
N
}
If
A
=
{
x
:
x
2
−
3
x
+
2
=
0
}
, and R is a universal relation on A, then R is
Report Question
0%
(
1
,
1
)
,
(
2
,
2
)
0%
(
1
,
1
)
0%
{
ϕ
}
0%
None of these.
Let
R
1
,
R
2
are relation defined on
Z
such that
a
R
1
b
⟺
(
a
−
b
)
is divisible by
3
and
a
R
2
b
⟺
(
a
−
b
)
is divisible by
4
. Then which of the two relation
(
R
1
∪
R
2
)
,
(
R
1
∩
R
2
)
is an equivalence relation?
Report Question
0%
(
R
1
∪
R
2
)
Only
0%
(
R
1
∩
R
2
)
Only
0%
Both
(
R
1
∪
R
2
)
,
(
R
1
∩
R
2
)
0%
Neither
(
R
1
∪
R
2
)
nor
(
R
1
∩
R
2
)
Explanation
Givn relations defined on z are,
R
1
=
a
R
1
b
↔
(
a
−
b
)
is divisible by 3.
and
R
2
=
a
R
2
b
↔
(
a
−
b
)
is divisible by 4.
Consider,
a
R
1
b
↔
a
−
b
is divisible by 3.
Reflexive
:
a
R
1
a
↔
a
−
a
is divisible by 3
True
∴
the given relation
R
1
is a reflexive relation.
Symmetric:
a
R
1
b
↔
a
−
b
is divisible by 3.
⇒
a
−
b
=
3
k
; where
k
is an integer.
then
b
R
1
a
↔
b
−
a
is divisible by 3.
because
b
−
a
=
−
(
a
−
b
)
=
−
3
k
which is divisible by 3.
∴
the given relation
R
is a symmetric relation.
Transitive:
a
R
1
b
↔
a
−
b
is divisible by 3.
⇒
a
−
b
=
3
k
;
k
is an integer.
b
R
1
c
↔
b
−
c
is divisible by 3.
⇒
b
−
c
=
3
p
;
p
is integer.
Then
a
R
1
c
↔
a
−
c
is divisible by 3.
Because
(
a
−
b
)
+
(
b
−
c
)
=
a
−
c
⇒
3
k
+
3
p
=
3
(
k
+
p
)
which is divisible by 3.
∴
The given relation
R
1
is transitive relation.
∴
R
1
satisfies the reflexive, symmetric and transitive relation properties.
∴
R
1
is an equivalence relation.
Similarly
R
2
is also an equivalence relation.
And as we know that,
"If
R
1
and
R
2
are equivalence relations then
R
1
∩
R
2
is also an equivalence relation."
∴
R
1
∩
R
2
is an equivalence relation.
Let
R
1
be a relation defined by
R
1
=
{
(
a
,
b
)
|
a
>
b
,
a
,
b
ϵ
R
}. Then
R
1
is
Report Question
0%
an equivalence relation on R
0%
reflexive, transitive but not symmetric
0%
symmetric, transitive but nor reflective
0%
neither transitive nor reflective but symmetric
If a relation { R } on the set { 1,2,3 } be defined
by R = { ( 1,2 ) } then { R } is
Report Question
0%
reflexive
0%
transitive
0%
Symmetric
0%
None of these
The relation R defined in N as
a
R
b
⇔
b
is divisible by a is
Report Question
0%
Reflexive but not symmetric
0%
Symmetric but not transitive
0%
Symmetric and transitive
0%
Equivalence relation
If
(
x
2
−
2
)
+
(
y
+
3
)
i
=
7
+
4
i
then x and y are
Report Question
0%
±
3
a
n
d
4
0%
±
√
5
a
n
d
4
0%
±
3
a
n
d
1
0%
None of these
Let T be the set of all triangles in the Euclidean plane, and let a relation R' on T be defined as aRb if a is congruent to b for all a, b
∈
T. Then, R is?
Report Question
0%
Reflexive but not symmetric
0%
Transitive but not symmetric
0%
Equivalence
0%
None of these
Let
R
=
{
(
2
,
3
)
,
(
3
,
3
)
,
(
2
,
2
)
,
(
5
,
5
)
,
(
2
,
4
)
,
(
4
,
4
)
,
(
4
,
3
)
}
be a relation on the set
{
2
,
3
,
4
,
5
}
, then
Report Question
0%
R
is reflexive and symmetric but not transitive
0%
R
is reflexive and transitive but not symmetric
0%
R
is symmetric and transitive but not reflexive
0%
R
is an equivalence relation
If
A
=
{
1
,
2
,
3
,
4
,
5
}
then
Report Question
0%
The number of relation on
A
is
2
25
0%
The number of relation on
A
is
2
20
0%
The number of reflexive relation on
A
is
20
20
0%
The number of reflexive relation on
A
is
2
15
If
A
=
{
1
,
2
,
4
}
,
B
=
{
1
,
4
,
6
,
9
}
and
R
is a relation from
A
to
B
defined by
x
is greater than
y
. The rangle of
R
is :
Report Question
0%
{
1
,
4
,
6
,
9
}
0%
{
4
,
6
,
9
}
0%
{
1
}
0%
none of these
If
g
(
f
(
x
)
)
=
|
s
i
n
x
|
and
g
(
f
(
x
)
)
=
s
i
n
2
√
x
,
then
Report Question
0%
f
(
x
)
=
√
x
,
g
(
x
)
=
s
i
n
2
x
0%
f
(
x
)
=
s
i
n
√
x
,
g
(
x
)
=
x
2
0%
f
(
x
)
=
√
s
i
n
x
,
g
(
x
)
=
x
2
0%
f
(
x
)
=
|
x
|
,
g
(
x
)
=
s
i
n
2
x
If
A
=
{
1
,
2
,
3
}
then the number of equivalance relation containing the element {1,2} is :
Report Question
0%
1
0%
2
0%
3
0%
14
Let S be the set of all straight lines in a plane. Let R be a relation on S defined by
a
R
b
⇔
a
|
|
b
. Then, R is?
Report Question
0%
Reflexive and symmetric but not transitive
0%
Reflexive and transitive but not symmetric
0%
Symmetric and transitive but not reflexive
0%
An equivalence relation
If
f
(
x
)
=
−
x
|
x
|
1
+
x
2
then
f
−
1
(
x
)
equals
Report Question
0%
√
x
|
x
|
1
−
|
x
|
0%
(
S
g
n
x
)
√
x
|
x
|
1
−
|
x
|
0%
−
√
x
1
−
x
0%
None of these
Explanation
Step-1: Apply the concept of function & simplify
Let y = f(x)
=
−
x
2
1
+
x
2
,
x
≥
0
=
x
2
1
+
x
2
,
x
<
0
f
−
1
(
y
)
=
√
−
y
1
+
y
,
y
<
0
=
−
√
y
1
−
y
,
y
>
0
f
′
−
1
(
x
)
=
√
−
x
1
+
x
,
x
<
0
=
√
−
x
1
−
x
,
x
>
0
= (sgn x)
√
|
x
|
1
−
|
x
|
Hence, option B
From the following relations defined on set Z of integers, which of the relation is not equivalence relation
Report Question
0%
a
R
1
b
⇔
(
a
+
b
)
is an even integer
0%
a
R
1
b
⇔
(
a
−
b
)
is an even integer
0%
a
R
3
b
⇔
(
a
+
b
)
a
<
b
0%
a
R
4
b
⇔
(
a
+
b
)
a
=
b
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0
Answered
1
Not Answered
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Correct : 0
Incorrect : 0
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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers
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