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Byju's Answer
Standard XII
Mathematics
Area between Two Curves
Let S=S1∩ S2∩...
Question
Let
S
=
S
1
∩
S
2
∩
S
3
,
where
S
1
=
{
z
∈
C
:
|
z
|
<
4
}
,
S
2
=
{
z
∈
C
:
Im
(
z
−
1
+
√
3
i
1
−
√
3
i
)
>
0
}
and
S
3
=
{
z
∈
C
:
Re
z
>
0
}
Area of
S
=
A
10
π
3
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B
20
π
3
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C
16
π
3
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D
32
π
3
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Solution
The correct option is
B
20
π
3
Let
z
=
x
+
i
y
S
1
:
x
2
+
y
2
<
16
S
2
:
Im
(
(
x
−
1
)
+
i
(
y
+
√
3
)
1
−
i
√
3
)
>
0
⇒
Im
(
(
x
−
1
)
+
i
(
y
+
√
3
)
1
−
i
√
3
×
1
+
i
√
3
1
+
i
√
3
)
>
0
⇒
√
3
(
x
−
1
)
+
y
+
√
3
>
0
⇒
√
3
x
+
y
>
0
S
3
:
x
>
0
S
=
S
1
∩
S
2
∩
S
3
Shaded area represents
S
.
Area of
S
=
1
2
r
2
θ
=
1
2
×
4
2
×
5
π
6
=
20
π
3
Suggest Corrections
1
Similar questions
Q.
Let
S
=
S
1
∩
S
2
∩
S
3
,
where
S
1
=
{
z
∈
C
:
|
z
|
<
4
}
,
S
2
=
{
z
∈
C
:
Im
(
z
−
1
+
√
3
i
1
−
√
3
i
)
>
0
}
and
S
3
=
{
z
∈
C
:
Re
z
>
0
}
min
z
∈
S
|
1
−
3
i
−
z
|
=
Q.
Let
S
=
S
1
∩
S
2
∩
S
3
,
where
S
1
=
{
z
ϵ
C
:
|
z
|
<
4
}
,
S
2
=
{
z
ϵ
C
:
I
m
[
z
−
1
+
√
3
i
1
−
√
3
i
]
>
0
}
a
n
d
S
3
=
{
z
ϵ
C
:
R
e
(
z
)
>
0
}
.
Area of
S
=
Q.
Let
S
1
,
S
2
and
S
3
be three sets defined as
S
1
=
{
z
∈
C
:
|
z
−
1
|
≤
√
2
}
S
2
=
{
z
∈
C
:
Re
(
(
1
−
i
)
z
)
≥
1
}
S
3
=
{
z
∈
C
:
Im
(
z
)
≤
1
}
Then the set
S
1
∩
S
2
∩
S
3
Q.
Let
C
be the set of all complex numbers. Let
S
1
=
{
z
∈
C
:
|
z
−
3
−
2
i
|
2
=
8
}
,
S
2
=
{
z
∈
C
:
R
e
(
z
)
≥
5
}
and
S
3
=
{
z
∈
C
:
|
z
−
¯
z
|
≥
8
}
.
Then the number of elements in
S
1
∩
S
2
∩
S
3
is equal to
Q.
min
z
∈
S
|
1
−
3
i
−
z
|
=
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