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KVPY 2019 SB SX Exam Previous Papers
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© examsnet.com
Question : 2
Total: 120
Let
A
=
{
θ
∊
R
:
(
1
3
sin
(
θ
)
+
2
3
c
o
s
(
θ
)
)
2
=
1
3
sin
2
(
θ
)
+
2
3
cos
2
(
θ
)
}
. Then
A
∩
[
0
,
π
]
is an empty set
A
∩
[
0
,
π
]
has exactly one point
A
∩
[
0
,
π
]
has exactly two points
A
∩
[
0
,
π
]
has more than two points
Validate
Solution:
sin
2
θ
+
4
cos
2
θ
+
4
sin
θ
cos
θ
9
=
sin
2
θ
+
2
cos
2
θ
3
⇒
2
sin
2
θ
+
2
cos
2
θ
−
4
sin
θ
cos
θ
=
0
⇒
sin
2
θ
=
1
⇒
2
θ
=
2
n
π
+
π
2
⇒
θ
=
n
π
+
π
4
⇒
A
∩
[
0
,
π
]
=
{
π
4
}
© examsnet.com
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