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Manipal Entrance Test 2013 Math Paper
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© examsnet.com
Question : 61
Total: 80
The area of the region
[
(
x
,
y
)
:
x
2
+
y
2
≤
1
≤
x
+
y
]
is;
π
5
π
4
π
2
3
π
4
−
1
2
Validate
Solution:
x
2
+
y
2
=
1
,
x
+
y
=
1
meet when
x
2
+
(
1
−
x
)
2
=
1
⇒
x
2
+
1
+
x
2
−
2
x
=
1
⇒
2
x
2
−
2
x
=
0
⇒
2
x
(
x
−
1
)
=
0
⇒
x
=
0
,
x
=
1
⇒ Meet at points
A
(
1
,
0
)
,
B
(
0
,
1
)
∴ Required area
=
π
4
−
1
2
(
1
)
.
(
1
)
=
π
4
−
1
2
i . e . [quad.
O
A
B
−
Δ
O
A
B
]
© examsnet.com
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