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AIEEE 2005 Math Solved Paper
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© examsnet.com
Question : 40
Total: 71
The parabolas
y
2
=
4
x
and
x
2
=
4
y
divide the square region bounded by the lines
x
=
4
,
y
=
4
and the coordinate axes. If
S
1
,
S
2
,
S
3
are respectively the areas of these parts numbered from top to bottom ; then
S
1
,
S
2
,
S
3
is
1
:
2
:
1
1
:
2
:
3
2
:
1
:
2
1
:
1
:
1
Validate
Solution:
Intersection points of
x
2
=
4
y
and
y
2
=
4
x
are
(
0
,
0
)
and
(
4
,
4
)
. The graph is as shown in the figure.
By symmetry, we observe
S
1
=
S
3
=
4
∫
0
y
dx
=
4
∫
0
x
2
4
dx
=
[
x
3
12
]
0
4
=
16
3
sq. unit
Also
S
2
=
4
∫
0
(
2
√
x
−
x
2
4
)
dx
=
[
2
x
3
2
3
2
−
x
3
12
]
0
4
=
4
3
×
8
−
16
3
=
16
3
∴
S
1
:
S
2
:
S
3
=
1
:
1
:
1
© examsnet.com
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