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AMU Engineering 2020 solved paper Solved Paper
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© examsnet.com
Question : 132
Total: 150
Let the straight line
x
=
b
divide the area enclosed by
y
=
(
1
−
x
)
2
,
y
=
0
and
x
=
0
into two parts
R
1
(
0
≤
x
≤
b
)
and
R
2
(
b
≤
x
≤
1
)
such that
R
1
−
R
2
=
1
4
. Then
b
equals.
3
4
1
2
1
3
1
4
Validate
Solution:
∴
R
1
=
b
∫
0
(
1
−
x
)
2
d
x
and
R
2
=
1
∫
b
(
1
−
x
2
)
d
x
⇒
R
1
=
[
(
x
−
1
)
3
3
]
0
b
and
R
2
=
[
(
x
−
1
)
3
3
]
b
1
⇒
R
1
=
(
b
−
1
)
3
3
+
1
3
and
R
2
=
−
(
b
−
1
)
3
3
∴
R
1
−
R
2
=
1
4
⇒
2
3
(
b
−
1
)
3
+
1
3
=
1
4
⇒
2
3
(
b
−
1
)
3
=
−
1
12
⇒
(
b
−
1
)
3
=
−
1
8
⇒
b
−
1
=
−
1
2
⇒
b
=
1
2
© examsnet.com
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