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Mathematics
Mathematics
Problem
Let
S
(
α
)
=
{
(
x
,
y
)
:
y
2
≤
x
,
0
≤
x
≤
α
}
S(\alpha) = \{(x,y) : y^2 \le x, 0 \le x \le \alpha\}
S
(
α
)
=
{(
x
,
y
)
:
y
2
≤
x
,
0
≤
x
≤
α
}
and
A
(
α
)
A(\alpha)
A
(
α
)
is area of the region
S
(
α
)
S(\alpha)
S
(
α
)
. If for a
λ
\lambda
λ
,
0
<
λ
<
4
0 < \lambda < 4
0
<
λ
<
4
,
A
(
λ
)
:
A
(
4
)
=
2
:
5
A(\lambda) : A(4) = 2 : 5
A
(
λ
)
:
A
(
4
)
=
2
:
5
, then
λ
\lambda
λ
equals [JEE-MAIN ONLINE-2019] (1)
2
(
4
25
)
1
3
2\left(\frac{4}{25}\right)^{\frac{1}{3}}
2
(
25
4
)
3
1
(2)
4
(
4
25
)
1
3
4\left(\frac{4}{25}\right)^{\frac{1}{3}}
4
(
25
4
)
3
1
(3)
2
(
2
5
)
1
3
2\left(\frac{2}{5}\right)^{\frac{1}{3}}
2
(
5
2
)
3
1
(4)
4
(
2
5
)
1
3
4\left(\frac{2}{5}\right)^{\frac{1}{3}}
4
(
5
2
)
3
1
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