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JEE Advanced 2017 Paper 2
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© examsnet.com
Question : 49
Total: 54
If
R
:
R
→
R
is differentiable function such that
f
′
(
x
)
>
2
f
(
x
)
for all
x
∊
R
and
f
(
0
)
=
1
, then:
f
(
x
)
is decreasing in
(
0
,
∞
)
f
′
(
x
)
<
e
2
x
in
(
0
,
∞
)
f
(
x
)
is increasing in
(
0
,
∞
)
f
′
(
x
)
>
e
2
x
in
(
0
,
∞
)
Validate
Solution:
f
′
(
x
)
>
2
f
(
x
)
f
′
(
x
)
−
2
f
(
x
)
>
0
d
y
d
x
−
2
y
>
0
e
−
2
x
d
y
d
x
−
2
e
−
2
x
y
>
0
d
d
x
(
e
−
2
x
y
)
>
0
⇒
e
−
2
x
f
(
x
)
is increasing
and
x
>
0
e
−
2
x
f
(
x
)
>
f
(
0
)
⇒
f
(
x
)
>
e
2
x
>
0
⇒
f
′
(
x
)
>
0
© examsnet.com
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