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JEE Main Math Class 12 Differential Equations Part 2 Questions
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© examsnet.com
Question : 33
Total: 124
Let
α
be a non-zero real number. Suppose
f
:
R
⟶
R
is a differentiable function such that
f
(
0
)
=
2
and
lim
x
⟶
−
∞
f
(
x
)
=
1
. If
f
′
(
x
)
=
α
f
(
x
)
+
3
, for all
x
∈
R
, then
f
(
−
log
e
2
)
is equal to
[1-Feb-2024 Shift 2]
3
5
9
7
Validate
Solution:
👈: Video Solution
f
(
0
)
=
2
,
lim
x
→
−
∞
f
(
x
)
=
1
f
′
(
x
)
−
α
⋅
f
(
x
)
=
3
I
⋅
F
=
e
−
α
x
y
(
e
−
α
x
)
=
∫
3
⋅
e
−
α
x
dx
f
(
x
)
⋅
(
e
−
α
x
)
=
3
e
−
α
x
−
α
+
c
x
=
0
⇒
2
=
−
3
α
+
c
⇒
3
α
=
c
−
2
f
(
x
)
=
−
3
α
+
c
⋅
e
α
x
x
→
−
∞
⇒
1
=
−
3
α
+
c
(
0
)
α
=
−
3
∴
c
=
1
f
(
−
ln
2
)
=
−
3
α
+
c
⋅
e
α
x
=
1
+
e
3
ln
2
=
9
(But
α
should be greater than 0 for finite value of c)
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