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JEE Main 10 Jan 2019 Shift 1 Solved Paper
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© examsnet.com
Question : 52
Total: 90
If
d
y
d
x
+
3
c
o
s
2
x
y =
1
c
o
s
2
x
, x ∊
(
−
π
3
,
π
3
)
and y
(
π
4
)
=
4
3
, then y
(
−
π
4
)
equals :
1
3
+
e
6
1
3
-
4
3
1
3
+
e
3
Validate
Solution:
d
y
d
x
+ 3
s
e
c
2
x , y =
s
e
c
2
x
I.F. =
e
3
∫
s
e
c
2
x
d
x
=
e
3
t
a
n
x
or , y
e
3
t
a
n
x
=
∫
s
e
c
2
x
.
e
3
t
a
n
x
dx
or y
e
3
t
a
n
x
=
1
3
e
3
t
a
n
x
+ C ... (1)
Given
y
(
π
4
)
=
4/3$$
∴
4
3
.
e
3
=
1
3
e
3
+ C
∴ C =
e
3
Now put x =
−
π
4
in eq (1)
∴ y .
e
−
3
=
1
3
e
−
3
+
e
3
∴ y =
1
3
+
e
6
∴ y
(
−
π
4
)
=
1
3
+
e
6
© examsnet.com
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