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JEE Main Mock Test 11
Q 1 / 25
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Section A - MCQ
Hard
JEE Main 2024
Question 1
+4 marks
Let
x
=
x
(
y
)
x=x(y)
x
=
x
(
y
)
be the solution of the differential equation
2
(
y
+
2
)
log
e
(
y
+
2
)
d
x
+
(
x
+
4
−
2
log
e
(
y
+
2
)
)
d
y
=
0
,
y
>
−
1
2(y+2) \log _{e}(y+2) d x+\left(x+4-2 \log _{e}(y+2)\right) d y=0, y>-1
2
(
y
+
2
)
lo
g
e
(
y
+
2
)
d
x
+
(
x
+
4
−
2
lo
g
e
(
y
+
2
)
)
d
y
=
0
,
y
>
−
1
with
x
(
e
4
−
2
)
=
1
x\left(e^{4}-2\right)=1
x
(
e
4
−
2
)
=
1
. Then
x
(
e
9
−
2
)
x\left(e^{9}-2\right)
x
(
e
9
−
2
)
is equal to :
A
4
9
\frac{4}{9}
9
4
B
32
9
\frac{32}{9}
9
32
C
10
3
\frac{10}{3}
3
10
D
3
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Section A - MCQ
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Section B - Numerical
1
2
3
4
5
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