1
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
Let y = y(x) be the solution of the differential equation, x$${{dy} \over {dx}}$$ + y = x loge x, (x > 1). If 2y(2) = loge 4 $$-$$ 1, then y(e) is equal to :
A
$$- {e \over 2}$$
B
$$- {{{e^2}} \over 2}$$
C
$${{{e^2}} \over 4}$$
D
$${e \over 4}$$
2
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
The solution of the differential equation,

$${{dy} \over {dx}}$$ = (x – y)2, when y(1) = 1, is :
A
$$-$$ loge $$\left| {{{1 + x - y} \over {1 - x + y}}} \right|$$ = x + y $$-$$ 2
B
loge $$\left| {{{2 - x} \over {2 - y}}} \right|$$ = x $$-$$ y
C
loge $$\left| {{{2 - y} \over {2 - x}}} \right|$$ = 2(y $$-$$ 1)
D
$$-$$ loge $$\left| {{{1 - x + y} \over {1 + x - y}}} \right|$$ = 2(x $$-$$ 1)
3
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
If y(x) is the solution of the differential equation $${{dy} \over {dx}} + \left( {{{2x + 1} \over x}} \right)y = {e^{ - 2x}},\,\,x > 0,\,$$ where $$y\left( 1 \right) = {1 \over 2}{e^{ - 2}},$$ then
A
y(loge2) = loge4
B
y(x) is decreasing in (0, 1)
C
y(loge2) = $${{{{\log }_e}2} \over 4}$$
D
y(x) is decreasing in $$\left( {{1 \over 2},1} \right)$$
4
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
The curve amongst the family of curves represented by the differential equation, (x2 – y2)dx + 2xy dy = 0 which passes through (1, 1) is :
A
a circle with centre on the y-axis
B
an ellipse with major axis along the y-axis
C
a circle with centre on the x-axis
D
a hyperbola with transverse axis along the x-axis
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