1
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 $$\left( {{1 \over 2},1} \right)$$
2
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
3
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
Let f be a differentiable function such that f '(x) = 7 - $${3 \over 4}{{f\left( x \right)} \over x},$$ (x > 0) and f(1) $$\ne$$ 4. Then $$\mathop {\lim }\limits_{x \to 0'} \,$$ xf$$\left( {{1 \over x}} \right)$$ :
A
does not exist
B
exists and equals $${4 \over 7}$$
C
exists and equals 4
D
exists and equals 0
4
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
If  $${{dy} \over {dx}} + {3 \over {{{\cos }^2}x}}y = {1 \over {{{\cos }^2}x}},\,\,x \in \left( {{{ - \pi } \over 3},{\pi \over 3}} \right)$$  and  $$y\left( {{\pi \over 4}} \right) = {4 \over 3},$$  then  $$y\left( { - {\pi \over 4}} \right)$$   equals -
A
$${1 \over 3} + {e^6}$$
B
$${1 \over 3}$$
C
$${1 \over 3}$$ + e3
D
$$-$$ $${4 \over 3}$$
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