1
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)
2
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
If  xloge(logex) $$-$$ x2 + y2 = 4(y > 0), then $${{dy} \over {dx}}$$ at x = e is equal to :
A
$${{\left( {1 + 2e} \right)} \over {2\sqrt {4 + {e^2}} }}$$
B
$${{\left( {1 + 2e} \right)} \over {\sqrt {4 + {e^2}} }}$$
C
$${{\left( {2e - 1} \right)} \over {2\sqrt {4 + {e^2}} }}$$
D
$${e \over {\sqrt {4 + {e^2}} }}$$
3
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
4
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
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