1
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
$${e \over {\sqrt {4 + {e^2}} }}$$
2
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
Let f : R $$\to$$ R be a function such that f(x) = x3 + x2f'(1) + xf''(2) + f'''(3), x $$\in$$ R. Then f(2) equals -
A
30
B
$$-$$ 2
C
$$-$$ 4
D
8
3
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
If   x $$=$$ 3 tan t and y $$=$$ 3 sec t, then the value of $${{{d^2}y} \over {d{x^2}}}$$ at t $$= {\pi \over 4},$$ is :
A
$${1 \over {3\sqrt 2 }}$$
B
$${1 \over {6\sqrt 2 }}$$
C
$${3 \over {2\sqrt 2 }}$$
D
$${1 \over 6}$$
4
JEE Main 2018 (Online) 16th April Morning Slot
+4
-1
If $$x = \sqrt {{2^{\cos e{c^{ - 1}}}}}$$ and $$y = \sqrt {{2^{se{c^{ - 1}}t}}} \,\,\left( {\left| t \right| \ge 1} \right),$$ then $${{dy} \over {dx}}$$ is equal to :
A
$${y \over x}$$
B
$${x \over y}$$
C
$$-$$ $${y \over x}$$
D
$$-$$ $${x \over y}$$
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