1
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
$${1 \over 6}$$
2
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
$$-$$ $${x \over y}$$
3
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
If    f(x) = sin-1 $$\left( {{{2 \times {3^x}} \over {1 + {9^x}}}} \right),$$ then f'$$\left( { - {1 \over 2}} \right)$$ equals :
A
$$- \sqrt 3 {\log _e}\sqrt 3$$
B
$$\sqrt 3 {\log _e}\sqrt 3$$
C
$$- \sqrt 3 {\log _e}\, 3$$
D
$$\sqrt 3 {\log _e}\, 3$$
4
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
If $$f\left( x \right) = \left| {\matrix{ {\cos x} & x & 1 \cr {2\sin x} & {{x^2}} & {2x} \cr {\tan x} & x & 1 \cr } } \right|,$$ then $$\mathop {\lim }\limits_{x \to 0} {{f'\left( x \right)} \over x}$$
A
does not exist.
B
exists and is equal to 2.
C
existsand is equal to 0.
D
exists and is equal to $$-$$ 2.
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