1
JEE Main 2019 (Online) 8th April Morning Slot
+4
-1
If $$2y = {\left( {{{\cot }^{ - 1}}\left( {{{\sqrt 3 \cos x + \sin x} \over {\cos x - \sqrt 3 \sin x}}} \right)} \right)^2}$$,

x $$\in$$ $$\left( {0,{\pi \over 2}} \right)$$ then $$dy \over dx$$ is equal to:
A
$$2x - {\pi \over 3}$$
B
$${\pi \over 6} - x$$
C
$${\pi \over 3} - x$$
D
$$x - {\pi \over 6}$$
2
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
For x > 1, if (2x)2y = 4e2x$$-$$2y,

then (1 + loge 2x)2 $${{dy} \over {dx}}$$ is equal to :
A
$${{x\,{{\log }_e}2x - {{\log }_e}2} \over x}$$
B
loge 2x
C
x loge 2x
D
$${{x\,{{\log }_e}2x + {{\log }_e}2} \over x}$$
3
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
$${e \over {\sqrt {4 + {e^2}} }}$$
4
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
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