1
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
If ey + xy = e, the ordered pair $$\left( {{{dy} \over {dx}},{{{d^2}y} \over {d{x^2}}}} \right)$$ at x = 0 is equal to :
A
$$\left( {{1 \over e}, - {1 \over {{e^2}}}} \right)$$
B
$$\left( { - {1 \over e},{1 \over {{e^2}}}} \right)$$
C
$$\left( { - {1 \over e}, - {1 \over {{e^2}}}} \right)$$
D
$$\left( {{1 \over e},{1 \over {{e^2}}}} \right)$$
2
JEE Main 2019 (Online) 10th April Evening Slot
+4
-1
Let f(x) = loge(sin x), (0 < x < $$\pi$$) and g(x) = sin–1 (e–x ), (x $$\ge$$ 0). If $$\alpha$$ is a positive real number such that a = (fog)'($$\alpha$$) and b = (fog)($$\alpha$$), then :
A
a$$\alpha$$2 + b$$\alpha$$ - a = -2$$\alpha$$2
B
a$$\alpha$$2 + b$$\alpha$$ + a = 0
C
a$$\alpha$$2 - b$$\alpha$$ - a = 0
D
a$$\alpha$$2 - b$$\alpha$$ - a = 1
3
JEE Main 2019 (Online) 8th April Evening Slot
+4
-1
If ƒ(1) = 1, ƒ'(1) = 3, then the derivative of ƒ(ƒ(ƒ(x))) + (ƒ(x))2 at x = 1 is :
A
33
B
12
C
9
D
15
4
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
$$x - {\pi \over 6}$$
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