1
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
If $$y\left( \alpha \right) = \sqrt {2\left( {{{\tan \alpha + \cot \alpha } \over {1 + {{\tan }^2}\alpha }}} \right) + {1 \over {{{\sin }^2}\alpha }}} ,\alpha \in \left( {{{3\pi } \over 4},\pi } \right)$$

$${{dy} \over {d\alpha }}\,\,at\,\alpha = {{5\pi } \over 6}is$$ :
A
4
B
-4
C
$${4 \over 3}$$
D
-$${1 \over 4}$$
2
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
The derivative of $${\tan ^{ - 1}}\left( {{{\sin x - \cos x} \over {\sin x + \cos x}}} \right)$$, with respect to $${x \over 2}$$ , where $$\left( {x \in \left( {0,{\pi \over 2}} \right)} \right)$$ is :
A
1
B
2
C
$${2 \over 3}$$
D
$${1 \over 2}$$
3
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
$$\left( {{1 \over e},{1 \over {{e^2}}}} \right)$$
4
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
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