1
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
If $$x = 2\sin \theta - \sin 2\theta$$ and $$y = 2\cos \theta - \cos 2\theta$$,
$$\theta \in \left[ {0,2\pi } \right]$$, then $${{{d^2}y} \over {d{x^2}}}$$ at $$\theta$$ = $$\pi$$ is :
A
$${3 \over 8}$$
B
$${3 \over 2}$$
C
$${3 \over 4}$$
D
-$${3 \over 4}$$
2
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
Let ƒ and g be differentiable functions on R such that fog is the identity function. If for some a, b $$\in$$ R, g'(a) = 5 and g(a) = b, then ƒ'(b) is equal to :
A
1
B
5
C
$${2 \over 5}$$
D
$${1 \over 5}$$
3
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
Let ƒ(x) = (sin(tan–1x) + sin(cot–1x))2 – 1, |x| > 1.
If $${{dy} \over {dx}} = {1 \over 2}{d \over {dx}}\left( {{{\sin }^{ - 1}}\left( {f\left( x \right)} \right)} \right)$$ and $$y\left( {\sqrt 3 } \right) = {\pi \over 6}$$, then y($${ - \sqrt 3 }$$) is equal to :
A
$${{5\pi } \over 6}$$
B
$$- {\pi \over 6}$$
C
$${\pi \over 3}$$
D
$${{2\pi } \over 3}$$
4
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
Let y = y(x) be a function of x satisfying

$$y\sqrt {1 - {x^2}} = k - x\sqrt {1 - {y^2}}$$ where k is a constant and

$$y\left( {{1 \over 2}} \right) = - {1 \over 4}$$. Then $${{dy} \over {dx}}$$ at x = $${1 \over 2}$$, is equal to :
A
$${2 \over {\sqrt 5 }}$$
B
$$- {{\sqrt 5 } \over 2}$$
C
$${{\sqrt 5 } \over 2}$$
D
$$- {{\sqrt 5 } \over 4}$$
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