1
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
$${{2\pi } \over 3}$$
2
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
For a > 0, let the curves C1 : y2 = ax and C2 : x2 = ay intersect at origin O and a point P. Let the line x = b (0 < b < a) intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, C1 and C2, and the area of
$$\Delta$$OQR = $${1 \over 2}$$, then 'a' satisfies the equation
A
x6 – 12x3 + 4 = 0
B
x6 – 12x3 – 4 = 0
C
x6 + 6x3 – 4 = 0
D
x6 – 6x3 + 4 = 0
3
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
The value of $$\alpha$$ for which
$$4\alpha \int\limits_{ - 1}^2 {{e^{ - \alpha \left| x \right|}}dx} = 5$$, is:
A
$${\log _e}2$$
B
$${\log _e}\sqrt 2$$
C
$${\log _e}\left( {{4 \over 3}} \right)$$
D
$${\log _e}\left( {{3 \over 2}} \right)$$
4
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
The area (in sq. units) of the region
{(x, y) $$\in$$ R2 | 4x2 $$\le$$ y $$\le$$ 8x + 12} is :
A
$${{125} \over 3}$$
B
$${{128} \over 3}$$
C
$${{127} \over 3}$$
D
$${{124} \over 3}$$
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