1
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
$${\log _e}\left( {{3 \over 2}} \right)$$
2
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
$${{124} \over 3}$$
3
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
If $$\theta$$1 and $$\theta$$2 be respectively the smallest and the largest values of $$\theta$$ in (0, 2$$\pi$$) - {$$\pi$$} which satisfy the equation,
2cot2$$\theta$$ - $${5 \over {\sin \theta }}$$ + 4 = 0, then
$$\int\limits_{{\theta _1}}^{{\theta _2}} {{{\cos }^2}3\theta d\theta }$$ is equal to :
A
$${\pi \over 9}$$
B
$${{2\pi } \over 3}$$
C
$${{\pi } \over 3}$$
D
$${\pi \over 3} + {1 \over 6}$$
4
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
The area of the region, enclosed by the circle x2 + y2 = 2 which is not common to the region bounded by the parabola y2 = x and the straight line y = x, is:
A
$${1 \over 6}\left( {24\pi - 1} \right)$$
B
$${1 \over 3}\left( {12\pi - 1} \right)$$
C
$${1 \over 3}\left( {6\pi - 1} \right)$$
D
$${1 \over 6}\left( {12\pi - 1} \right)$$
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