1
JEE Main 2020 (Online) 4th September Evening Slot
+4
-1
The integral
$$\int\limits_{{\pi \over 6}}^{{\pi \over 3}} {{{\tan }^3}x.{{\sin }^2}3x\left( {2{{\sec }^2}x.{{\sin }^2}3x + 3\tan x.\sin 6x} \right)dx}$$
is equal to:
A
$$- {1 \over {9}}$$
B
$$- {1 \over {18}}$$
C
$${7 \over {18}}$$
D
$${9 \over 2}$$
2
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Let $$f(x) = \left| {x - 2} \right|$$ and g(x) = f(f(x)), $$x \in \left[ {0,4} \right]$$. Then
$$\int\limits_0^3 {\left( {g(x) - f(x)} \right)} dx$$ is equal to:
A
1
B
0
C
$${1 \over 2}$$
D
$${3 \over 2}$$
3
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
If the value of the integral
$$\int\limits_0^{{1 \over 2}} {{{{x^2}} \over {{{\left( {1 - {x^2}} \right)}^{{3 \over 2}}}}}} dx$$

is $${k \over 6}$$, then k is equal to :
A
$$2\sqrt 3 + \pi$$
B
$$3\sqrt 2 - \pi$$
C
$$3\sqrt 2 + \pi$$
D
$$2\sqrt 3 - \pi$$
4
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
Suppose f(x) is a polynomial of degree four, having critical points at –1, 0, 1. If
T = {x $$\in$$ R | f(x) = f(0)}, then the sum of squares of all the elements of T is :
A
6
B
2
C
8
D
4
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