1
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
$$2\sqrt 3 - \pi$$
2
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
3
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
If x3dy + xy dx = x2dy + 2y dx; y(2) = e and
x > 1, then y(4) is equal to :
A
$${{\sqrt e } \over 2}$$
B
$${1 \over 2} + \sqrt e$$
C
$${3 \over 2} + \sqrt e$$
D
$${3 \over 2}\sqrt e$$
4
JEE Main 2020 (Online) 3rd September Morning Slot
+4
-1
The area (in sq. units) of the region

{ (x, y) : 0 $$\le$$ y $$\le$$ x2 + 1, 0 $$\le$$ y $$\le$$ x + 1,
$${1 \over 2}$$ $$\le$$ x $$\le$$ 2 } is :
A
$${{79} \over {16}}$$
B
$${{79} \over {24}}$$
C
$${{23} \over {6}}$$
D
$${{23} \over {16}}$$
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