1
JEE Main 2020 (Online) 3rd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
MCQ (Single Correct Answer)
+4
-1
Change Language
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 Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\int\limits_{ - \pi }^\pi {\left| {\pi - \left| x \right|} \right|dx} $$ is equal to :
A
$${\pi ^2}$$
B
2$${\pi ^2}$$
C
$$\sqrt 2 {\pi ^2}$$
D
$${{{\pi ^2}} \over 2}$$
4
JEE Main 2020 (Online) 9th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let a function ƒ : [0, 5] $$ \to $$ R be continuous, ƒ(1) = 3 and F be defined as :

$$F(x) = \int\limits_1^x {{t^2}g(t)dt} $$ , where $$g(t) = \int\limits_1^t {f(u)du} $$

Then for the function F, the point x = 1 is :
A
a point of inflection.
B
a point of local maxima.
C
a point of local minima.
D
not a critical point.
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