1
JEE Main 2020 (Online) 3rd September Morning Slot
+4
-1
$$\int\limits_{ - \pi }^\pi {\left| {\pi - \left| x \right|} \right|dx}$$ is equal to :
A
$${\pi ^2}$$
B
2$${\pi ^2}$$
C
$$\sqrt 2 {\pi ^2}$$
D
$${{{\pi ^2}} \over 2}$$
2
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
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.
3
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
The value of
$$\int\limits_0^{2\pi } {{{x{{\sin }^8}x} \over {{{\sin }^8}x + {{\cos }^8}x}}} dx$$ is equal to :
A
4$$\pi$$
B
2$$\pi$$
C
$$\pi$$2
D
2$$\pi$$2
4
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
If for all real triplets (a, b, c), ƒ(x) = a + bx + cx2; then $$\int\limits_0^1 {f(x)dx}$$ is equal to :
A
$${1 \over 6}\left\{ {f(0) + f(1) + 4f\left( {{1 \over 2}} \right)} \right\}$$
B
$$2\left\{ 3{f(1) + 2f\left( {{1 \over 2}} \right)} \right\}$$
C
$${1 \over 3}\left\{ {f(0) + f\left( {{1 \over 2}} \right)} \right\}$$
D
$${1 \over 2}\left\{ {f(1) + 3f\left( {{1 \over 2}} \right)} \right\}$$
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