1
JEE Main 2020 (Online) 6th September Morning Slot
+4
-1
$$\mathop {\lim }\limits_{x \to 1} \left( {{{\int\limits_0^{{{\left( {x - 1} \right)}^2}} {t\cos \left( {{t^2}} \right)dt} } \over {\left( {x - 1} \right)\sin \left( {x - 1} \right)}}} \right)$$
A
is equal to 0
B
is equal to $${1 \over 2}$$
C
does not exist
D
is equal to $$- {1 \over 2}$$
2
JEE Main 2020 (Online) 6th September Morning Slot
+4
-1
If I1 = $$\int\limits_0^1 {{{\left( {1 - {x^{50}}} \right)}^{100}}} dx$$ and
I2 = $$\int\limits_0^1 {{{\left( {1 - {x^{50}}} \right)}^{101}}} dx$$ such
that I2 = $$\alpha$$I1 then $$\alpha$$ equals to :
A
$${{5051} \over {5050}}$$
B
$${{5050} \over {5051}}$$
C
$${{5050} \over {5049}}$$
D
$${{5049} \over {5050}}$$
3
JEE Main 2020 (Online) 5th September Morning Slot
+4
-1
The value of $$\int\limits_{{{ - \pi } \over 2}}^{{\pi \over 2}} {{1 \over {1 + {e^{\sin x}}}}dx}$$ is:
A
$$\pi$$
B
$${{3\pi \over 2}}$$
C
$${{\pi \over 2}}$$
D
$${{\pi \over 4}}$$
4
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
$${9 \over 2}$$
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