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Questions
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1
JEE Main 2020 (Online) 5th September Morning Slot
MCQ (Single Correct Answer)
+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
$${{\pi \over 4}}$$
2
JEE Main 2020 (Online) 4th September Evening Slot
MCQ (Single Correct Answer)
+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
$${9 \over 2}$$
3
JEE Main 2020 (Online) 4th September Morning Slot
MCQ (Single Correct Answer)
+4
-1
Let $$f\left( x \right) = \int {{{\sqrt x } \over {{{\left( {1 + x} \right)}^2}}}dx\left( {x \ge 0} \right)} $$. Then f(3) – f(1) is eqaul to :
A
$$ - {\pi \over {12}} + {1 \over 2} + {{\sqrt 3 } \over 4}$$
B
$$ {\pi \over {12}} + {1 \over 2} - {{\sqrt 3 } \over 4}$$
C
$$ - {\pi \over 6} + {1 \over 2} + {{\sqrt 3 } \over 4}$$
D
$${\pi \over 6} + {1 \over 2} - {{\sqrt 3 } \over 4}$$
4
JEE Main 2020 (Online) 4th September Morning Slot
MCQ (Single Correct Answer)
+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
$${3 \over 2}$$
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