1
JEE Main 2020 (Online) 8th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
If $$\int {{{\cos xdx} \over {{{\sin }^3}x{{\left( {1 + {{\sin }^6}x} \right)}^{2/3}}}}} = f\left( x \right){\left( {1 + {{\sin }^6}x} \right)^{1/\lambda }} + c$$

where c is a constant of integration, then $$\lambda f\left( {{\pi \over 3}} \right)$$ is equal to
A
$${9 \over 8}$$
B
2
C
-2
D
$$-{9 \over 8}$$
2
JEE Main 2019 (Online) 12th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Let $$a \in \left( {0,{\pi \over 2}} \right)$$ be fixed. If the integral

$$\int {{{\tan x + \tan \alpha } \over {\tan x - \tan \alpha }}} dx$$ = A(x) cos 2$$\alpha$$ + B(x) sin 2$$\alpha$$ + C, where C is a

constant of integration, then the functions A(x) and B(x) are respectively :
A
$$x - \alpha$$ and $${\log _e}\left| {\cos \left( {x - \alpha } \right)} \right|$$
B
$$x + \alpha$$ and $${\log _e}\left| {\sin \left( {x - \alpha } \right)} \right|$$
C
$$x + \alpha$$ and $${\log _e}\left| {\sin \left( {x + \alpha } \right)} \right|$$
D
$$x - \alpha$$ and $${\log _e}\left| {\sin \left( {x - \alpha } \right)} \right|$$
3
JEE Main 2019 (Online) 12th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
The integral $$\int {{{2{x^3} - 1} \over {{x^4} + x}}} dx$$ is equal to :
(Here C is a constant of integration)
A
$${\log _e}{{\left| {{x^3} + 1} \right|} \over {{x^2}}} + C$$
B
$${1 \over 2}{\log _e}{{\left| {{x^3} + 1} \right|} \over {{x^2}}} + C$$
C
$${\log _e}\left| {{{{x^3} + 1} \over x}} \right| + C$$
D
$${1 \over 2}{\log _e}{{{{\left( {{x^3} + 1} \right)}^2}} \over {\left| {{x^3}} \right|}} + C$$
4
JEE Main 2019 (Online) 10th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
If $$\int {{x^5}} {e^{ - {x^2}}}dx = g\left( x \right){e^{ - {x^2}}} + c$$, where c is a constant of integration, then $$g$$(–1) is equal to :
A
1
B
- 1
C
$$- {5 \over 2}$$
D
$$- {1 \over 2}$$
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