1
JEE Main 2021 (Online) 24th February Morning Shift
+4
-1
If $$\int {{{\cos x - \sin x} \over {\sqrt {8 - \sin 2x} }}} dx = a{\sin ^{ - 1}}\left( {{{\sin x + \cos x} \over b}} \right) + c$$, where c is a constant of integration, then the ordered pair (a, b) is equal to :
A
(-1, 3)
B
(1, 3)
C
(1, -3)
D
(3, 1)
2
JEE Main 2020 (Online) 5th September Evening Slot
+4
-1
If
$$\int {{{\cos \theta } \over {5 + 7\sin \theta - 2{{\cos }^2}\theta }}} d\theta$$ = A$${\log _e}\left| {B\left( \theta \right)} \right| + C$$,

where C is a constant of integration, then $${{{B\left( \theta \right)} \over A}}$$
can be :
A
$${{2\sin \theta + 1} \over {5\left( {\sin \theta + 3} \right)}}$$
B
$${{2\sin \theta + 1} \over {\sin \theta + 3}}$$
C
$${{5\left( {2\sin \theta + 1} \right)} \over {\sin \theta + 3}}$$
D
$${{5\left( {\sin \theta + 3} \right)} \over {2\sin \theta + 1}}$$
3
JEE Main 2020 (Online) 5th September Morning Slot
+4
-1
If
$$\int {\left( {{e^{2x}} + 2{e^x} - {e^{ - x}} - 1} \right){e^{\left( {{e^x} + {e^{ - x}}} \right)}}dx}$$ = $$g\left( x \right){e^{\left( {{e^x} + {e^{ - x}}} \right)}} + c$$

where c is a constant of integration, then g(0) is equal to :
A
1
B
2
C
e
D
e2
4
JEE Main 2020 (Online) 4th September Morning Slot
+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
$${\pi \over 6} + {1 \over 2} - {{\sqrt 3 } \over 4}$$
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