Javascript is required
1
JEE Main 2021 (Online) 16th March Evening Shift
+4
-1
Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy

$${\sin ^{ - 1}}\left( {{{3x} \over 5}} \right) + {\sin ^{ - 1}}\left( {{{4x} \over 5}} \right) = {\sin ^{ - 1}}x$$ is equal to :
A
2
B
0
C
3
D
1
2
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
If 0 < a, b < 1, and tan$$-$$1a + tan$$-$$1b = $${\pi \over 4}$$, then the value of

$$(a + b) - \left( {{{{a^2} + {b^2}} \over 2}} \right) + \left( {{{{a^3} + {b^3}} \over 3}} \right) - \left( {{{{a^4} + {b^4}} \over 4}} \right) + .....$$ is :
A
$${\log _e}$$2
B
e
C
$${\log _e}\left( {{e \over 2}} \right)$$
D
e2 = 1
3
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
If $${{{{\sin }^1}x} \over a} = {{{{\cos }^{ - 1}}x} \over b} = {{{{\tan }^{ - 1}}y} \over c}$$; $$0 < x < 1$$,
then the value of $$\cos \left( {{{\pi c} \over {a + b}}} \right)$$ is :
A
$${{1 - {y^2}} \over {2y}}$$
B
$${{1 - {y^2}} \over {y\sqrt y }}$$
C
$$1 - {y^2}$$
D
$${{1 - {y^2}} \over {1 + {y^2}}}$$
4
JEE Main 2021 (Online) 25th February Evening Shift
cosec$$\left[ {2{{\cot }^{ - 1}}(5) + {{\cos }^{ - 1}}\left( {{4 \over 5}} \right)} \right]$$ is equal to :
$${{75} \over {56}}$$
$${{65} \over {56}}$$
$${{56} \over {33}}$$
$${{65} \over {33}}$$