1
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
2
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
$${{1 - {y^2}} \over {1 + {y^2}}}$$
3
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
cosec$$\left[ {2{{\cot }^{ - 1}}(5) + {{\cos }^{ - 1}}\left( {{4 \over 5}} \right)} \right]$$ is equal to :
A
$${{75} \over {56}}$$
B
$${{65} \over {56}}$$
C
$${{56} \over {33}}$$
D
$${{65} \over {33}}$$
4
JEE Main 2021 (Online) 24th February Evening Shift
+4
-1
A possible value of $$\tan \left( {{1 \over 4}{{\sin }^{ - 1}}{{\sqrt {63} } \over 8}} \right)$$ is :
A
$$\sqrt 7 - 1$$
B
$${1 \over {\sqrt 7 }}$$
C
$$2\sqrt 2 - 1$$
D
$${1 \over {2\sqrt 2 }}$$
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