1
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
$${1 \over {2\sqrt 2 }}$$
2
JEE Main 2020 (Online) 5th September Morning Slot
+4
-1
If S is the sum of the first 10 terms of the series

$${\tan ^{ - 1}}\left( {{1 \over 3}} \right) + {\tan ^{ - 1}}\left( {{1 \over 7}} \right) + {\tan ^{ - 1}}\left( {{1 \over {13}}} \right) + {\tan ^{ - 1}}\left( {{1 \over {21}}} \right) + ....$$

then tan(S) is equal to :
A
$${10 \over {11}}$$
B
$${5 \over {11}}$$
C
-$${6 \over {5}}$$
D
$${5 \over {6}}$$
3
JEE Main 2020 (Online) 3rd September Morning Slot
+4
-1
2$$\pi$$ - $$\left( {{{\sin }^{ - 1}}{4 \over 5} + {{\sin }^{ - 1}}{5 \over {13}} + {{\sin }^{ - 1}}{{16} \over {65}}} \right)$$ is equal to :
A
$${{7\pi } \over 4}$$
B
$${{5\pi } \over 4}$$
C
$${{3\pi } \over 2}$$
D
$${\pi \over 2}$$
4
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
The domain of the function
f(x) = $${\sin ^{ - 1}}\left( {{{\left| x \right| + 5} \over {{x^2} + 1}}} \right)$$ is (– $$\infty$$, -a]$$\cup$$[a, $$\infty$$). Then a is equal to :
A
$${{\sqrt {17} - 1} \over 2}$$
B
$${{1 + \sqrt {17} } \over 2}$$
C
$${{\sqrt {17} } \over 2} + 1$$
D
$${{\sqrt {17} } \over 2}$$
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