1
JEE Main 2022 (Online) 29th June Morning Shift
+4
-1

The domain of the function $${\cos ^{ - 1}}\left( {{{2{{\sin }^{ - 1}}\left( {{1 \over {4{x^2} - 1}}} \right)} \over \pi }} \right)$$ is :

A
$$R - \left\{ { - {1 \over 2},{1 \over 2}} \right\}$$
B
$$( - \infty , - 1] \cup [1,\infty ) \cup \{ 0\}$$
C
$$\left( { - \infty ,{{ - 1} \over 2}} \right) \cup \left( {{1 \over 2},\infty } \right) \cup \{ 0\}$$
D
$$\left( { - \infty ,{{ - 1} \over {\sqrt 2 }}} \right] \cup \left[ {{1 \over {\sqrt 2 }},\infty } \right) \cup \{ 0\}$$
2
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

The value of $$\cot \left( {\sum\limits_{n = 1}^{50} {{{\tan }^{ - 1}}\left( {{1 \over {1 + n + {n^2}}}} \right)} } \right)$$ is :

A
$${{26} \over {25}}$$
B
$${{25} \over {26}}$$
C
$${{50} \over {51}}$$
D
$${{52} \over {51}}$$
3
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

$${\sin ^1}\left( {\sin {{2\pi } \over 3}} \right) + {\cos ^{ - 1}}\left( {\cos {{7\pi } \over 6}} \right) + {\tan ^{ - 1}}\left( {\tan {{3\pi } \over 4}} \right)$$ is equal to :

A
$${{11\pi } \over {12}}$$
B
$${{17\pi } \over {12}}$$
C
$${{31\pi } \over {12}}$$
D
$$-$$$${{3\pi } \over {4}}$$
4
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1

If the inverse trigonometric functions take principal values then

$${\cos ^{ - 1}}\left( {{3 \over {10}}\cos \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right) + {2 \over 5}\sin \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right)} \right)$$ is equal to :

A
0
B
$${\pi \over 4}$$
C
$${\pi \over 3}$$
D
$${\pi \over 6}$$
EXAM MAP
Medical
NEET