1
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

The set of all values of k for which

$${({\tan ^{ - 1}}x)^3} + {({\cot ^{ - 1}}x)^3} = k{\pi ^3},\,x \in R$$, is the interval :

A
$$\left[ {{1 \over {32}},{7 \over 8}} \right)$$
B
$$\left( {{1 \over {24}},{{13} \over {16}}} \right)$$
C
$$\left[ {{1 \over {48}},{{13} \over {16}}} \right]$$
D
$$\left[ {{1 \over {32}},{9 \over 8}} \right)$$
2
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

The domain of the function

$$f(x) = {{{{\cos }^{ - 1}}\left( {{{{x^2} - 5x + 6} \over {{x^2} - 9}}} \right)} \over {{{\log }_e}({x^2} - 3x + 2)}}$$ is :

A
$$( - \infty ,1) \cup (2,\infty )$$
B
$$(2,\infty )$$
C
$$\left[ { - {1 \over 2},1} \right) \cup (2,\infty )$$
D
$$\left[ { - {1 \over 2},1} \right) \cup (2,\infty ) - \left\{ 3,{{{3 + \sqrt 5 } \over 2},{{3 - \sqrt 5 } \over 2}} \right\}$$
3
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
$${\cos ^{ - 1}}(\cos ( - 5)) + {\sin ^{ - 1}}(\sin (6)) - {\tan ^{ - 1}}(\tan (12))$$ is equal to :

(The inverse trigonometric functions take the principal values)
A
3$$\pi$$ $$-$$ 11
B
4$$\pi$$ $$-$$ 9
C
4$$\pi$$ $$-$$ 11
D
3$$\pi$$ + 1
4
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
The domain of the function

$$f(x) = {\sin ^{ - 1}}\left( {{{3{x^2} + x - 1} \over {{{(x - 1)}^2}}}} \right) + {\cos ^{ - 1}}\left( {{{x - 1} \over {x + 1}}} \right)$$ is :
A
$$\left[ {0,{1 \over 4}} \right]$$
B
$$[ - 2,0] \cup \left[ {{1 \over 4},{1 \over 2}} \right]$$
C
$$\left[ {{1 \over 4},{1 \over 2}} \right] \cup \{ 0\}$$
D
$$\left[ {0,{1 \over 2}} \right]$$
EXAM MAP
Medical
NEET