1
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1

$${\tan ^{ - 1}}\left( {{{1 + \sqrt 3 } \over {3 + \sqrt 3 }}} \right) + {\sec ^{ - 1}}\left( {\sqrt {{{8 + 4\sqrt 3 } \over {6 + 3\sqrt 3 }}} } \right)$$ is equal to :

A
$${\pi \over 2}$$
B
$${\pi \over 3}$$
C
$${\pi \over 6}$$
D
$${\pi \over 4}$$
2
JEE Main 2022 (Online) 29th July Evening Shift
+4
-1

The domain of the function $$f(x)=\sin ^{-1}\left(\frac{x^{2}-3 x+2}{x^{2}+2 x+7}\right)$$ is :

A
$$[1, \infty)$$
B
$$[-1,2]$$
C
$$[-1, \infty)$$
D
$$(-\infty, 2]$$
3
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1

The sum of the absolute maximum and absolute minimum values of the function $$f(x)=\tan ^{-1}(\sin x-\cos x)$$ in the interval $$[0, \pi]$$ is :

A
0
B
$$\tan ^{-1}\left(\frac{1}{\sqrt{2}}\right)-\frac{\pi}{4}$$
C
$$\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)-\frac{\pi}{4}$$
D
$$\frac{-\pi}{12}$$
4
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

Considering only the principal values of the inverse trigonometric functions, the domain of the function $$f(x)=\cos ^{-1}\left(\frac{x^{2}-4 x+2}{x^{2}+3}\right)$$ is :

A
$$\left(-\infty, \frac{1}{4}\right]$$
B
$$\left[-\frac{1}{4}, \infty\right)$$
C
$$(-1 / 3, \infty)$$
D
$$\left(-\infty, \frac{1}{3}\right]$$
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