1
COMEDK 2024 Morning Shift
+1
-0

$$\text { The value of } \sin ^{-1}\left[\cot \left(\frac{1}{2} \tan ^{-1} \frac{1}{\sqrt{3}}+\cos ^{-1} \frac{\sqrt{12}}{4}+\sin ^{-1} \frac{1}{\sqrt{2}}\right)\right]$$ is

A
$$\frac{\pi}{6}$$
B
$$\frac{\pi}{2}$$
C
$$\frac{\pi}{4}$$
D
0
2
COMEDK 2023 Evening Shift
+1
-0

$$\text { Let } f(x)=\cos ^{-1}(3 x-1) \text {, then domain of } f(x) \text { is equal to }$$

A
$$\left[0, \frac{2}{3}\right]$$
B
$$\left(0, \frac{2}{3}\right)$$
C
$$\left(-\frac{2}{3}, \frac{2}{3}\right)$$
D
$$\left[-\frac{2}{3}, \frac{2}{3}\right]$$
3
COMEDK 2023 Evening Shift
+1
-0

$$\text { The value of } \sin ^{-1}\left[\cos \left(39 \frac{\pi}{5}\right)\right] \text { is }$$

A
$$\frac{\pi}{2}$$
B
$$\frac{3 \pi}{10}$$
C
$$\frac{3 \pi}{5}$$
D
$$\frac{-3 \pi}{10}$$
4
COMEDK 2020
+1
-0

The value of $$\sin \left[ {2{{\cos }^{ - 1}}{{\sqrt 5 } \over 3}} \right]$$ is

A
$${{2\sqrt 5 } \over 3}$$
B
$${{\sqrt 5 } \over 3}$$
C
$${{2\sqrt 5 } \over 9}$$
D
$${{4\sqrt 5 } \over 9}$$
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