21
MCQ (Single Correct Answer)
Which of the following is the principal value branch of $\operatorname{cosec}^{-1} x$ ?
A
$\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$
B
$[0, \pi]-\left\{\frac{\pi}{2}\right\}$
C
$\left[\frac{\pi}{2}, \frac{\pi}{2}\right]$
D
$\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]-[0]$
22
MCQ (Single Correct Answer)
If $3 \tan ^{-1} x+\cot ^{-1} x=\pi$, then $x$ equals to
A
0
B
1
C
$-$1
D
$\frac{1}{2}$
23
MCQ (Single Correct Answer)
The value of $\sin ^{-1}\left[\cos \left(\frac{33 \pi}{5}\right)\right]$ is
A
$\frac{3 \pi}{5}$
B
$\frac{-7 \pi}{5}$
C
$\frac{\pi}{10}$
D
$\frac{-\pi}{10}$
24
MCQ (Single Correct Answer)
The domain of the function $\cos ^{-1}(2 x-1)$ is
A
$[0,1]$
B
$[-1,1]$
C
$(-1,1)$
D
$[0, \pi]$
25
MCQ (Single Correct Answer)
The domain of the function defined by $f(x)=\sin ^{-1} \sqrt{x-1}$ is
A
$[1,2]$
B
$[-1,1]$
C
$[0,1]$
D
None of these