1
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\tan ^{-1}\left(\frac{x+1}{x-1}\right)+\tan ^{-1}\left(\frac{x-1}{x}\right)=\tan ^{-1}(-7)$, then $x$ is equal to

A
$-$1
B
1
C
2
D
4
2
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\tan ^{-1}(-\sqrt{3})-\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)+\cos ^{-1}\left(\frac{-1}{2}\right)$ is

A
$\frac{-\pi}{4}$
B
$\frac{4 \pi}{3}$
C
$\frac{\pi}{12}$
D
$\frac{7 \pi}{12}$
3
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\sin ^{-1}\left(\frac{x}{5}\right)+\operatorname{cosec}^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2}$, then the value of $x$ is

A
4
B
5
C
1
D
3
4
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let the function $g:(-\infty, \infty) \rightarrow\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ be given by $g(u)=2 \tan ^{-1}\left(e^u\right)-\frac{\pi}{2}$. Then $g$ is

A
even and is strictly increasing in $(0, \infty)$.
B
odd and is strictly decreasing in $(-\infty, \infty)$.
C
odd and is strictly increasing in $(-\infty, \infty)$.
D
neither even nor odd, but is strictly increasing in $(-\infty, \infty)$.
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