1
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
2
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 $(-\infty, \infty)$.
3
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\sin ^{-1}\left(\frac{x}{13}\right)+\operatorname{cosec}^{-1}\left(\frac{13}{12}\right)=\frac{\pi}{2}$, then the value of

A
4
B
12
C
5
D
11
4
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\cos ^{-1} x=\alpha(0< x < 1)$ and $\sin ^{-1}\left(2 x \sqrt{1-x^2}\right)+\sec ^{-1}\left(\frac{1}{2 x^2-1}\right)=\frac{2 \pi}{3}$, then $\alpha$ is

A
$\frac{\pi}{2}$
B
$\frac{\pi}{6}$
C
$\frac{\pi}{3}$
D
$\frac{\pi}{4}$
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