1
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$2 \pi-\left(\sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{16}{65}\right)$ is equal to

A
$\frac{\pi}{2}$
B
$\frac{5 \pi}{4}$
C
$\frac{7 \pi}{4}$
D
$\frac{3 \pi}{2}$
2
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

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

A
1
B
2
C
3
D
4
3
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\sin ^{-1}\left(\frac{\log x^2}{1+(\log x)^2}\right)$, then $\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)_{\mathrm{at ~} x=1}=$

A
$2$
B
$\frac{1}{2}$
C
$\frac{2}{3}$
D
$-2$
4
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\tan ^{-1}\left\{\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right\}+\frac{1}{2} \cos ^{-1} x$ is

A
$\frac{\pi}{2}$
B
$\frac{\pi}{4}$
C
0
D
$\frac{\pi}{3}$
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