1
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
2
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
$\frac{\pi}{4}$
3
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x$, then the value of $\sin x$ is

A
$\cot ^2\left(\frac{\alpha}{2}\right)$
B
$\tan ^2\left(\frac{\alpha}{2}\right)$
C
$\tan \alpha$
D
$\cot \left(\frac{\alpha}{2}\right)$
4
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $0< x<1$, then $\sqrt{1+x^2}\left[\left\{x \cos \left(\cot ^{-1} x\right)+\sin \left(\cot ^{-1} x\right)\right\}^2-1\right]^{\frac{1}{2}}$ is equal to

A
$x^2 \sqrt{1+x^2}$
B
$x$
C
$x \sqrt{1+x^2}$
D
$\sqrt{1+x^2}$
MHT CET Subjects
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