1
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $a^2+b^2+c^2=r^2$, then the value of $\tan ^{-1}\left(\frac{\mathrm{ab}}{\mathrm{cr}}\right)+\tan ^{-1}\left(\frac{\mathrm{bc}}{\mathrm{ar}}\right)+\tan ^{-1}\left(\frac{\mathrm{ca}}{\mathrm{br}}\right)=$

A
$\frac{\pi}{2}$
B
$\frac{\pi}{3}$
C
$\frac{\pi}{4}$
D
$\frac{\pi}{6}$
2
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$\frac{1}{5}$
B
1
C
0
D
$-\frac{1}{5}$
3
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
The sum to infinite terms of the series $\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{2}{9}\right)+\ldots \ldots . .+\tan ^{-1}\left(\frac{2^{n-1}}{1+2^{2 n-1}}\right)+\ldots \ldots$. is
A
$\frac{\pi}{4}$
B
$\frac{\pi}{2}$
C
$\frac{\pi}{6}$
D
$\frac{\pi}{3}$
4
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If $4 \sin ^{-1} x+\cos ^{-1} x=\pi$ then $x=$
A
$\frac{\sqrt{3}}{2}$
B
$0$
C
$\frac{1}{2}$
D
$\frac{1}{\sqrt{2}}$
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