1
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The number of real solutions of $\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^2+x+1}=\frac{\pi}{2}$ is

A
one
B
zero
C
two
D
infinite
2
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$\tan \left(\frac{\pi}{4}+\frac{1}{2} \cos ^{-1}\left(\frac{\mathrm{a}}{\mathrm{b}}\right)\right)+\tan \left(\frac{\pi}{4}-\frac{1}{2} \cos ^{-1}\left(\frac{\mathrm{a}}{\mathrm{b}}\right)\right)$ is

A
$\frac{2 a}{b}$
B
$\frac{2 \mathrm{~b}}{\mathrm{a}}$
C
$\frac{\mathrm{a}}{\mathrm{b}}$
D
$\frac{\mathrm{b}}{\mathrm{a}}$
3
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\tan \left(2 \tan ^{-1}\left(\frac{\sqrt{5}-1}{2}\right)\right)$ is

A
$2 \sqrt{5}$
B
4
C
2
D
$\sqrt{5}-1$
4
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $f(\theta)=\sin \left(\tan ^{-1}\left(\frac{\sin \theta}{\sqrt{\cos 2 \theta}}\right)\right)$, where $\frac{-\pi}{4}<\theta<\frac{\pi}{4}$, then the value of $\frac{d}{d(\tan \theta)}(f(\theta))$ is

A
$-1$
B
$1$
C
$\frac{1}{\sqrt{2}}$
D
$\sqrt{2}$
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