1
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
$\sqrt{5}-1$
2
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
$\sqrt{2}$
3
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right)$ at $x=\frac{1}{5}$ where $0 \leq \cos ^{-1} x \leq \pi$ and $-\frac{\pi}{2} \leq \sin ^{-1} x \leq \frac{\pi}{2}$, is

A
$\frac{\sqrt{6}}{5}$
B
$-\frac{\sqrt{6}}{5}$
C
$\frac{2 \sqrt{6}}{5}$
D
$-\frac{2 \sqrt{6}}{5}$
4
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Considering only the principal values of inverse function, the set

$$A=\left\{x \geq 0 / \tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\frac{\pi}{4}\right\}$$

A
is an empty set.
B
is a singleton set.
C
contains more than two elements.
D
contains two elements.
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