1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $0 < x < \frac{1}{2}$ and $\alpha=\sin ^{-1} x+\cos ^{-1}\left(\frac{x}{2}+\frac{\sqrt{3-3 x^2}}{2}\right)$, then $\tan \alpha+\cot \alpha$ is equal to

A
$\frac{4}{\sqrt{3}}$
B
$4 \sqrt{3}$
C
$\frac{4 x}{1-x^2}$
D
$x \sqrt{1-x^2}$
2
AP EAPCET 2024 - 22th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\cot \left(\sum\limits_{n=1}^{50} \tan ^{-1}\left(\frac{1}{1+n+n^2}\right)\right)$ is equal to
A
$\frac{26}{25}$
B
$\frac{25}{26}$
C
$\frac{50}{51}$
D
$\frac{52}{51}$
3
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The value of $x$ such that $\sin \left(2 \tan ^{-1} \frac{3}{4}\right)=\cos \left(2 \tan ^{-1} x)\right.$
A
7
B
$\frac{3}{7}$
C
$\frac{1}{7}$
D
$\frac{4}{7}$
4
AP EAPCET 2024 - 21th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The range of the real valued function $f(x)=\sin ^{-1}\left(\frac{1+x^2}{2 x}\right)+\cos ^{-1}\left(\frac{2 x}{1+x^2}\right)$ is
A
$\left\{\frac{\pi}{2}\right\}$
B
$R$
C
$Q$
D
$\left\{-\frac{\pi}{2}, \frac{\pi}{2}\right\}$
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