1
TG EAPCET 2025 (Online) 2nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $y=\left(\sin ^{-1} x\right)^2$, then $\left(1-x^2\right) \frac{d^2 y}{d x^2}-x \frac{d y}{d x}=$

A

$\frac{1}{2}$

B

2

C

$-\frac{1}{2}$

D

4

2
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The range of the real value function $f(x)=\sin ^{-1}\left(\sqrt{x^2+x+1}\right)$ is

A
$\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$
B
$\left[0, \frac{\pi}{2}\right]$
C
$\left[\frac{\pi}{6}, \frac{\pi}{2}\right]$
D
$\left[\frac{\pi}{3}, \frac{\pi}{2}\right]$
3
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \tan ^{-1} \frac{3}{5}+\tan ^{-1} \frac{6}{41}+\tan ^{-1} \frac{9}{191}= $$

A

$\tan ^{-1} \frac{9}{10}$

B

$\tan ^{-1} \frac{18}{19}$

C

$\tan ^{-1} \frac{3}{191}$

D

$\tan ^{-1} \frac{6}{205}$

4
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $2 \tanh ^{-1} x=\sinh ^{-1}\left(\frac{4}{3}\right)$, then $\cosh ^{-1}\left(\frac{1}{x}\right)=$

A

$\log (\sqrt{2}+1)$

B

$\log (\sqrt{2}-1)$

C

$\log (2+\sqrt{3})$

D

$\log (2-\sqrt{3})$

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