1
AP EAPCET 2025 - 26th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $y=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$ and $\left(\frac{d^2 y}{d x^2}\right)_{x=2}=k$, then $25 k=$

A

$(-3)^2$

B

$(-2)^3$

C

3

D

$(-2)^5$

2
AP EAPCET 2025 - 26th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $f(x)=\sec ^{-1}\left(\frac{1}{2 x^2-1}\right)$ and $g(x)=\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$, then the derivative of $f(x)$ with respect to $g(x)$ is

A

$\frac{1+x^2}{4 \sqrt{1-x^2}}$

B

$\frac{\left(1-x^2\right)}{4 \sqrt{1+x^2}}$

C

$-\frac{4\left(1-x^2\right)}{\sqrt{1+x^2}}$

D

$-\frac{4\left(1+x^2\right)}{\sqrt{1-x^2}}$

3
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $A=\left\{x \in R / \sin ^{-1}\left(\sqrt{x^2+x+1}\right) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\right\}$ and $B=\left\{y \in R / y=\sin ^{-1}\left(\sqrt{x^2+x+1}\right), x \in A\right\}$, then
A

$A \cap B \neq \phi$

B

$A \cap B^C=[0,1]$

C

$A^C \cap B=\left[\frac{\pi}{3}, \frac{\pi}{2}\right]$

D

$A \cup B=R-\left\{[-1,0] \cup\left[\frac{\pi}{3}, \frac{\pi}{2}\right]\right\}$

4
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The domain of the function, $f(x)=\sqrt{\log _e\left(\frac{1}{x^2-4 x+4}\right)}+\sin ^{-1}\left(x^2-2\right)$ is

A

$[1,3]$

B

$[1,3)$

C

$[1, \sqrt{3}]$

D

$[1, \sqrt{3})$

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