1
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $y=(\log x)^{1 / x}+x^{\log x}$, at $x=e, \frac{d y}{d x}=$

A

$2+\frac{1}{e}$

B

$e^2+\frac{1}{2}$

C

$\frac{1}{e^2}+2$

D

$e+\frac{1}{e}$

2
AP EAPCET 2025 - 23rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $x=\sqrt{2} e^t(\sin t-\cos t)$ and $y=\sqrt{2} e^t(\sin t+\cos t)$, then $\left(\frac{d^2 y}{d x^2}\right)_{t=\frac{\pi}{4}}=$

A

$-e^{\frac{-\pi}{4}}$

B

$\sqrt{2} e^{\frac{\pi}{4}}$

C

$\sqrt{2} e^{\frac{-\pi}{4}}$

D

$e^{\frac{-\pi}{4}}$

3
AP EAPCET 2025 - 22nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $g$ is the inverse of the function $f(x)$ and $g(x)=x+\tan x$, then $f^{\prime}(x)=$

A

$1+\sec ^2 x$

B

$\frac{1}{1+\sec ^2 f(x)}$

C

$\frac{1}{1+\sec ^2 g(x)}$

D

$1+\sec ^2 f(x)$

4
AP EAPCET 2025 - 22nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\sqrt{x-x y}+\sqrt{y-x y}=1$, then $\frac{d y}{d x}=$

A

$-\sqrt{\frac{y-y^2}{x-x^2}}$

B

$-\sqrt{\frac{1-y^2}{1-x^2}}$

C

$-\sqrt{\frac{1-y}{1-x}}$

D

$-\sqrt{\frac{x-y}{x+y}}$

AP EAPCET Subjects

Browse all chapters by subject