1
TG EAPCET 2025 (Online) 3rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

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

A

$\frac{2 x y}{\left(1+x^2\right)^2}$

B

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

C

$\frac{2(x y)}{1-x^2}$

D

$-\frac{2(x+y)}{1-x^2}$

2
TG EAPCET 2025 (Online) 3rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $f(x)=\log _{\left(x^2-2 x+1\right)}\left(x^2-3 x+2\right), x \in R-[1,2]$ and $x \neq 0$, then $f^{\prime}(3)=$

A

1

B

0

C

$\log _e 4$

D

$\log _4 \mathrm{e}$

3
TG EAPCET 2025 (Online) 2nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\frac{d}{d x}\left\{\left(\frac{x-1}{x-\sqrt{x}}\right) e^{2 x+1}\right\}=\frac{x-1}{x-\sqrt{x}} e^{2 x+1} f(x)$, then $f(4)=$

A

0

B

1

C

$\frac{35}{24}$

D

$\frac{47}{24}$

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

If $y=f(\cosh x)$ and $f^{\prime}(x)=\log \left(x+\sqrt{x^2-1}\right)$, then $\frac{d^2 y}{d x^2}=$

A

$\sinh x+x \cosh x$

B

$x \sinh x$

C

$\log \left(x+\sqrt{x^2+1}\right)$

D

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

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