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

If $y=\sqrt{\frac{x^4 \sqrt{3 x-5}}{\left(x^2-3\right)(2 x-3)}}$, then $\left(\frac{d y}{d x}\right)_{x=2}=$

A

5

B

0

C

1

D

-5

2
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $x^2+y^2+\sin y=4$, then the value of $\frac{d^2 y}{d x^2}$ at $x=-2$ is

A

-30

B

-34

C

-32

D

-18

3
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A

$\frac{\sinh x\left(2 y^2+2 \cosh x+1\right)}{4 y\left(y^2+\cosh x\right)}$

B

$\frac{\sinh x\left(2 y^2-2 \cosh x-1\right)}{4 y\left(y^2-\cosh x\right)}$

C

$\frac{\sinh x(1-2 \sqrt{\cosh x})}{4 y \sqrt{\cosh x}}$

D

$\frac{\sinh x(1+2 \sqrt{\cosh x})}{4 y \sqrt{\cosh x})}$

4
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\tan ^{-1} \sqrt{x^2-1}+\sinh ^{-1} \sqrt{x^2-1}, x>1$, then $\frac{d y}{d x}=$
A

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

B

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

C

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

D

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

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