1
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

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

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

If $\left(x^2-3 x+2\right)^{\frac{y}{x^{2-1}}}=x+2$, then $\left(\frac{d y}{d x}\right)_{x=0}=$

A

2

B

-2

C

1

D

-1

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

If $x=\frac{t^2}{1+t^5}, y=\frac{2 t^3}{1+t^5}$ and $t \neq-1$ is a perimeter, then $\frac{d y}{d x}=$

A

$\frac{2\left(3+2 t^5\right)}{\left(2-3 t^5\right)}$

B

$\frac{2 t\left(3-2 t^5\right)}{\left(2-3 t^5\right)}$

C

$\frac{2 t\left(3-2 t^5\right)}{\left(2+3 t^5\right)}$

D

$\frac{2\left(3+2 t^5\right)}{\left(2+3 t^5\right)}$

4
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
A function $f: R \rightarrow R$ is such that $y f(x+y)+\cos m x y=1+y f(x)$. If $m=2$, then $f^{\prime}(x)=$
A
$-2 \sin 2 x y$
B
$4 x$
C
$\frac{2 \sin 2 x y}{y}$
D
$2 x^{2}$

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