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1
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

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

2
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
$2 x^{2}$
3
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\sqrt{\sin (\log 2 x)+\sqrt{\sin (\log 2 x)+\sqrt{\sin (\log 2 x)+\ldots \infty,}}}$ then $\frac{d y}{d x}=$
A
$\frac{\cos (\log 2 x)}{2 x(2 y-1)}$
B
$\frac{\cos (\log 2 x)}{(2 y-1)}$
C
$\frac{\cos (\log 2 x)}{x(2 y-1)}$
D
$\frac{\sin (\log 2 x)}{x(2 y-1)}$
4
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\tan ^{-1}\left[\frac{\sin ^{3}(2 x)-3 x^{2} \sin (2 x)}{3 x \sin ^{2}(2 x)-x^{3}}\right]$, then $\frac{d y}{d x}=$
A
$\frac{6 x \cos (2 x)-3 \sin (2 x)}{x^{2}-\sin ^{2}(2 x)}$
B
$\frac{6 x \sin (2 x)-3 \cos (2 x)}{x^{2}+\sin ^{2}(2 x)}$
C
$\frac{2 x \cos (2 x)-\sin (2 x)}{x^{2}+\sin ^{2}(2 x)}$
D
$\frac{6 x \cos (2 x)-3 \sin (2 x)}{x^{2}+\sin ^{2}(2 x)}$
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