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

If $x=\sin 2 \theta \cos 3 \theta, y=\sin 3 \theta \cos 2 \theta$, then $\frac{d y}{d x}=$

A

$\frac{2 \cos 5 \theta+\sin 3 \theta \sin 2 \theta}{2 \cos 5 \theta-\cos 3 \theta \cos 2 \theta}$

B

$\frac{2 \cos 5 \theta-\sin 3 \theta \sin 2 \theta}{2 \cos 5 \theta+\cos 3 \theta \cos 2 \theta}$

C

$\frac{2 \cos 5 \theta+\cos 3 \theta \cos 2 \theta}{2 \cos 5 \theta-\sin 3 \theta \sin 2 \theta}$

D

$\frac{2 \cos 5 \theta-\sin 3 \theta \sin 2 \theta}{2 \cos 5 \theta-\cos 3 \theta \cos 2 \theta}$

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

If $3^x y^x=x^{3 y}$, then the value of $\frac{d y}{d x}$ at $x=1$ is

A

-3

B

3

C

$-\frac{1}{3}$

D

$\frac{1}{3}$

3
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

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

4
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

$\log _4 \mathrm{e}$

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