1
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\tan ^{-1}\left(\frac{2-3 \sin x}{3-2 \sin x}\right)$, then $\frac{d y}{d x}=$
A
$\frac{(3-2 \sin x)^2}{13 \sin ^2 x-24 \sin x+13}$
B
$\frac{-5 \cos x}{13 \sin ^2 x-24 \sin x+19}$
C
$\frac{5 \sin x}{13 \sin ^2 x-24 \sin x+13}$
D
$\frac{-5 \sin x}{13 \sin ^2 x-24 \sin x+13}$
2
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $x=3\left[\sin t-\log \left(\cot \frac{t}{2}\right)\right]$ and $y=6\left[\cos t+\log \left(\operatorname{tin} \frac{t}{2}\right)\right]$ then $\frac{d y}{d x}=$
A
$\frac{2 \sin ^2 t}{1+\sin t \cos t}$
B
$\frac{2 \cos ^2 t}{1+\sin 2 t}$
C
$\frac{2 \cos ^2 t}{1+\sin t \cos t}$
D
$\frac{1+\cos g}{1+\sin a}$
3
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The length of the tangent drawn at the point $P\left(\frac{\pi}{4}\right)$ on the curve $x^{2 / 3}+y^{2 / 3}=2^{2 / 3}$ is
A
$\frac{2}{3}$
B
1
C
$\frac{4}{3}$
D
2
4
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

Assertion (A) $$\frac{d}{d x}\left(\frac{x^2 \sin x}{\log x}\right)=\frac{x^2 \sin x}{\log x}\left(\cot x+\frac{2}{x}-\frac{1}{x \log x}\right)$$

Reason (R) $$\frac{d}{d x}\left(\frac{u v}{w}\right)=\frac{u v}{w}\left[\frac{u^{\prime}}{u}+\frac{v^{\prime}}{v}+\frac{w^{\prime}}{w}\right]$$

A
A is true, R is true and R is correct explanation of A
B
A is true, R is true and R is not correct explanation of A
C
A is true, R is not correct
D
A is not correct, R is correct
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