1
AP EAPCET 2024 - 21th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\frac{d}{d x}\left(\frac{1+x^2+x^4}{1+x+x^2}\right)=a x+b$, then $(a, b)=$
A
$(-1,2)$
B
$(-2,1)$
C
$(2,-1)$
D
$(1,2)$
2
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The rate of change of $x^{\sin x}$ with respect to $(\sin x)^x$ is
A
$\frac{x^{\sin x}\left(\frac{\sin x}{x}+\cos x \cdot \log x\right)}{(\sin x)^x(x \cdot \cot x+\log \sin x)}$
B
$\frac{(\sin x)^x(x \cot x+\log \sin x)}{x^{\sin x}\left(\frac{\sin x}{x}+\cos x \cdot \log x\right)}$
C
$y\left(\frac{\sin x}{x}+\cos x \log x\right)$
D
$(\sin x)^x(x \cot x+\log \sin x)$
3
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\frac{\alpha x+\beta}{\gamma \alpha+\delta}$, then $2 y_1 y_3=$
A
$2 y_2{ }^3$
B
$3 y_2{ }^2$
C
$y_2{ }^2$
D
$3 y_3{ }^2$
4
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
Which one of the following is false ?
A
$\frac{d}{d x}\left[\sec ^{-1}(\cosh x)\right]=\operatorname{sech} x$
B
$\frac{d}{d x}\left[\cos ^{-1}(\operatorname{sech} x)\right]=\operatorname{sech} x$
C
$\frac{d}{d x}\left[\tan ^{-1}(\sinh x)\right]=\operatorname{sech} x$
D
$\frac{d}{d x}\left[\tan ^{-1}\left(\tan \frac{x}{2}\right)\right]=\sec x$

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