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1
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

    If $y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\ldots \infty}}}$, then the value of $\frac{d^2 y}{d x^2}$ at the point $(\pi, 1)$ is

A
2
B
-2
C
$-\frac{1}{2}$
D
$\frac{1}{2}$
2
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
64. If $f(0)=0, f^{\prime}(0)=3$, then the derivative of $y=f(f(f(f(f(x)))))$ at $x=0$ is
A
16
B
32
C
81
D
243
3
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
$(1,2)$
4
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
$(\sin x)^x(x \cot x+\log \sin x)$
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