1
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\int_0^\pi x\left(\sin ^2(\sin x)+\cos ^2(\cos x)\right) d x=$$

A
$$\pi^2$$
B
$$\pi^2 / 2$$
C
$$2 \pi$$
D
$$\pi / 4$$
2
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$\lim _\limits{n \rightarrow \infty}\left(\frac{1}{1^5+n^5}+\frac{2^4}{2^5+n^5}+\frac{3^4}{3^5+n^5}+\ldots+\frac{n^4}{n^5+n^5}\right)=$$

A
$$\frac{1}{5} \log 3$$
B
$$\frac{1}{3} \log 5$$
C
$$\frac{1}{2} \log 5$$
D
$$\log \sqrt[5]{2}$$
3
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the solution of $$\frac{d y}{d x}-y \log _e 0.5=0, y(0)=1$$, and $$y(x) \rightarrow k$$, as $$x \rightarrow \infty$$, then $$k=$$

A
$$\infty$$
B
$$-1$$
C
1
D
0
4
AP EAPCET 2022 - 4th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

At any point $$(x, y)$$ on a curve if the length of the subnormal is $$(x-1)$$ and the curve passes through $$(1,2)$$, then the curve is a conic. A vertex of the curve is

A
$$(1,0)$$
B
$$(0,1)$$
C
$$(\sqrt{5}, 0)$$
D
$$(0, \sqrt{5})$$
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