1
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
A point is moving on the curve $y=x^3-3 x^2+2 x-1$ and the $y$-coordinate of the point is increasing at the rate d 6 units per second. When the point is at $(2,-1)$, the rate of change of $x$-coordinate of the point is
A
3
B
$\frac{1}{2}$
C
$-\frac{1}{2}$
D
-3
2
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
3
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The set of all real values of a such that the real valued function $f(x)=x^3+2 a x^2+3(a+1) x+5$ is strictly increasing in its entire domain is
A
$\left(-\infty-\frac{3}{4}\right) \cup(3, \infty)$
B
$\left(-\frac{3}{4}, 3\right)$
C
( 13
D
$(-\infty, 1) \cup(3-=)$
4
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{1}{x^5 \sqrt[3]{x^3+1}} d x=$
A
$\frac{4}{\sqrt{x^5+1}}+c$
B
$4 x^4\left(x^5+1\right)^{4 / 3}+0$
C
$=\frac{\left(x^3+1\right)^{4 / 3}}{4 x^4}+c$
D
$-\frac{\left(x^5+1\right)^{45}}{4 x^5}+c$
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