1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$A$ is a point on the circle with radius 8 and centre at $O$. A particle $P$ is moving on the circumference of the circle starting from $A . M$ is the foot of the perpendicular from $P$ on $O A$ and $\angle P O M=\theta$. When $O M$ $=4$ and $\frac{d \theta}{d t}=6$ radians $/ \mathrm{sec}$, then the rate of change of $P M$ is (in units/sec)
A
$24 \sqrt{3}$
B
24
C
$15 \sqrt{3}$
D
$48 \sqrt{3}$
2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the length of the sub-tangent at any $P$ on a curve is proportional to the abscissa of the point $P$, then the equation of that curve is ( $C$ is an arbitrary constant)
A
$y^k+x^k=C$
B
$x^{\frac{1}{k}} C=y^k$
C
$(x+y)^k=C$
D
$y=x^{\frac{1}{k}} C$
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
In each of the following options, a function and an interval are given. Choose the option containing the function and the interval for which Lagrange's mean value theorem is not applicable
A
$f(x)=|x|, 1 \leq x \leq 5$
B
$f(x)=[x],[\sqrt{2}, \sqrt{3}]$
C
$f(x)=\log \left(x^2-1\right),\left[\frac{1}{e}, e-2\right]$
D
$f(x)=e^x,[-e, e]$
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The function $f(x)=\left\{\begin{array}{cc}\frac{x-|x|}{x}, & x \neq 0 \\ 2, & x=0\end{array}\right.$
A
is continuous, $\forall x \in R$
B
has maximum value 2
C
has neither minimum nor maximum
D
has minimum value 2
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