1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $f(x)=\left\{\begin{array}{cc}a x^2+b x-\frac{13}{8}, & x \leq 1 \\ 3 x-3, & 1 < x \leq 2 \text { is differentiable } \\ b x^3+1, & x > 2\end{array}\right.$ $\forall x \in R$, then $a-b$ is equal to
A
$\frac{9}{8}$
B
$\frac{5}{4}$
C
$\frac{11}{8}$
D
$\frac{1}{4}$
2
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
$48 \sqrt{3}$
3
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
$y=x^{\frac{1}{k}} C$
4
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
$f(x)=e^x,[-e, e]$
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