AP EAPCET 2025 - 21st May Morning Shift | Application of Derivatives Question 37 | Mathematics

If the function $y=g(x)$ representing the slopes of the tangents drawn to the curve $y=3 x^4-5 x^3-12 x^2+18 x+3$ is strictly increasing, then the domain of $g(x)$ is

$\left[-\frac{1}{2}, \frac{4}{3}\right]$

$\left(\frac{-1}{2}, \frac{4}{3}\right)$

$R-\left(\frac{-1}{2}, \frac{3}{4}\right)$

$R-\left[\frac{-1}{2}, \frac{4}{3}\right]$

AP EAPCET 2024 - 23th May Morning Shift

MCQ (Single Correct Answer)

-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)

$24 \sqrt{3}$

$15 \sqrt{3}$

$48 \sqrt{3}$

AP EAPCET 2024 - 23th May Morning Shift

MCQ (Single Correct Answer)

-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)

$y^k+x^k=C$

$x^{\frac{1}{k}} C=y^k$

$(x+y)^k=C$

$y=x^{\frac{1}{k}} C$

AP EAPCET 2024 - 22th May Evening Shift

MCQ (Single Correct Answer)

-0

The semi-vertical angle of a right circular cone is $45^{\circ} \%$ If the radius of the base of the cone is measured as 14 cm with an error of $\left(\frac{\sqrt{2}-1}{11}\right) \mathrm{cm}$, then the approximate error in measuring its total surface area is (in sq cm)

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