COMEDK 2025 Morning Shift | Application of Derivatives Question 4 | Mathematics

Oil from a conical funnel is dripping at the rate of $5 \mathrm{~cm}^3 / \mathrm{s}$. If the radius and height of the funnel are 10 cm and 20 cm respectively, then the rate at which the oil level drops when it is 5 cm from the top is

$\frac{8}{45 \pi} \mathrm{~cm} / \mathrm{s}$

$-\frac{2 \pi}{45} \mathrm{~cm} / \mathrm{s}$

$-\frac{4 \pi}{45} \mathrm{~cm} / \mathrm{s}$

$-\frac{4}{45 \pi} \mathrm{~cm} / \mathrm{s}$

COMEDK 2025 Morning Shift

MCQ (Single Correct Answer)

-0

A solid S is made from a cylinder surmounted by a hemisphere on top with both its circular faces sharing a common centre. The radius of cylinder and radius of hemisphere are $x \mathrm{~cm}$. The height of the cylinder is $(20-4 x) \mathrm{cm}$ and the volume of S is $V=\frac{1}{3} \pi y$. Find the maximum value of $y$.

480

360

320

160

COMEDK 2024 Evening Shift

MCQ (Single Correct Answer)

-0

$$ \text { The rate of change of the volume of a sphere with respect to its surface area } \mathrm{S} \text { is } $$

$$ \frac{1}{2} \sqrt{\frac{S}{\pi}} $$

$$ \sqrt{\frac{S}{\pi}} $$

$$ \frac{2}{3} \sqrt{\frac{S}{\pi}} $$

$$ \frac{1}{4} \sqrt{\frac{S}{\pi}} $$

COMEDK 2024 Evening Shift

MCQ (Single Correct Answer)

-0

The turning point of the function $$y=\frac{a x-b}{(x-1)(x-4)}$$ at the point $$P(2,-1)$$ is

neither a maximum nor a minimum

both maximum and a minimum

a minimum

a maximum

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