1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-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 $y$.
A
480
B
360
C
320
D
160
2
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$$ \frac{1}{2} \sqrt{\frac{S}{\pi}} $$
B
$$ \sqrt{\frac{S}{\pi}} $$
C
$$ \frac{2}{3} \sqrt{\frac{S}{\pi}} $$
D
$$ \frac{1}{4} \sqrt{\frac{S}{\pi}} $$
3
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A
neither a maximum nor a minimum
B
both maximum and a minimum
C
a minimum
D
a maximum
4
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

The side of a cube is equal to the diameter of a sphere. If the side and radius increase at the same rate then the ratio of the increase of their surface area is

A
$$3: \pi$$
B
$$\pi: 6$$
C
$$2 \pi: 3$$
D
$$3: 2 \pi$$
COMEDK Subjects
EXAM MAP