1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The curve $a x^3+b x^2+c x+d$ has a point of minima at $x=1$, then
A
$3 a+b<0$
B
$3 a+b>0$
C
$3 a+b=0$
D
$a+3 b>0$
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
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
A
$\frac{8}{45 \pi} \mathrm{~cm} / \mathrm{s}$
B
$-\frac{2 \pi}{45} \mathrm{~cm} / \mathrm{s}$
C
$-\frac{4 \pi}{45} \mathrm{~cm} / \mathrm{s}$
D
$-\frac{4}{45 \pi} \mathrm{~cm} / \mathrm{s}$
3
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
4
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
$$ \frac{1}{4} \sqrt{\frac{S}{\pi}} $$
COMEDK Subjects
EXAM MAP