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

What is the nature of the function $$f(x)=x^3-3 x^2+4 x$$ on real numbers?

A
Strictly decreasing
B
Decreasing
C
Increasing
D
Constant
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