1
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
$$3: 2 \pi$$
2
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
3
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The side of an equilateral triangle expands at the rate of $$\sqrt{3} \mathrm{~cm} / \mathrm{sec}$$. When the side is $$12 \mathrm{~cm}$$, the rate of increase of its area is

A
$$18 \mathrm{~cm}^2 / \mathrm{sec}$$
B
$$12 \mathrm{~cm}^2 / \mathrm{sec}$$
C
$$10 \mathrm{~cm}^2 / \mathrm{sec}$$
D
$$3 \sqrt{3} \mathrm{~cm}^2 / \mathrm{sec}$$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$f(x)=2 x^3+9 x^2+\lambda x+20$$ is a decreasing function of $$x$$ in the largest possible interval $$(-2,-1)$$, then $$\lambda$$ is equal to

A
$$-12$$
B
$$-6$$
C
$$12$$
D
$$6$$
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