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 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } f(x)=\frac{a \sin x+b \cos x}{c \sin x+d \cos x} \text { is decreasing for all } x \text {, then } $$

A
$$ a b-c d<0 $$
B
$$ a d-b c<0 $$
C
$$ a b-c d>0 $$
D
$$ a d-b c>0 $$
4
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { The function } y=\tan x-x \text { is } $$

A
$$ \text { decreasing in }\left(0, \frac{\pi}{4}\right) \text { and increasing in }\left(\frac{\pi}{4}, \frac{\pi}{2}\right) $$
B
$$ \text { a decreasing function in }\left(0, \frac{\pi}{2}\right) $$
C
$$ \text { an increasing function in }\left(0, \frac{\pi}{2}\right) $$
D
$$ \text { increasing in }\left(0, \frac{\pi}{4}\right) \text { and decreasing in }\left(\frac{\pi}{4}, \frac{\pi}{2}\right) $$
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