1
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
2
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
$$3 \sqrt{3} \mathrm{~cm}^2 / \mathrm{sec}$$
3
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
$$6$$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { The point on the curve } x^2=x y \text { which is closest to }(0,5) \text { is } $$

A
$$ \left(\frac{5}{2}, \frac{5}{2}\right) $$
B
(0, 5)
C
(0, 2)
D
$$ \left(-\frac{5}{2}, \frac{5}{2}\right) $$
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