1
COMEDK 2024 Morning Shift
+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
$$3 \sqrt{3} \mathrm{~cm}^2 / \mathrm{sec}$$
2
COMEDK 2024 Morning Shift
+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
$$6$$
3
COMEDK 2024 Morning Shift
+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
$$\left(-\frac{5}{2}, \frac{5}{2}\right)$$
4
COMEDK 2024 Morning Shift
+1
-0

For a given curve $$y=2 x-x^2$$, when $$x$$ increases at the rate of 3 units/sec, then how does the slope of the curve change?

A
Decreasing at 3 units/sec
B
Increasing at 3 units/sec
C
Decreasing at 6 units/sec
D
Increasing at 6 units/sec
EXAM MAP
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