1
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
$$\left(-\frac{5}{2}, \frac{5}{2}\right)$$
2
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
3
COMEDK 2024 Morning Shift
+1
-0

The most economical proportion of the height of a covered box of fixed volume whose base is a rectangle with one side three times as long as the other, is

A
$$\frac{3}{2} \times$$ shorter side of base
B
Equal to shorter side of base
C
$$\frac{1}{2} \times$$ shorter side of base
D
3 times shorter side of base
4
COMEDK 2023 Morning Shift
+1
-0

The slope of the tangent to the curve, $$y=x^2-x y$$ at $$\left(1, \frac{1}{2}\right)$$ is

A
$$\frac{4}{3}$$
B
$$\frac{2}{3}$$
C
$$\frac{3}{4}$$
D
$$\frac{3}{2}$$
EXAM MAP
Medical
NEET