$A$ stone thrown vertically upwards has its motion described by the equation $s = 13.8t - 4.9t^2$,where $s$ is in meters and $t$ is in seconds. The velocity at $t = 1$ second will be ...... $m/s$.

Let $x$ and $y$ be the sides of two squares such that $y = x - x^2$. The rate of change of the area of the second square with respect to the area of the first square is

The rate of change of the volume of the sphere with respect to its surface area $S$ is . . . . . . .

$A$ spherical iron ball of radius $10 \text{ cm}$ is coated with a layer of ice of uniform thickness that melts at a rate of $50 \text{ cm}^3/\text{min}$. When the thickness of ice is $5 \text{ cm}$, the rate at which the thickness of ice decreases is...

$A$ particle moves along the curve $y = x^{3/2}$ in the first quadrant in such a way that its distance from the origin increases at the rate of $11$ units per second. The value of $\frac{dx}{dt}$ when $x = 3$ is

$A$ triangle has two fixed vertices $A(a, 0)$ and $B(0, b)$. Let its third vertex $C$ move along the line $x = y$. If $s$ is the area of triangle $ABC$, then $\frac{ds}{dx} =$