A tank in the shape of a rectangular parallelopiped has volume 27 cubic meters. This tank is filled with water such that the rate of change of level of the water is thrice the rate of change water quantity falling in the tank, then the height of the tank (in meters) is

$$ \text { Match the functions of List I with the items of List II. } $$

If the area of a circle increases at the rate of $\frac{1}{\sqrt{\pi}}$ sq. units/sec, then the rate (in units/sec) at which the perimeter of the circle changes, when perimeter is $\sqrt{\pi}$ units, is

Let $a$ be a fixed positive real number and $n$ be an arbitrary constant. For the curve $y=\frac{x^n}{a^{n-1}}$, if the length of the subnormal at any point $(\alpha, \beta)$ is proportional to $a^2$, then $n=$