A movie screen on a wall is $\mathbf{2 0}$ feet high and $\mathbf{1 0}$ feet above the floor. What is the maximum viewing angle $\boldsymbol{\theta}$ (in radians) that can be achieved by positioning yourself at the optimal distance from the wall?

A square plate is contracting at a uniform rate of $2 \mathrm{~cm}^2 / \mathrm{min}$. The rate at which the perimeter is decreasing when the side of the square is 16 cm is:

If $\mathbf{3 ~ c m} / \mathbf{s}$ is the rate at which the side of an equilateral triangle increases, then the rate of change of area, when the side is $\mathbf{1 2 ~ c m}$ is:

If the function $f(x)=x^4-31 x^2+\boldsymbol{a} x+5$ has a turning point at $x=1$, then the value of ' $\boldsymbol{a}$ ' is $\_\_\_\_$ and the function attains a $\_\_\_\_$ at $x=1$