Let $f(x) = x - 5$.
If $g(x) = [f(4h(x) + 3)]^2$ and $h(1) = 4, h'(1) = -2$, then $g'(1) =$ .....

The equation of the normal to the curve $xy + 7 = 0$ is $Ax + By + C = 0$, then

A wire 40 metre in length is to be cut into two pieces. One piece is formed into a square and the other piece into a circle. The lengths of the two pieces so that the combined area of the square and the circle is minimum, are respectively

If a spherical balloon has a variable diameter $3x + \dfrac{9}{2}$ units, then the rate of change of its volume with respect to $x$ is