The least value of ' $a$ ' such that the function $x^2+a x+1$ is increasing on $[1,2]$ is

A spherical snowball is melting such that its volume is decreasing at the rate of $1 \mathrm{~cm}^3 / \mathrm{min}$. The rate at which the diameter is decreasing when the diameter is 10 cm is

The curve $a x^3+b x^2+c x+d$ has a point of minima at $x=1$, then

Oil from a conical funnel is dripping at the rate of $5 \mathrm{~cm}^3 / \mathrm{s}$. If the radius and height of the funnel are 10 cm and 20 cm respectively, then the rate at which the oil level drops when it is 5 cm from the top is