A given quantity of metal is to be case into a half cylinder (i.e. with a rectangular base and semicircular ends). If the total surface area is to be minimum, then the ratio of the height of the half cylinder to the diameter of the semicircular ends is

The minimum distance from the point (4, 2) to y² = 8x is equal to

What is the minimum value of a²x + b²y where xy = c² ?

For the following three (03) items:
Let $y=f(x)=\frac{x\sin ^{-1}x}{\sqrt{1-x^{2}}}+\ln \sqrt{1-x^{2}}.$

What is the slope of the tangent to the curve y = f(x) at x = 0.5