For the past m days, the average daily production at a company was 100 units per day.

If today’s production of 180 units changes the average to 110 units per day, what is the value of m?

Consider the following functions for non-zero positive integers, p and q.

$\rm f(p,q)=\frac{p\times p\times p\times.......\times p}{q\ terms}=p^q;\;$; f(p, 1) = p

$g(p,q)=p^{p^{p^{p^{p^{..^{..^{..^{up\ to\ q\ terms}}}}}}}}$; g(p, 1) = p

Which one of the following options is correct based on the above? 

Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet as shown.

What is the ratio of the areas of unshaded regions of case M to that of case N?

A rhombus is formed by joining the midpoints of the sides of a unit square.

What is the diameter of the largest circle that can be inscribed within the rhombus?