Consider a string P of length $l$ that is laid out as a straight-line segment. Another string K is laid out as a semicircular arc with string P as its diameter, as represented in Figure (i). When both the strings are shortened by a length $x$ they can be re-arranged such that the shortened string K forms a full circle with the shortened string P as its diameter, as represented in Figure (ii). The value of $x / l$ is $\_\_\_\_$

How many combinations of non-null sets A, B, C are possible from the subsets of {2, 3, 5} satisfying the conditions: (i) A is a subset of B, and (ii) B is a subset of C?

Four equilateral triangles are used to form a regular closed three-dimensional object by joining along the edges. The angle between any two faces is