How many pairs of sets (S,T) are possible among the subsets of 1, 2, 3, 4, 5, 6 that satisfy the condition that S is a subset of T?
An opaque pyramid (shown below), with a square base and isosceles faces, is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The pyramid can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT possible?
The symbols O, *, \(\Delta\), and \(\square\) are to be filled, one in each box, as shown below. The rules for filling in the four symbols are as follows. 1) Every row and every column must contain each of the four symbols. 2) Every 2x2 square delineated by bold lines must contain each of the four symbols. Which symbol will occupy the box marked with ‘?’ in the partially filled figure?
A certain country has 504 universities and 25951 colleges. These are categorised into Grades I, II, and III as shown in the given pie charts. What is the percentage, correct to one decimal place, of higher education institutions (colleges and universities) that fall into Grade III?