Let S = {1, 2, 3, … , 100}. The number of non-empty subsets A of S such that the product of elements in A is even is :

The area (in sq. units) of the region bounded by the parabola, y = x² + 2 and the lines, y = x + 1, x = 0 and x = 3, is

If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is :

The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, y = 12 – x² such that the rectangle lies inside the parabola, is :