The following is the incomplete operation table of a 4-element group. The last row of the table is

Two n bit binary stings, S1 and, are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings different) is equal to d is

An examination paper has 150 multiple-choice questions of one mark each, with each question having four choices. Each incorrect answer fetches-0.25 mark. Suppose 1000 students choose all their answers randomly with uniform probability. The sum total of the expected marks obtained all these students is

A point is randomly selected with uniform probability in the X-Y plane within the rectangle with corners at
(0, 0), (1, 0), (1, 2) and (0, 2). If p is the length of the position vector of the point, the expected value of $${p^2}$$ is