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 p2 is
Explanation: Here minimum value of p can be 0 (if point chosen is (0,0), then length of position vector will be 0), and maximum value can be 5√ when point chosen is (1,2), because that is the farthest point from origin. So p can vary from 0 to 5√.
Now we know that
Since p is a uniform random variable,
So option (D) is correct.