If G is the geometric mean of numbers 1, 2, 2², 2³,.....2^n-1, then what is the value of 1 + 2log₂G ?

If H is the harmonic mean of numbers 1, 2, 2², 2³, ......2^n-1 what is n/H equal to ? 

Let P be the median, Q be the mean and R be the mode of observations x_1, x_2, x₃, .....x_n. Let $S=\sum\limits_{i=1}^n\left(2 x_i-a\right)^2$ S takes minimum value, when a is equal to

One bag contains 3 white and 2 black balls, another bag contains 2 white and 3 black balls. Two balls are drawn from the first bag and put it into the second bag and then a ball is drawn from the second bag. What is the probability that it is white ?