The sum $$\sum\limits_{k = 1}^{20} {k{1 \over {{2^k}}}} $$ is equal to

The sum of all natural numbers 'n' such that 100 < n < 200 and H.C.F. (91, n) > 1 is :

If   ⁿC₄, ⁿC₅ and ⁿC₆ are in A.P., then n can be :

If the sum of the first 15 terms of the series $${\left( {{3 \over 4}} \right)^3} + {\left( {1{1 \over 2}} \right)^3} + {\left( {2{1 \over 4}} \right)^3} + {3^3} + {\left( {3{3 \over 4}} \right)^3} + ....$$ is equal to 225 k, then k is equal to :