If sin⁴$$\alpha $$ + 4 cos⁴$$\beta $$ + 2 = 4$$\sqrt 2 $$ sin $$\alpha $$ cos $$\beta $$; $$\alpha $$, $$\beta $$ $$ \in $$ [0, $$\pi $$],
then cos($$\alpha $$ + $$\beta $$) $$-$$ cos($$\alpha $$ $$-$$ $$\beta $$) is equal to :

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 :

Let  S_k = $${{1 + 2 + 3 + .... + k} \over k}.$$ If   $$S_1^2 + S_2^2 + .....\, + S_{10}^2 = {5 \over {12}}$$A,  then A is equal to :