The remainder when $$(2021)^{2022}+(2022)^{2021}$$ is divided by 7 is

$$\sum\limits_{\matrix{ {i,j = 0} \cr {i \ne j} \cr } }^n {{}^n{C_i}\,{}^n{C_j}} $$ is equal to

The remainder when $$(11)^{1011}+(1011)^{11}$$ is divided by 9 is

For two positive real numbers a and b such that $${1 \over {{a^2}}} + {1 \over {{b^3}}} = 4$$, then minimum value of the constant term in the expansion of $${\left( {a{x^{{1 \over 8}}} + b{x^{ - {1 \over {12}}}}} \right)^{10}}$$ is :