The sum of the coefficients of the plynomial $${\left( {1 + x - 3{x^2}} \right)^{2163}}$$ is ...............

The value of the expression $$\,{}^{47}{C_4} + \sum\limits_{j = 1}^5 {^{52 - j}\,{C_3}} $$ is equal to

The larger of $${99^{50}} + {100^{50}}$$ and $${101^{50}}$$ is ..............

If $$z = {\left( {{{\sqrt 3 } \over 2} + {i \over 2}} \right)^5} + {\left( {{{\sqrt 3 } \over 2} - {i \over 2}} \right)^5},$$ then