The number of terms in the expansion of $${(1 + 5\sqrt {2x} )^9} + {(1 - 5\sqrt {2x} )^9}$$ is

If the sum of the coefficients in the expansion of (x + y)ⁿ is 1024, then the value of the greatest coefficient in the expansion is

$${{{C_1}} \over {{C_0}}} + 2{{{C_2}} \over {{C_1}}} + 3{{{C_3}} \over {{C_2}}} + 4{{{C_4}} \over {{C_3}}} + ....20{{{C_{20}}} \over {{C_{19}}}} = $$

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