If $f(y) = 1 - (y - 1) + {(y - 1)^2} - {(y - 1)^{^3}} + ... - {(y - 1)^{17}},$ then the coefficient of $y^2$ in it is

${C_1} + 2{C_2} + 3{C_3} + 4{C_4} + .... + n{C_n} = $

The sum of the coefficients in the expansion of ${(1 + x - 3{x^2})^{3148}}$ is

The number $111......1 $ ( $ 91$ times) is

The sum, of the coefficients of the first $50$ terms in the binomial expansion of $(1-x)^{100}$, is equal to

If ${(1 + x)^n} = {C_0} + {C_1}x + {C_2}{x^2} + ... + {C_n}{x^n}$, then the value of ${C_0} + {C_2} + {C_4} + {C_6} + .....$ is