If $(10)^9+2(11)^1 (10)^8+ 3(11)^7+.....+10(11)^9=k(10)^9,$ then $k$ is equal to

Question

$\begin{array}{1 1}(A)\;\large\frac{121}{10}\\ (B)\;\large\frac{441}{100} \\(C)\;100 \\(D)\;110 \end{array} $