# The value of $^nC_0.^{2n}C_r$ - $^nC_1^{2-2}C_r$ + $^nC_2.^{2n-4}C_r$ - ...., if $r \lt n$ is
$\begin{array}{1 1} (A) 2^{2n-r}.^nC_{r-n}\\ (B) 2^{2n-r+2}.^nC_{r-n+1}\\ (C) 2^{2n-r}.^nC_{r} \\ (D) 0 \end{array}$