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# The value of $13C_2+13C_3+13C_4+....13C_{13}$ is

$\begin{array}{1 1}(A)\;2^{13}-13\\(B)\;2^{13}-14\\(C)\;\text{an odd No. }\neq 2^{13}-12\\(D)\;\text{an even No. }\neq 2^{13}-14\end{array}$

$13C_2+13C_3+13C_4+....13C_{13}$
$\Rightarrow (13C_0+13C_1+.......+13C_{15})-13C_0-13C_1$
$\Rightarrow 2^{13}-1-13$
$\Rightarrow 2^{13}-14$
Hence (B) is the correct answer.