A.
$\frac{{\rm{d}}}{{{\rm{d}}t}}\left( {\frac{{\partial T}}{{\partial {{\dot q}_k}}}} \right) - \frac{{\partial T}}{{\partial {q_k}}} = 0$
B.
$\frac{{\rm{d}}}{{{\rm{d}}t}}\left( {\frac{{\partial T}}{{\partial {{\dot q}_k}}}} \right) - \frac{{\partial T}}{{\partial {q_k}}} = {Q_k}$
C.
$\frac{{\rm{d}}}{{{\rm{d}}t}}\left( {\frac{{\partial T}}{{\partial {{\dot q}_k}}}} \right) + \frac{{\partial T}}{{\partial {q_k}}} = {Q_k}$