The gaseous mixture commonly used for welding metals is acetylene (C$_2$H$_2$) and oxygen (O$_2$). This mixture is used in oxy-acetylene welding, where acetylene burns in the presence of oxygen to produce a high-temperature flame (around 3,500°C), which is sufficient to melt and join metals. Among the options, C$_2$H$_4$ (ethylene) and C$_2$H$_{10}$ (butane) are not typically used for welding, and N$_2$ (nitrogen) is not a suitable gas for creating the necessary flame.
Thus, the correct answer is C$_2$H$_2$, O$_2$.