c
According to Avogadro's hypothesis, Volume of a gas \((V) \propto\) number of moles \((n)\) Therefore, the ratio of the volumes of gases can be determined in terms of their moles. The ratio of volumes of \(\mathrm{H}_{2}: \mathrm{O}_{2}:\) methane \(\left(\mathrm{CH}_{4}\right)\) is given by

\(v_{H_{2}}: v_{O_{2}}: v_{C H_{2}}=n_{H_{12}}: n_{O_{2}}: n_{C H_{4}}\)

\(\Rightarrow v_{H_{2}}: v_{O_{2}}: v_{C H_{4}}=\frac{m_{H_{2}}}{M_{H_{2}}}: \frac{m_{O_{2}}}{M_{O_{2}}}: \frac{m_{C H_{4}}}{M_{C H_{4}}}\)

But \(m_{H_{2}}=m_{O_{2}}=m_{C H_{4}}=m\left[\therefore n=\frac{\text { mass }}{\text { molar massd }}\right]\)

Thus, \(\quad v_{H_{2}}: v_{O_{2}}: v_{C H_{4}}=\frac{m}{2}=\frac{m}{1}=\frac{m}{16}=16: 1: 2\)