Balance the following chemical equations
(a) \[ \mathrm{C_6H_{12}O_6 + 6\,O_2 \;\longrightarrow\; 6\,CO_2 + 6\,H_2O} \]
\[ \mathrm{CaCO_3 + 2\,HCl \;\longrightarrow\; CaCl_2 + H_2O + CO_2} \]
\[ \mathrm{N_2 + 3\,H_2 \;\longrightarrow\; 2\,NH_3} \]
\[ \mathrm{MnO_2 + 4\,HCl \;\longrightarrow\; MnCl_2 + Cl_2 + 2\,H_2O} \]