Balance the following chemical equations and identify the type of chemical reaction.
$(a)$ $TiCl_4(l) + Mg(s) \to Ti(s) + MgCl_2(s)$
$(b)$ $CaO(s) + SiO_2(s) \to CaSiO_3(s)$
$(c)$ $H_2O_2(l) \xrightarrow{UV} H_2O(l) + O_2(g)$

(N/A) Balanced equation: $TiCl_4(l) + 2Mg(s) \to Ti(s) + 2MgCl_2(s)$. This is a displacement reaction because $Mg$ displaces $Ti$ from its chloride.
$(b)$ Balanced equation: $CaO(s) + SiO_2(s) \to CaSiO_3(s)$. This is a combination reaction because two reactants combine to form a single product.
$(c)$ Balanced equation: $2H_2O_2(l) \to 2H_2O(l) + O_2(g)$. This is a decomposition reaction because a single reactant breaks down into simpler products.