Answer :
$$ (a) \;\;\; 2KBr(aq) + BaI_{2}(aq) $$
$$ \downarrow$$
$$ \;\;\; 2KI(aq) + BaBr_{2} $$
It is a Double Decomposition Reaction.
This is a type of chemical change in which two compounds in a solution react to form two new compounds by mutual exchange of radicals.It is also called double displacement reaction.
$$(b) ZnCO_{3}(s) \rightarrow ZnO(s) + CO_{2}(g) $$
It is Decomposition reaction.
The chemical reaction in which a compound splits into two or more simpler substances (elements or compounds) is called decomposition reaction.
$$(c) H_{2}(g) + Cl_{2}(g) \rightarrow 2HCl $$
It is a Direct Combination reaction.
A reaction in which two or more substances combine together to form a single substance is called a combination reaction or synthesis.
$$(d) \;\;\; Mg(s) + 2HCl(aq) $$
$$ \downarrow$$
$$ \;\;\; MgCl_{2} (aq) + H_{2}(g) $$
It is a Displacement reaction.
It is a chemical change in which a more active element displaces a less active element from its salt solution.