Let's analyze each reaction in List - II and match it with the type of reaction in List - I.
Reaction i) AgNO$_3$ + CaCl$_2$ $\rightarrow$ AgCl + Ca(NO$_3$)$_2$
This is a double displacement reaction (also called metathesis). Two ionic compounds exchange ions to form two new compounds. Specifically, AgCl often precipitates.
This is a type of displacement reaction where ions are displaced.
Balanced: $2\text{AgNO}_3\text{(aq)} + \text{CaCl}_2\text{(aq)} \rightarrow 2\text{AgCl(s)} + \text{Ca(NO}_3\text{)}_2\text{(aq)}$.
This matches D Displacement reaction. So, D-(i).
Reaction ii) Cl$_2$ $\rightarrow$ Cl$^-$ + ClO$_3^-$
In this reaction, elemental chlorine (Cl$_2$, oxidation state 0) is converted into chloride ion (Cl$^-$, oxidation state -1) and chlorate ion (ClO$_3^-$, oxidation state of Cl is +5).
Chlorine is simultaneously oxidized (0 to +5) and reduced (0 to -1). This is a disproportionation reaction.
This reaction usually occurs in basic medium: $3\text{Cl}_2 + 6\text{OH}^- \rightarrow 5\text{Cl}^- + \text{ClO}_3^- + 3\text{H}_2\text{O}$.
This matches C Disproportionation reaction. So, C-(ii).
Reaction iii) Mg + N$_2$ $\rightarrow$ Mg$_3$N$_2$
Two elements, magnesium (Mg) and nitrogen (N$_2$), combine to form a single compound, magnesium nitride (Mg$_3$N$_2$).
This is a combination reaction (also called synthesis reaction).
Balanced: $3\text{Mg} + \text{N}_2 \rightarrow \text{Mg}_3\text{N}_2$.
This matches A Combination reaction. So, A-(iii).
Reaction iv) KClO$_3$ $\xrightarrow{\Delta$ KCl + O$_2$}
A single compound, potassium chlorate (KClO$_3$), breaks down into simpler substances, potassium chloride (KCl) and oxygen (O$_2$), upon heating.
This is a decomposition reaction.
Balanced: $2\text{KClO}_3 \xrightarrow{\Delta} 2\text{KCl} + 3\text{O}_2$.
This matches B Decomposition reaction. So, B-(iv).
Summarizing the matches:
A - (iii)
B - (iv)
C - (ii)
D - (i)
This set of matches corresponds to option (d).
\[ \boxed{\text{A-(iii); B-(iv); C-(ii); D-(i)}} \]