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Which of the following is an example of double displacement reaction?
 i)\[AgN{O_3} + NaCl\] gives \[AgCl + NaN{O_3}\]
ii) \[Zn + 2HCl\] gives \[ZnC{l_2} + {H_2}\]
iii) \[C{H_4} + 2{O_2}\] gives \[C{O_2} + 4{H_2}O\]
iv) \[{H_2}S + C{l_2}\] gives \[2HCl + S\]

Answer
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Hint: We need to know and study the different types of reactions and analyze the given reactions to classify it into one of the types of the reactions. There exist five basic types of reactions. These are combination, decomposition, single-displacement, double-displacement, and combustion type of reactions. Analysing the reactants and products of the given reaction will help us to categorize it into the double-displacement type of reaction

Complete answer:
We know that there are five types of basic reactions in chemistry namely combination, decomposition, single-displacement, double-displacement, and combustion. We study each of these reactions.
Combination reactions: A combination reaction is the reaction in which two or more elements or compounds combine to form a new single product. A representation of such a reaction would be $A + B \to AB$. For example, the reaction: $4Al + 3{O_2} \to 2A{l_2}{O_3}$where aluminium combines with oxygen to form aluminium oxide. This reaction is represented by $A + B \to AB$. Hence this is a combination reaction.
Decomposition reactions: Types of reactions where a single compound breaks down to two or more substances are called decomposition reactions. This reaction is represented by $AB \to A + B$. For example, the reaction: $2KCl{O_3}\xrightarrow{{heat}}2KCl + 3{O_2}$where potassium chlorate is broken down into potassium chloride and oxygen on application of heat.
Single-displacement reactions: Types of reactions where a more reactive element displaces a less reactive element from a compound are called displacement reactions. This reaction is represented by $A + BC \to AC + B$. For example, the reaction $Zn + FeS{O_4} \to ZnS{O_4} + Fe$ where Zinc reacts with ferrous sulphate to form zinc sulphate and iron. Here only one element gets displaced hence called Single-displacement reactions.
Double-displacement reactions: This is also a displacement type of reaction which is represented by \[AB + CD \to AD + CB\].For example, the reaction \[2KI + Pb{(N{O_3})_2} \to 2KN{O_3} + Pb{I_2}\] where the cation from one reactant displaces or replaces the cation from another reactant to form two new compounds.
Combustion reactions: Combustion reactions are types of reactions in which a substance is burnt in the presence of oxygen to produce energy. The reaction \[{C_3}{H_8} + 5{O_2} \to 3C{O_2} + 4{H_2}O\]is a combination type of reaction.
From the given reactions, i)\[AgN{O_3} + NaCl\] gives \[AgCl + NaN{O_3}\] is a double displacement reaction since it is represented by \[AB + CD \to AD + CB\].

Note:
It is to be noted that displacement reactions occur when one reactive element replaces the less reactive element. Also, note that double-displacement reaction is sometimes also known as a salt metathesis reaction.