Write the balanced chemical equations for the following reactions and identify the type of reaction in each case.
$(a)$ Thermit reaction,iron $(III)$ oxide reacts with aluminium and gives molten iron and aluminium oxide.
$(b)$ Magnesium ribbon is burnt in an atmosphere of nitrogen gas to form solid magnesium nitride.

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(N/A) $Fe_{2}O_{3}(s) + 2Al(s) \longrightarrow Al_{2}O_{3}(s) + 2Fe(l) + \text{Heat}$
This is a displacement reaction (specifically a thermit reaction) and also a redox reaction.
$(b)$ $3Mg(s) + N_{2}(g) \longrightarrow Mg_{3}N_{2}(s)$
This is a combination reaction.

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