The pair that does not require calcinations is:
A. ZnO and MgO
B. $F{{e}_{2}}{{O}_{3}}\text{ and CaC}{{\text{O}}_{3}}.MgC{{O}_{3}}$
C. ZnO and $F{{e}_{2}}{{O}_{3}}.x{{H}_{2}}O$
D. $ZnC{{O}_{3}}$ and CaO

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Hint: Calcination is a process which is used in metallurgy for the purification of the ores. So to solve this question, we need to see which of the following compounds can be decomposed without any other physical means to remove the impurities. The basic step for metallurgy for any ore is the formation of oxides of the metals.

Complete step by step solution:
-Metal compounds found in nature are called minerals. Minerals from which we can extract metals conveniently as well as economically are called ores. It contains impurities which are called gangue.
-Extraction of metals from ores is called metallurgy. Metals are extracted from the earth’s surface and so along with the metals, certain impurities also appear with it which needs to be removed in order to increase the efficiency of the metals.
-The mixture of oxides with the impurities is called slag. It is present in molten state along with the molten metal. The process by which this impurity containing slag is removed from the metal is called smelting.
-The best way to extract the metal is to add oxygen to the ore so that all the impurities present in the metal react with oxygen to form the oxides. Once oxides are formed, they are removed easily as they are generally insoluble.
Eg. $\begin{align}
& 2CuFe{{S}_{2}}+4{{O}_{2}}\to 2FeO+C{{u}_{2}}S+3S{{O}_{2}} \\
& FeO+C{{u}_{2}}S+Si{{O}_{2}}\to FeSi{{O}_{3}}\left( slag \right)+C{{u}_{2}}S \\
-Calcination involves heating the metal ores to a very high temperature. It causes the removal of all the volatile substances. It converts an ore into oxide by heating it below its melting point. The furnace used for this purpose is a three layered furnace of muffle, reverberatory and a shaft furnace.
-In the given options, we see that all all the options are carbonates or contain water of crystallization which can result in their conversion to their respective oxides.
-Only the first option contains the simple oxides of both the metals which cannot be reduced further by any physical means. So we cannot use the process of calcinations for this option.

Therefore the correct option is A.

Note: The process of calcinations can be done both in the absence of air as well as the presence of air. It does not create any impact on the process or on the ability of the impurities to get removed. It is used generally for carbonates and hydroxides.