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Cryolite is:
(A) \[N{{a}_{3}}Al{{F}_{6}}\] and is used in the electrolysis of alumina for decreasing electrical conductivity.
(B) \[N{{a}_{3}}Al{{F}_{6}}\]​ and is used in the electrolysis of alumina for lowering the melting point of alumina only.
(C) \[N{{a}_{3}}Al{{F}_{6}}\] and is used in the electrolysis of alumina for lowering the melting point and increasing the conductivity of alumina.
(D) \[N{{a}_{3}}Al{{F}_{6}}\] ​ and is used in the electrolytic refining of alumina.

Answer
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Hint: Molten cryolite is essential in the Hall-Héroult process which is used to refine Aluminium. Try and remember this chemical reaction to try and figure out how cryolite is used with respect to alumina.

Step-by-Step Solution:
Cryolite, also known as sodium hexafluoro aluminate, is a colourless compound forming cube-like crystals consisting of aluminium 3+ cations binding six fluoride \[{{F}^{-}}\] anions, forming octahedral like \[Al{{F}_{6}}^{3-}\]with smaller mono-positive sodium ions to balance the charge.
Molten cryolite is used as a solvent for aluminium oxide (\[A{{l}_{2}}{{O}_{3}}\]) in the Hall–Héroult process, used in the refining of aluminium, the reaction of which is given by:
\[2\text{ }A{{l}_{2}}{{O}_{3}}~+\text{ }3\text{ }C\text{ }\to \text{ }4\text{ }Al\text{ }+\text{ }3\text{ }C{{O}_{2}}\]
Besides having a relatively low melting point, cryolite is used as an electrolyte because, among other things, it also dissolves alumina well, conducts electricity, dissociates electrolytically at higher voltage than alumina, and also has a lower density than aluminium at the temperatures required by the electrolysis.
It also decreases the melting point of molten (liquid state) aluminium oxide from 2000–2500 °C to 900–1000 °C, and increases its conductivity thus making the extraction of aluminium more economical.
Therefore, the answer to this question is (C).

Note: Cryolite is also used as a solvent for bauxite in the electrolytic production of aluminium and has various other metallurgical applications, and it is used in the glass and enamel industries, in bonded abrasives as a filler, and in the manufacture of insecticides.