The correct statement is:

We begin by reading all the four statements one by one and recalling the fundamental facts of metallurgy and surface chemistry that are needed to judge their correctness.

Statement (A) reads: “Aniline is a froth stabilizer.”  In the froth-flotation process, collectors such as $$KCN$$, xanthates etc. adsorb on the mineral surface and make it hydrophobic, while froth stabilizers are substances that keep the bubbles from breaking too quickly.  Text-book froth stabilizers include cresols and aniline.  Therefore, Statement (A) is true.

Statement (B) says: “Zone refining process is used for the refining of titanium.”  The zone-refining (or zone-melting) technique is based on the principle that impurities are more soluble in the melt than in the solid, so a narrow molten zone moved along a bar sweeps the impurities ahead of it.  This method is employed for extremely high-purity elements of high electronic grade such as silicon, germanium and gallium.  Titanium, however, is purified industrially by the van Arkel-de Boer (iodide) process, not by zone refining.  Hence Statement (B) is false.

Statement (C) claims: “Zincite is a carbonate ore.”  Zincite has the formula $$ZnO$$ and is therefore an oxide ore.  Typical carbonate ores of zinc would be smithsonite $$ZnCO_{3}$$, not zincite.  Thus Statement (C) is false.

Statement (D) declares: “Sodium cyanide cannot be used in the metallurgy of silver.”  The well-known MacArthur-Forrest cyanide leaching process dissolves both gold and silver by forming the complex $$[Ag(CN)2]^-$$ in the presence of oxygen and water:

$$4\,Ag + 8\,NaCN + O_{2} + 2\,H_{2}O \;\longrightarrow\; 4\,Na[Ag(CN)2] + 4\,NaOH$$

Because $$NaCN$$ is actually the reagent used for extracting silver, Statement (D) is also false.

Out of the four statements, only Statement (A) is correct.

Hence, the correct answer is Option A.