Among statements (a) - (d), the correct ones are:
(a) Lime stone is decomposed to CaO during the extraction of iron from its oxides.
(b) In the extraction of silver, silver is extracted as an anionic complex.
(c) Nickel is purified by Mond's process.
(d) Zr and Ti are purified by Van Arkel method.

We begin by recalling the basic facts connected with the common metallurgical processes mentioned in the four statements, then we check each one.

First, consider statement (a). In the blast-furnace extraction of iron, limestone, whose formula is $$\text{CaCO}_3$$, is added as a flux. Inside the furnace the temperature gradually rises beyond $$\approx 800^{\circ}\text{C}$$, and at that point limestone undergoes thermal decomposition. The decomposition reaction is stated as

$$\text{CaCO}_3 \;\xrightarrow{\ \Delta\ }\; \text{CaO} + \text{CO}_2 \uparrow.$$

This freshly formed $$\text{CaO}$$ then reacts with the gangue (mainly $$\text{SiO}_2$$) to produce the fusible slag $$\text{CaSiO}_3$$. Because the first step definitely is the conversion of $$\text{CaCO}_3$$ to $$\text{CaO}$$, we see that statement (a) is correct.

Now we look at statement (b). Silver is commonly extracted from its sulphide ore (argentite, $$\text{Ag}_2\text{S}$$) by the cyanide, or Mac-Arthur Forest, process. The key chemical step is the formation of a soluble anionic complex of silver with the cyanide ion. We write the balanced reaction in two stages.

First, the sulphide ore reacts with aqueous sodium cyanide and atmospheric oxygen (or hydrogen peroxide added in practice) to give the soluble complex:

$$\text{Ag}_2\text{S} + 4\,\text{NaCN} + \tfrac{1}{2}\,\text{O}_2 + \text{H}_2\text{O} \;\longrightarrow\; 2\,\text{Na[Ag(CN)}_2] + \text{Na}_2\text{S} + 2\,\text{OH}^-.$$

The species $$\text{[Ag(CN)}_2]^-$$ is clearly an anionic complex of silver. Silver is later recovered from this solution by displacement with zinc, but the extraction indeed proceeds through an anionic complex. Hence statement (b) is also correct.

Next, examine statement (c). Mond’s process, also called the carbonyl process, is employed for the purification of nickel. The principle is the formation and subsequent decomposition of volatile nickel tetracarbonyl. We state the two crucial reactions.

Formation of the carbonyl at about $$320\ \text{K}:$$

$$\text{Ni}(s) + 4\,\text{CO}(g) \;\rightleftharpoons\; \text{Ni(CO)}_4(g).$$

Thermal decomposition of the carbonyl at about $$450\ \text{K}:$$

$$\text{Ni(CO)}_4(g) \;\xrightarrow{\ 450\ \text{K}\ }\; \text{Ni}(s) + 4\,\text{CO}(g).$$

This sequence removes almost all impurities and gives extremely pure nickel, verifying that statement (c) is right.

Finally, consider statement (d). The Van Arkel (or iodide) method purifies certain transition metals that form volatile iodides and then revert to the pure metal on a hot filament. For titanium we write

$$\text{Ti}(impure) + 2\,\text{I}_2 \;\xrightarrow{\ 500\ \text{K}\ }\; \text{TiI}_4(g),$$

followed by

$$\text{TiI}_4(g) \;\xrightarrow{\ 1800\ \text{K}\ on\ hot\ W\ or\ Ti\ filament }\; \text{Ti}(pure) + 2\,\text{I}_2.$$

An analogous pair of reactions holds for zirconium:

$$\text{Zr}(impure) + 2\,\text{I}_2 \;\xrightarrow{\ 500\ \text{K}\ }\; \text{ZrI}_4(g),$$

$$\text{ZrI}_4(g) \;\xrightarrow{\ 1800\ \text{K} }\; \text{Zr}(pure) + 2\,\text{I}_2.$$

Because both Ti and Zr are indeed purified by this iodide route, statement (d) is correct.

We have now checked every statement, and all four—(a), (b), (c) and (d)—are correct.

Hence, the correct answer is Option A.