Match List - I with List - II and choose the correct answer.

List - I	List - II
(a) Nitrococcus	(i) Denitrification
(b) Rhizobium	(ii) Conversion of ammonia to nitrite
(c) Thiobacillus	(iii) Conversion of nitrite to nitrate
(d) Nitrobacter	(iv) Conversion of atmospheric nitrogen to ammonia

The correct option is a - (ii) b - (iv) c - (i) d - (iii).

To match List-I (organisms) with List-II (their functions in the nitrogen cycle), let's examine each item step-by-step:

(a) Nitrococcus:
Nitrococcus is a genus of nitrifying bacteria. These bacteria obtain energy by oxidizing inorganic nitrogen compounds. Specifically, Nitrococcus is involved in the conversion of ammonia (${\mathrm{NH}}_3$) to nitrite (${\mathrm{NO}}_2^{-}$).
Therefore, (a) matches with (ii).

(b) Rhizobium:
Rhizobium is a genus of Gram-negative soil bacteria that forms a symbiotic relationship with the roots of leguminous plants. It is well-known for biological nitrogen fixation, which is the conversion of atmospheric nitrogen ($N_2$) to ammonia (${\mathrm{NH}}_3$).
Therefore, (b) matches with (iv).

(c) Thiobacillus:
Thiobacillus is a genus of bacteria involved in nitrogen metabolism as well as sulfur oxidation. Along with Pseudomonas, certain species of Thiobacillus (such as Thiobacillus denitrificans) perform denitrification, a process that reduces nitrates or nitrites back into gaseous atmospheric nitrogen ($N_2$).
Therefore, (c) matches with (i).

(d) Nitrobacter:
Nitrobacter is another genus of nitrifying bacteria. Unlike Nitrococcus, Nitrobacter is responsible for the subsequent oxidation step in nitrification, which is the conversion of nitrite (${\mathrm{NO}}_2^{-}$) to nitrate (${\mathrm{NO}}_3^{-}$).
Therefore, (d) matches with (iii).

Combining all the individual matches, we get:
a - (ii), b - (iv), c - (i), d - (iii)