Nitrifying bacteria perform which of the following processes?

Match the organisms given in Column $I$ to their functions given in Column $II$ and choose the correct option.

Column $I$	Column $II$
$A$. Thiobacillus	$1$. Free-living nitrogen-fixing cyanobacteria
$B$. Nitrosomonas	$2$. Denitrification
$C$. Nostoc	$3$. Free-living aerobic nitrogen-fixing bacteria
$D$. Azotobacter	$4$. $NH_{3}$ to Nitrite

Codes:
$A \quad B \quad C \quad D$

Select the correct matches.
$I$ Nitrosomonas - Nitrite to nitrate
$II$ Thiobacillus - Denitrification
$III$ Nostoc - Free-living nitrogen-fixer
$IV$ Azotobacter - Anaerobic nitrogen-fixer

Reaction carried out by $N_{2}$ metabolising microbes include:
$I.$ $2 NH_{3} + 3 O_{2} \rightarrow 2 NO_{2}^{-} + 2 H^{+} + 2 H_{2} O$
$II.$ $2 NO_{2}^{-} + O_{2} \rightarrow 2 NO_{3}^{-}$
Which of the following statements about these equations is not true?

Thiobacillus is a group of bacteria helpful in carrying out

Which of the following diagrams correctly depicts the $N_{2}$-cycle?