The correct formula of the complex formed in the brown ring test for nitrates is:
$\left[ Fe \left( H _{2} O \right)_{5} NO \right]^{2+}$
It is formed through the following reaction:
$FeSO _{4}+5 H _{2} O + NO \rightarrow\left[ Fe \left( H _{2} O \right)_{5} NO \right] SO _{4}$