How many electrons are present in $t_{2g}$ set of $d-orbitals$ of central metal cation in $\left[Fe\right(H_{2}O{)}_5\left(NO\right)]S{O}_4$ brown ring complex?

The central iron atom is in +1 oxidation state. It has $3d^7$ electronic configuration.
Due to weak-field ligands, the pairing energy is higher than ${\Delta }_o$. So, $t_{2g}$ has 5 electrons.