Which of the following pair have similar magnetic moment?

Mn²⁺, Fe³⁺

Magnetic moment is given  by \(\mu\) = \(\sqrt {n(n+2) }\) ; where n is the number of electrons

Same no of electrons will give same magnetic moment.

₂₅Mn : [Ar]4s²3d⁵

Mn²⁺ : [Ar]3d⁵

₂₆Fe : [Ar]4s²3d⁶

Fe³⁺ : [Ar]3d⁵ 

Both contain 5 unpaired electrons, Hence they possess same magnetic moment.