Fluorine exhibits only $-1$ oxidation state whereas other halogens exhibit $+1, +3, +5$ and $+7$ oxidation states also. Explain.

(N/A) Fluorine is the most electronegative element in the periodic table and has no $d$-orbitals in its valence shell. Due to its high electronegativity and absence of $d$-orbitals,it cannot exhibit any positive oxidation state.
Other halogens (like $Cl, Br, I$) possess vacant $d$-orbitals in their valence shell. This allows them to expand their octets and promote electrons to higher energy levels,enabling them to exhibit $+1, +3, +5$ and $+7$ oxidation states in addition to $-1$.