The minimum equivalent conductance in fused state is shown by

Be is alkaline earth metal that belongs to the S group elements.The periodic sequence is Be, Mg, Ca, Cr. Here, the equivalent conductance is directly proportional to the number of ions. Since BeCl₂ is the most covalent compound because down the group it decreases covalency and therefore it does not ionize. The compound which is not ionized i.e.BeCl₂ the equivalent conductance is minimum in a fused state. 

Hence the correct answer would be ${\mathrm{BeCl}}_2$.