The correct options are
B A has non-polar covalent linkage
C B is ionic in nature
D C has polar covalent bonds
A does not conduct electricity in the solid and molten state suggests that A is not an ionic compound and it can be a covalent compound.
A is not conducting electricity in aqueous solution also, it suggests that all the element in compound A has the same electronegativity.
Hence, A can be non-polar covalent compound that means it has non-polar covalent linkage.
B conducts electricity in a fused state and in aqueous states, This represents that the electronegativity difference in the compound is very high.
Hence, B can be an ionic bond
C conducts electricity in only in the aqueous state. It means that C does not conduct electricity in a molten state that means C is not an ionic compound.
It can be a covalent compound and as it is conducting electricity in the aqueous state, there must be small electronegativity difference.
Hence, C can be a polar covalent compound.