The correct options are
A Potassium hydroxide
B Nitric acid
D Sodium chloride
Potassium hydroxide is an alkali, nitric acid is an acid and sodium chloride is a salt. These do not conduct electricity in the solid state, although they contain ions as these ions are held in fixed positions and are not able to move. When they are melted or dissolved in water, their structure breaks up and the ions are free to move.
Graphite has free electrons in its solid form and hence it conducts electricity in solid state.