Which among these substances would dissolve in distilled water: alum, sodium chloride, or sucrose?

All these substances will dissolve in water. Alum and sodium chloride are both ionic and sucrose is sugar. Sodium chloride will dissolve the fastest, then Alum. Since Alum is a larger molecule it is likely to dissolve more slowly. Sucrose dissolves the slowest since it is an organic compound. In an aqueous form the substances may to p through filter paper depending and the kind of filter paper used and the size of the molecule.