Let's match the chemical tests with their respective target compounds:

1. Carbylamine test: This is a characteristic test for primary amines (both aliphatic and aromatic). Aniline is a primary aromatic amine and gives a positive carbylamine test by forming a foul-smelling isocyanide. [(a) $\rightarrow$ (iv)]
2. Baeyer's test: This test is used to detect the presence of unsaturation (carbon-carbon double or triple bonds). Ethylene contains a double bond and will decolourise the cold, dilute alkaline $KMnO_4$ solution (Baeyer's reagent). [(b) $\rightarrow$ (iii)]
3. Iodoform test: This test is given by compounds having a methyl ketone group ($-COCH_3$) or a methyl carbinol group. Acetone ($CH_3COCH_3$) contains a methyl ketone group and forms a yellow precipitate of iodoform ($CHI_3$) upon reaction with iodine and alkali. [(c) $\rightarrow$ (ii)]
4. Phthalein dye test: This test is specific for phenols. Phenol reacts with phthalic anhydride in the presence of concentrated $H_2SO_4$ to form phenolphthalein, which turns pink in an alkaline medium. [(d) $\rightarrow$ (i)]

Therefore, the correct matching is (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i).