Give distinguishing tests for the following:
$(a)$ Ethane and ethyne (Alkane and Alkyne $RC \equiv CH$)
$(b)$ Ethene and Ethyne (Alkene and Alkyne $RC \equiv CH$)
$(c)$ Dimethyl ethyne and ethyne
$(d)$ Ethane and Ethene (Alkane and alkene)

(N/A) Ethane and ethyne: Ethyne $(HC \equiv CH)$ has acidic hydrogen,so it reacts with $NaNH_2$ or ammoniacal $AgNO_3$ (Tollens' reagent),whereas ethane does not.
$(b)$ Ethene and Ethyne: Ethyne reacts with $NaNH_2$ or ammoniacal $AgNO_3$ due to acidic hydrogen,while ethene does not.
$(c)$ Dimethyl ethyne and ethyne: Ethyne reacts with $NaNH_2$ or ammoniacal $AgNO_3$ due to acidic hydrogen,while dimethyl ethyne $(CH_3C \equiv CCH_3)$ does not have acidic hydrogen.
$(d)$ Ethane and Ethene: Ethene reacts with $Br_2$ water (decolorizes) or Baeyer's reagent $(KMnO_4)$,while ethane does not.