(a) Zinc and aluminium cannot be distinguished by heating the metal powder with concentrated sodium hydroxide solution as they both react with conc. alkalis to form soluble sodium salts and hydrogen gas.
Zinc reacts to form sodium zincate
Zn + 2NaOH ⟶ H2 + Na2ZnO2 [sodium zincate]
Aluminium reacts to form sodium aluminate
2Al + 2NaOH + 2H2O ⟶ 3H2 + 2NaAlO2 [sodium aluminate]
(b) Yes, calcium nitrate and lead nitrate can be distinguished using ammonium hydroxide solution. Ammonium hydroxide on reaction with lead nitrate gives chalky white precipitate of Pb(OH)2. No precipitation occurs on adding Ammonium hydroxide to calcium nitrate even when it is added in excess.
Pb(NO3)2 + 2NH4OH ⟶ Pb(OH)2 + 2NH4NO3