The characteristic test for 

(a) 

• Carbon dioxide (CO₂) gas turns lime water milky when passed through it due to the formation of insoluble calcium carbonate. 
• Ca(OH)₂ + CO₂ → CaCO₃ + H₂O
• Lime water Carbon Calcium dioxide carbonate 

(b) 

• Sulphur dioxide (SO₂) gas when passed through acidic potassium permanganate solution (purple in colour) turns
• it colourless because SO₂ is a strong reducing agent 
• 2KMnO₄ + 2H₂O + 5SO₂→ K₂SO₄ + 2MnSO₄ + 2H₂SO₄
• Potasssium Sulphur Potassium Manganese permanganate dioxide sulphate sulphate (Purple) (Colourless) (Colourless).
• Sulphur dioxide gas when passed through acidic dichromate solution (orange in colour) turns it to green because sulphur dioxide is a strong reducing agent. 

(c) 

• The evolution of oxygen (O₂) gas during a reaction can be confirmed by bringing a burning candle near the mouth of the test tube containing the reaction mixture.
• The intensity of the flame increases because oxygen supports burning.

 (d) 

• Hydrogen (H₂) gas burns with a pop sound when a burning candle is brought near it.