Which of the following are the products of electrolysis of aqueous solution of sodium chloride?

Cathode - $H_2$ gas, anode - $Cl_2$ gas

The correct answer is Option (3) → Cathode - $H_2$ gas, anode - $Cl_2$ gas.

When an aqueous solution of sodium chloride \((NaCl)\), also known as brine, undergoes electrolysis, the key reactions at the electrodes are determined by the ions present in the solution:

At the cathode (negative electrode): Reduction occurs. The reduction potential of water is higher than that of sodium ions. Hence, water is reduced instead of sodium ions. The reaction is:

\(2H_2O + 2e^- \longrightarrow H_2 (g) + 2OH^- (aq)\)

So, hydrogen gas \((H_2)\) is liberated at the cathode.

At the anode (positive electrode): Oxidation occurs. Chloride ions \((Cl^-)\) are oxidized to chlorine gas \((Cl_2)\) instead of water being oxidized to oxygen. The reaction is:

\(2Cl^- (aq) \longrightarrow Cl_2 (g) + 2e^-\) 

So, chlorine gas \((Cl_2)\) is liberated at the anode.

Net Reaction:

\(2NaCl (aq) + 2H_2O (l) \longrightarrow 2NaOH (aq) + H_2 (g) + Cl_2 (g)\)

Thus, hydrogen gas is produced at the cathode, and chlorine gas is produced at the anode.

Therefore, the correct option is: Cathode - H₂ gas, Anode - Cl₂ gas.