The gas produced during the hydrolysis of beryllium carbide (Be₂C) and aluminium carbide (Al₄C₃) is methane (CH₄).

Here's why:

* Beryllium carbide (Be₂C): When beryllium carbide reacts with water, it undergoes hydrolysis to produce beryllium hydroxide (Be(OH)₂) and methane gas:

```

Be₂C + 4H₂O → 2Be(OH)₂ + CH₄

```

* Aluminium carbide (Al₄C₃): Similar to beryllium carbide, aluminium carbide reacts with water to produce aluminium hydroxide (Al(OH)₃) and methane gas:

```

Al₄C₃ + 12H₂O → 4Al(OH)₃ + 3CH₄

```

Therefore, in both cases, methane gas is the primary product of hydrolysis.