name the gas evolved at cathode and anode on electrolysis of water and what is the ratio of the gases evolved?

Water dissociates slightly to give hydrogen ions and hydroxide ions.

Hydrogen ions are attracted to the cathode and are then reduced to hydrogen gas.
2H⁺(aq) + 2e⁻ → H₂(g)

On the other hand, hydroxide ions are attracted to the anode and are then oxidized to oxygen gas.
4OH⁻(aq) → 2H₂O(l) + O₂(g) + 4e⁻

The equation of the overall reaction is :
2H₂O(l) → 2H₂(g) + O₂(g)
According to the equation, mole ratio and volume ratio H₂ : O₂ = 2 : 1

Conclusively, hydrogen gas is evolved at the cathode while oxygen gas at the anode. The mole ratio and volume ratio of hydrogen gas to oxygen gas are 2 : 1.

During electrolysis: 2H2O --> O2 (g) + 2H2 (g)
O2 is formed at the positive electrode
H2 is formed at the negative electrode
The ratio would be 1 molecule of O2 to every 2 molecules of H2 (1:2) becuase of the equation at the top - you get 1 mole of oxygen for every 2 moles of hydrogen