Given below are two statements :
1 M aqueous solution of each of $$Cu(NO_3)_2$$, $$AgNO_3$$, $$Hg_2(NO_3)_2$$; $$Mg(NO_3)_2$$ are electrolysed using inert electrodes.
Given : $$E_{Ag^{+}/Ag}^{\theta} = 0.80V, E_{Hg_{2}^{2+}/Hg}^{\theta} = 0.79V,$$
           $$E_{Cu^{2+}/Cu}^{\theta} = 0.24V$$ and $$E_{Mg^{2+}/Mg}^{\theta} = -2.37V$$
Statement (I) : With increasing voltage, the sequence of deposition of metals on the cathode will be Ag, Hg and Cu
Statement (II) : Magnesium will not be deposited at cathode instead oxygen gas will be evolved at the cathode.
In the light of the above statement, choose the most appropriate answer from the options given below : 

For electrolysis using inert electrodes we compare the standard reduction potentials $$E^{\circ}$$ of all possible cathodic reactions. The species having the highest (most positive) $$E^{\circ}$$ gets reduced (deposited) first. All solutions are 1 M, so the numerical values of $$E^{\circ}$$ may be used directly without any Nernst correction.

Standard reduction potentials involved:

$$Ag^{+}+e^{-}\rightarrow Ag;\;E^{\circ}=+0.80\;{\rm V}$$
$$Hg_2^{2+}+2e^{-}\rightarrow 2Hg;\;E^{\circ}=+0.79\;{\rm V}$$
$$Cu^{2+}+2e^{-}\rightarrow Cu;\;E^{\circ}=+0.34\;{\rm V}$$

Because $$E^{\circ}_{Ag^{+}/Ag}\gt E^{\circ}_{Hg_2^{2+}/Hg}\gt E^{\circ}_{Cu^{2+}/Cu}$$, the sequence of metal deposition on the cathode as the external voltage is increased will be Ag (first) → Hg (second) → Cu (third).

Therefore Statement I is correct.

For the magnesium salt two possible cathodic reductions are important:

$$Mg^{2+}+2e^{-}\rightarrow Mg;\;E^{\circ}=-2.37\;{\rm V}$$
$$2H_2O+2e^{-}\rightarrow H_2+2OH^{-};\;E^{\circ}=-0.83\;{\rm V}$$

The reduction of water (giving hydrogen gas) requires a far smaller over-potential than the reduction of $$Mg^{2+}$$. Hence, at the cathode hydrogen gas will evolve, and metallic magnesium will not be deposited.

Oxygen gas is produced at the anode (oxidation of water), not at the cathode. Thus Statement II is incorrect.

Conclusion: Statement I is correct, Statement II is incorrect → Option B.