Match the entries of column I with appropriate entries of column II and choose the correct option out of the four options given.

(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)

The correct answer is option 1. (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii).

(a) Faraday's first law of Electrolysis - (ii) m = Zit:

Faraday's first law of Electrolysis states that the amount of substance deposited or liberated at an electrode during electrolysis is directly proportional to the quantity of electricity passed through it (where \( m \) is the mass, \( Z \) is the electrochemical equivalent, \( i \) is the electric current, and \( t \) is time). Therefore, \( m = Zit \) directly corresponds to Faraday's first law.

(b) Kohlrausch's law - (i) \(\Lambda^0_{A_xB_y} = x\lambda^0_+ +y\lambda^0_-\):

Kohlrausch's law deals with the equivalent conductance of an electrolyte, stating that the molar conductance of an electrolyte at infinite dilution is the sum of the molar conductances of its ions. Hence, \(\Lambda^0_{A_xB_y} = x\lambda^0_+ +y\lambda^0_-\) describes this relationship accurately.

(c) Faraday's second law of Electrolysis - (iv) m ∝ E; E = Equivalent weight:

Faraday's second law of Electrolysis relates the masses of different substances liberated by the same quantity of electricity. It states that the masses are proportional to their chemical equivalents. 

\( m ∝ E \) directly relates to this law, where \( E \) is the equivalent weight of the substance.

(d) Thermodynamic relationship of cell - (iii) ΔG = -nFE_cell:

The thermodynamic relationship of a cell relates the Gibbs free energy change of a reaction to the electromotive force (emf) or cell potential (\( E_{\text{cell}} \)).

\( ΔG = -nFE_{\text{cell}} \) quantifies the relationship between the change in Gibbs free energy (ΔG), the number of moles of electrons transferred (n), the Faraday constant (F), and the cell potential.

Therefore, the correct option that matches each law or relationship with its appropriate expression is: (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)