Statement I: \([Co(en)_2(NH_3)Br]SO_4\) has lower electrical conductivity as compared to \([Co(en)_2(NH_3)SO_4]Br\)

Statement II: Both complexes produce the same number of ions in the solution

Statement I is false but Statement II is correct

The correct option is 4. Statement I is false, but Statement II is correct.

Statement I is false. The electrical conductivity of a solution depends on the total number of ions present in the solution. Both complexes, \([Co(en)_2(NH_3)Br]SO_4\) and \([Co(en)_2(NH_3)SO_4]Br\), will produce the same total number of ions when they dissociate in the solution.

Statement II is correct. Both complexes will produce the same number of ions in the solution. In the first complex, \([Co(en)_2(NH_3)Br]SO_4\), when it dissociates, it will produce the ions \([Co(en)_2(NH_3)Br]^{2+}\) and \(\text{SO}_4^{2-}\). In the second complex, \([Co(en)_2(NH_3)SO_4]Br\), when it dissociates, it will produce the ions \([Co(en)_2(NH_3)SO_4]^{+}\) and \(\text{Br}^{-}\). Both complexes will result in two ions in the solution.

Therefore, the correct answer is Option 4: Statement I is false, but Statement II is correct.