1) In 3d-series of transition metals, manganese has an atomic number of 25 that gives the electronic configuration as [Ar] 3d⁵4s² ,where we see that the maximum number of unpaired electrons is found in manganese atom; so, it can show a maximum oxidation state upto +7.

2) Copper is the transition metal of 3d series that exhibits positive E⁰ (M²⁺/M). The value of E⁰(M²⁺/M) for copper  is  (+0.34). This happens because the E⁰ (M²⁺/M) value of a metal depends on the energy changes involved in the following:

(i) Sublimation energy:  The energy required for converting one mole of an atom from the solid state to the gaseous state.

        M(s)--> M(g)                                 _sH (Sublimation energy)

(ii) Ionisation energy:  The energy required to take out electrons from one mole of atom in the isolated gaseous state.

         M(g)--> M²⁺(g)                        _iH (Ionisation energy)

(iii) Hydration energy:  The energy released when one mole of ions are hydrated.

         M²⁺(g)--> M²⁺(aq)                      _hydH (Hydration energy)

Since, copper has a high energy of atomization and low hydration energy, the E⁰(M²⁺/M) value for copper is positive.

3) Out of Cr³⁺ and Mn³⁺, Mn³⁺ is a stronger oxidising agent because it has 4 electrons in its valence shell and when it gains one electron to form Mn²⁺, it results in the half-filled (d⁵) configuration that has extra stability.

4) Europium (Eu) is well-known to exhibit +2 oxidation state due to its half filled f orbital in +2 oxidation state.

5) MnO₄^- + 8H⁺ + 5e^- --->     Mn²⁺ + 4 H₂O