Which of the following represents the correct order of stability of ions in solution? 

$\left(\mathrm{a}\right) {\mathrm{Cu}}^{2+}>{\mathrm{Cu}}^{+}; \left(\mathrm{b}\right) {\mathrm{Fe}}^{2+}>{\mathrm{Fe}}^{3+}; \left(\mathrm{c}\right) {\mathrm{Cr}}^{2+}>{\mathrm{Cr}}^{3+}; \left(\mathrm{d}\right) {\mathrm{Mn}}^{2+}>{\mathrm{Mn}}^{3+}$

Cu²⁺ ion has a greater charge density than Cu⁺ ion, thus forms much stronger bonds releasing more energy. The extra energy needed for the second ionization of the copper is more than compensated for by the hydration, so much so that the Cu⁺ ion loses an electron to become Cu²⁺ which can then release this hydration energy.
In aqueous solution, Cu⁺ disproportionate to Cu²⁺ and Cu
$2{\mathrm{Cu}}^{+}\to {\mathrm{Cu}}^{2+}+\mathrm{Cu}$

In an aqueous media, Fe²⁺(3d⁶) quickly oxidizes to Fe³⁺(3d⁵), which is more stable.

Cr³⁺ is more stable in aqueous solution, due to higher hydration energy which is due to smaller size and higher charge

Electronic configuration of Mn²⁺ is [Ar]3d⁵4s⁰ and Mn³⁺ is [Ar]3d⁴4s⁰. Because of having maximum number of unpaired electrons, Mn²⁺ is more stable than Mn³⁺.