c
At equilibrium : \(\frac{{dU(x)}}{{dx}} = 0\)

\( \Rightarrow \frac{{ - 12a}}{{{x^{11}}}} = \frac{{ - 6a}}{{{x^5}}} \Rightarrow x = {\left( {\frac{{2a}}{b}} \right)^{\frac{1}{6}}}\)

\(\begin{gathered}
  {U_{at}}\,equilibrium = \frac{a}{{{{\left( {\frac{{2a}}{b}} \right)}^2}}} - \frac{b}{{\left( {\frac{{2a}}{b}} \right)}} \hfill \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{b^2}}}{{a4}}\,and\,{U_{\left( {x = \infty } \right)}} = 0 \hfill \\ 
\end{gathered} \)

\(\therefore \) \(D = 0\)\( - \left( { - \frac{{{b^2}}}{{4a}}} \right) = \frac{{{b^2}}}{{4a}}\)