\documentclass{exam}
\usepackage[
  a4paper,
  left = 10mm,
  right = 10mm,
  includehead,
  top = 10mm,
  headheight = 60mm,
  headsep = 0pt,
  includefoot,
  foot = 0mm,
  bottom = 25mm
]{geometry}
\usepackage{xparse,xcolor,mdframed}

\usepackage{blindtext}


\ExplSyntaxOn
\keys_define:nn { diaa / answers }
 {
  d .dim_set:N = \l__diaa_answers_distance_dim,
  t .dim_set:N = \l__diaa_answers_thickness_dim,
  c .tl_set:N  = \l__diaa_answers_color_tl,
  d .initial:n = 10mm,
  t .initial:n = 0.2pt,
  c .initial:n = gray,
 }

\NewDocumentCommand{\FillAnswerRules}{O{}}
 {
 \begin{mdframed}[linewidth = 1pt, nobreak = false]
  \group_begin:
  \keys_set:nn { diaa / answers } { #1 }
  \leaders \hbox:n
   {
    \makebox[\textwidth][s]{
      \color{\l__diaa_answers_color_tl}
      \vrule width 0pt height \l__diaa_answers_distance_dim % the distance
      \leaders\hrule height \l__diaa_answers_thickness_dim\hfill
    }
   }\vfill
  \clearpage
  \group_end:
  \end{mdframed}
 }

\ExplSyntaxOff

\begin{document}

\begin{questions}
\question short question\FillAnswerRules[d=2cm]

\question \blindtext[3]\FillAnswerRules[t=1pt,c=red]

\end{questions}

\end{document}