a
Redrawing the given structures we get,  From the above structure, it is evident than structure \((a)\) will show cis-trans isomerism and it also has a chiral carbon. On the other hand, structure \((b)\) although shows cistrans isomerism, it has no chiral carbon.

\(\mathop {\begin{array}{*{20}{c}}
  {H\,\,\,\,\,\,\,} \\ 
  {|\,\,\,\,\,\,\,\,} \\ 
  {C{H_3} - C = C - C{H_3}} \\ 
  {\,\,\,\,\,\,\,\,\,|} \\ 
  {\,\,\,\,\,\,{H_3}C - {C^*} - H} \\ 
  {\,\,\,\,\,\,\,\,|} \\ 
  {\,\,\,\,\,\,\,\,H - C - H} \\ 
  {\,\,\,\,\,\,\,\,|} \\ 
  {\,\,\,\,\,\,\,\,\,\,\,C{H_3}} 
\end{array}}\limits_{(a)} \)

\(\mathop {\begin{array}{*{20}{c}}
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,H\,\,\,\,\,\,\,H\,\,\,\,\,\,\,C{H_3}} \\ 
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,|} \\ 
  {C{H_3} - C - C = C} \\ 
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,|} \\ 
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,H\,{H_3}C - C - H} \\ 
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,|} \\ 
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,C{H_3}} 
\end{array}}\limits_{(b)} \)