Which ethanol derivatives display the gauche effect?
As per this source, there is evidence for the gauche effect for most of these groups on basis of intramolecular hydrogen bonding:


  


I tried looking for a similar evidence for 2-nitroethanol, and found this paper on the same:


  
  Figure 4. OCCN gauche structures with an intramolecular H-bond for 2-aminoethanol (7) and 2-nitroethanol (9); Conformations 8 and 10 indicate disrupted H-bonds after rotations by approximately 120º about the O-C axes


So it seems like all the groups shown here can show the gauche effect on the grounds of intramolecular hydrogen bonding,and so your answer should be 8