The correct answer is: B. To maintain the two tongue rails at the exact distance.
A stretcher bar is a metal bar that is used to keep the two tongue rails of a railway switch at the correct distance apart. This is important to ensure that the switch operates correctly and that trains can pass over it safely.
The other options are incorrect. Option A is incorrect because the stretcher bar does not permit lateral movement of the tongue rail. Option C is incorrect because the stretcher bar does not ensure exact gauge at the toe of the switch as well as the nose of crossing. Option D is incorrect because the stretcher bar does not prevent any vertical movement between the wing rail and nose of crossing.