The correct answer is: A. down.
An increase in base resistance will decrease the current through the base-emitter junction, which will decrease the collector current. This will cause the Q point to move down the load line.
Option B is incorrect because an increase in base resistance will decrease the collector current, not increase it.
Option C is incorrect because the Q point will move, not stay in the same place.
Option D is incorrect because the Q point will move along the load line, not off of it.
Option E is incorrect because the answer is A.