Normal reaction Consider a plank on a frictionless surface and a ball from a height H is dropped on this plank. There is no friction between the plank and ball. Can the plank jump up in air for any value of H?
I don't want to know the value of H for which would happen. I just want to know that is this even possible that the plank jumps due to the normal impulse being greater than the collision impulse. This is no numerical, just a conceptual doubt.
 A: This is an interesting question.  
An ideal plank (rigid, much heavier than the ball) will not rebound, but a real plank has some elasticity - either in the material itself or as a structure (eg if the plank is supported at the ends and the middle is raised off the ground).  If a heavy solid object is dropped onto it, it will rebound to some extent and jump off its supports.  
This is an example of a multiple collision : body A collides with body B which collides with body C.  Here body C is the Earth.  Except for ideal situations and materials, it is very difficult to predict whether B will lift off the ground and how far.  But you would need to know much more than simply the height from which A is dropped. 
Apart from the masses of the ball m and plank M and the height H from which the ball is dropped, you also need to know something about the elasticity of each collision (A-B and B-C).  This is related to how much kinetic energy is lost during the collision and is conveniently expressed in terms of the Coefficient of Restitution which is defined as :
e = relative speed of separation / relative speed of approach.
A similar problem (Bouncing Superballs) is solved in the following links (p 15 in the first link) :
http://web.mit.edu/8.01t/www/materials/modules/chapter15.pdf
http://hep.physics.wayne.edu/~harr/courses/2130/f99/demonstration1.htm

UPDATE after you addition to the question :
Yes, this is definitely possible.  I have seen it happen myself when a brick has been dropped onto a plank.  Try it for yourself using eg a tennis ball and a ruler. 
