Using a Transistor to "Fully" Illuminate a Lamp
What is meant by "fully illuminate"? Does it mean that the maximum current that can possibly flow through the lamp in the circuit is 100mA?


It's slightly sloppy wording. The reasoning employed by the question is: "If the transistor was replaced by a short circuit between the collector and emitter, how much current would flow?" In that situation, the lamp would have 100mA flowing through it. Therefore we declare that this is the maximum current that would be seen if there was a transistor there.

This figure can be used to (a) determine the base current required and (b) pick a transistor of appropriate size.


  If my interpretation is correct, then I am not able to undersand the reson behind it. If we choose RB very small, then the base current is high. Thus so is the collector current.


No matter how much current you put through the base, the collector current is still limited by Ohm's law applying to the lamp.