Main answer: VERY poorly worded question. As given, NONE of the answers are correct, and the best one can do it give a "best" answer - meaning, the least wrong.
"Amount of heat given off ... " I assume actually meant to ask the heat output RATE, or WATTS of heat being given off. Actually, Watts x time gives the real "amount of heat", but I really expect the questioner thought in terms of heating rate.
IF we are asked about heat rate, or Watts, the formula for Power in Watts is P = V x I. We are not given any V or I values, or even an option to give one of those as an answer! If voltage V is connected across a Resistor R, then the P = V^2/R. Or, if one applies whatever voltage across a Resistor R to achieve a current flow of I amps, P=I^2R. So, the Power (heating RATE) is determined by any TWO of: Voltage, Current, Resistance. None of these choices is available for an answer.
Among the answers available, which is "best"? Well, neither Tolerance nor Temperature Coefficient has any direct impact on the heat output rate. Resistance alone does not determine that, either. BUT, from another perspective, the amount of heat that a resistor can give off WITHOUT breaking down due to overheating is determined mainly by its physical size. A larger unit but with the same Resistance value can work at larger voltages and currents without overheating.
One clue to the "best" answer is not in the question - it's where the question was asked: in a Military Technical School test. From the very practical perspective of an electronics tech working on equipment, "where does the most heat comes from" as you examine a circuit board relates to things like:
Where and how do we need to ensure good cooling?
What components are most likely to be hot enough to burn you when touched?
And the easy answer you can literally SEE as you work is: the LARGER resistors, because they have to be large to dissipate all the heat being generated without being destroyed themselves.