Introduction:
The propulsive efficiency of a turbo-jet aircraft is a measure of how effectively it converts fuel energy into useful thrust. It is an important parameter that determines the overall performance of the aircraft. In this question, we are asked to determine at what thrust level the propulsive efficiency of a turbo-jet aircraft approaches 100%.

Explanation:
To understand why the correct answer is option 'D' (zero thrust), let's first understand what propulsive efficiency is and how it is related to thrust.

Propulsive Efficiency:
Propulsive efficiency is defined as the ratio of useful work done (thrust) to the energy input (fuel) required to produce that work. Mathematically, it is given by the equation:
Propulsive Efficiency = Thrust Power / Shaft Power

Thrust Power:
The thrust power is the power generated by the engine to produce the thrust force. It is directly related to the thrust force and the aircraft's velocity. As the thrust force increases, the thrust power also increases.

Shaft Power:
The shaft power is the power generated by the engine to drive the compressor and other accessories. It is the power required to operate the engine itself. The shaft power remains relatively constant regardless of the thrust level.

Relationship between Thrust and Propulsive Efficiency:
The propulsive efficiency of a turbo-jet aircraft is inversely proportional to the thrust. This means that as the thrust force decreases, the propulsive efficiency increases.

Explanation of the Answer:
When the thrust force approaches zero, it means that the engine is not producing any useful work or thrust. In this case, the propulsive efficiency approaches 100% because there is no thrust being produced, but the engine is still consuming fuel to operate.

At zero thrust, the numerator of the propulsive efficiency equation becomes zero, while the denominator (shaft power) remains relatively constant. This results in a propulsive efficiency that approaches 100%.

Therefore, the correct answer is option 'D' (zero thrust) because the propulsive efficiency of a turbo-jet aircraft approaches 100% when there is no thrust being produced.