Introduction:
An axial flow compressor is a type of compressor used in gas turbine engines to compress the incoming air. The degree of reaction is an important parameter that characterizes the performance of an axial flow compressor. It is defined as the ratio of the change in static pressure to the change in total pressure across each stage of the compressor.

Explanation:
The degree of reaction in an axial flow compressor is expressed as a percentage. A degree of reaction of 50% means that half of the total pressure rise across each stage is converted into static pressure rise, while the other half is converted into kinetic energy. This has several implications:

1. Symmetrical blades:
When the degree of reaction is 50%, it implies that the compressor blades are symmetrical. Symmetrical blades are designed to have equal pressure rise on both the pressure and suction sides, resulting in a balanced flow through the compressor. This helps to minimize losses and improve the overall efficiency of the compressor.

2. Optimum pressure after compression:
A degree of reaction of 50% ensures that the pressure after compression is optimized. This is because the equal distribution of pressure rise between static pressure and kinetic energy ensures that the overall pressure ratio is maximized while minimizing losses due to excessive kinetic energy.

3. Effective stages:
Contrary to option (b), a degree of reaction of 50% does not imply that 50% of the stages of the compressor will be ineffective. Each stage of the compressor plays a crucial role in increasing the pressure of the air. The degree of reaction simply characterizes the distribution of pressure rise across each stage, but it does not determine the effectiveness of the stages.

4. Work done in compression:
Option (a) states that the work done in compression will be the least when the degree of reaction is 50%. This is not necessarily true. The work done in compression is determined by the pressure ratio across each stage and the overall compression ratio of the compressor. The degree of reaction does not directly affect the work done in compression.

Conclusion:
In summary, when the degree of reaction is 50% in an axial flow compressor, it implies that the compressor blades are symmetrical, the pressure after compression is optimized, and the overall efficiency of the compressor is improved. It does not imply that 50% of the stages will be ineffective or that the work done in compression will be the least.