The question asks about the sector that received the largest share of Foreign Direct Investment (FDI) between 1997 and 2000. The correct answer is option 2, the Engineering sector. Let`s break this down:

Option 1: Food and food-product sector - While this sector attracts a good proportion of FDI, it didn`t receive the largest share in this period. It caters to a basic need, but it wasn`t the largest recipient during the specified timeframe.

Option 2: Engineering sector - This is the correct answer. The Engineering sector often attracts significant FDI because of its dynamic nature and wide applications. During 1997-2000, this sector received the greatest share of FDI.

Option 3: Electronics and electric equipment sector - This sector also attracts substantial FDI due to high demand and rate of technological advancement, but it wasn`t the top recipient in the given period.

Option 4: Service sector - Although the service sector is a major area for FDI, it didn`t receive the largest share of FDI between 1997-2000.

In summary, while all these sectors typically attract FDI, the Engineering sector was the largest recipient during the specified period.