Step 1: Understand the question.
We must find why Navodaya Vidyalayas were started. These are special residential schools run by the central government.
Step 2: Recall their background.
The National Policy on Education of 1986 planned these schools. The aim was to give good quality, free education to talented children.
Step 3: Find the target group.
These schools were meant mainly for bright children from villages who often miss out on good schooling. So the focus is rural children.
Step 4: Compare the options.
The options about urban children do not match, because the scheme targets villages. The phrase rural children of central government is too narrow and wrongly worded.
Step 5: Pick the clean answer.
The simple and correct aim is to serve the rural children. That option says exactly this.
Step 6: Match with the options.
The third option, To serve the rural children, is correct.
\[ \boxed{\text{To serve the rural children.}} \]