Step 1: Know the term.
A National Research Centre, or NRC, is a special ICAR centre that works on one chosen crop or topic.
Step 2: Count them in Bihar.
Bihar has just one such centre, the National Research Centre for Litchi at Muzaffarpur. Other ICAR units in the state, like the centre in Patna, fall under different groups and are not counted as NRCs.
Step 3: Final pick.
So the number of NRCs in Bihar is one.
\[ \boxed{\text{One}} \]