2. There is a class of four-digit numbers that, when divided by 5, leave a remainder of 1; when divided by 7, leave a remainder of 4; and when divided by 11, leave a remainder of 9. What is the smallest four-digit number in this class?
【Analysis】Let the required number be $5a+1$, then we have $5a+1 \equiv 4(\bmod 7) \Rightarrow a \equiv 2(\bmod 7)$. Let $a=7b+2$, then the required number is $35b+11$, and we have $35b+11 \equiv 9(\bmod 11) \Rightarrow b \equiv 10(\bmod 11)$. Let $b=11c+10$, then the required number is $385c+361$. Therefore, the smallest four-digit number is $385 \times 2+361=1131$.