**a number N is formed by writing 9 for 99 times what is the remainder if N is divided by 13 **

**11****9****7****1**

we get remainder 0 when 9 is six times ‘999999’. It means The remainder of 999999…99 (96) times is 0 when divide by 13.

So the required remainder =(Remaining **9 for 3 times **)/13= 999/13⇒511