Since irifan2015 and Sourav has explained you clearly everything many times, you fail again and again to understand the reality. It is a valid question as to why long distance passenger trains are not operated from the state capital in TN. I'll again tell you the fact behind the operation of long distance passenger trains in Karnataka connecting state capital.
As you know, in Tamil Nadu ---> Buses are operated to everywhere and thousands of buses are operated to Chennai in a day by the state government at nominal rates so that the "poor" people of the state get benefitted. That's why in TN, long distance passenger trains are not operated connecting the state capital instead express and superfast trains are...
more...

operated.
As our friends Sourav and irifan2015 said, in Karnataka ---> Buses are operated by the state government from all over the state to Bengaluru, but at not so nominal prices, which the "poor" people of Karnataka cannot afford. Instead, SWR does the duty and runs passenger trains to the state capital Bengaluru.
Now I think you might have understood as to why passenger trains are operated in Karnataka to and from the state capital and not in Tamil Nadu.
Am I right Sourav and irifan2015?