1.Rajdhani Express trains are a series of trains that are operated between the national capital(Rajdhani means capital in Hindi) and the state capitals(there do exist some exceptions like BSP Rajdhani where Rajdhani doesnt terminate at state capital and runs to BSP which is an important place in the state). They are operated at high speeds with AC classes of accomodation and on board catering and are supposed to provide fastest connectivity between the state and the national capital.
2.Shatabdi(means 100 years in Hindi and other languages) Express trains were introduced to commemmorate former PM Jawaharlal Nehru's birth centenary. Shatabdis are almost like Rajdhanis at the state level. They are used to provide faster connectivities between metros and important places which are separated...
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by a shorter distance within or outside the state. They are fully air conditioned trains and have onboard catering. They return to their base on the same day.
3. Duronto means fast or restless in Bengali. They are supposed to be faster than Rajdhanis and Shatabdis or atleast equal them in speed and service.. The original concept of Duronto was to provide a non stop service between source and destination with only technical stops in between. But later on, they were converted into commercial halts and additional halts were added. They provide faster connectivity among national and state capitals and also important metros and places of various states. Duronto may be fully air conditioned train or have SL class of accomodation with onboard catering.