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The correct answer is option 1: Sikkim.
Sikkim does not have a railway station. Although it is the second smallest state in India, it is landlocked and does not have a railway network. This means that there are no train services available for transportation within the state.
On the other hand, options 2, 3, and 4 - Himachal Pradesh, Jammu & Kashmir, and Nagaland, respectively - do have railway stations within their territories. Himachal Pradesh has a narrow gauge railway line called the Kalka-Shimla Railway, Jammu & Kashmir has several railway stations including Jammu Tawi and Udhampur, and Nagaland has the Dimapur railway station.
It`s important to note that while Sikkim does not have a railway station within its borders, neighboring states like West Bengal and Bihar have railway connections that can be accessed from Sikkim.