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Among the options provided, the Sabarmati river basin is the shortest in length and smallest in terms of catchment area. The Sabarmati river is located in the state of Gujarat in western India.
Option 1: The Cauvery river basin is not the shortest or the smallest in terms of catchment area. The Cauvery river flows through the states of Karnataka and Tamil Nadu and has a larger catchment area.
Option 2: The Mahi river basin is not the shortest or the smallest in terms of catchment area. The Mahi river flows through the states of Madhya Pradesh and Gujarat and has a larger catchment area.
Option 3: The Penner river basin is not the shortest or the smallest in terms of catchment area. The Penner river flows through the states of Andhra Pradesh and Tamil Nadu and has a larger catchment area.
Therefore, among the given options, the correct answer is option 4, Sabarmati.