The question asks us to identify the river that Shirosha, Hemavati, and Arkavati are tributaries of.
Option 1: Tapti - Shirosha, Hemavati, and Arkavati are not tributaries of the Tapti river.
Option 2: Tungabhadra - Shirosha, Hemavati, and Arkavati are not tributaries of the Tungabhadra river.
Option 3: Kaveri - Shirosha, Hemavati, and Arkavati are all tributaries of the Kaveri river. This means that they flow into and contribute to the water flow of the Kaveri river.
Option 4: Krishna - Shirosha, Hemavati, and Arkavati are not tributaries of the Krishna river.
Therefore, the correct answer is option 3: Kaveri. Shirosha, Hemavati, and Arkavati are tributaries of the Kaveri river.