Option 1 - Periyar. This river does not join the Arabian Sea. It is located in the state of Kerala and flows through the Western Ghats before merging with the Vembanad Lake.

Option 2 - Cauvery. This is the correct answer. The Cauvery river originates in the state of Karnataka and flows through Tamil Nadu before emptying into the Bay of Bengal. It does not join the Arabian Sea.

Option 3 - Narmada. This river also does not join the Arabian Sea. It originates in the state of Madhya Pradesh and flows through Gujarat before merging with the Arabian Sea.

Option 4 - Tapti. This river, like the Narmada, does not join the Arabian Sea. It originates in Madhya Pradesh, flows through Maharashtra, and then empties into the Arabian Sea in Gujarat.

In summary, the correct answer is option 2 - Cauvery. It is the only river among the options that does not join the Arabian Sea.