The correct answer is option 4, Kaveri. The river Kaveri does not flow towards the West and does not drain into the Arabian Sea. The Narmada river (option 1) is a West-flowing river that flows into the Arabian Sea. The Tapi river (option 2) is also a West-flowing river that drains into the Arabian Sea. The Periyar river (option 3) is a south-flowing river that drains into the Arabian Sea. Therefore, the only option among the given rivers that does not flow towards the Arabian Sea is Kaveri.