Correct Answer: Option A - 1 only
Idukki and Pathanamthitta are landlocked and share border with Tamil Nadu.
This statement is correct. Both Idukki and Pathanamthitta are landlocked districts of Kerala. Idukki shares a border with Tamil Nadu in the east, and Pathanamthitta also shares a border with Tamil Nadu in its eastern part.
Alappuzha is surrounded by districts on all sides and has no coastline.
This statement is incorrect. Alappuzha is famous for its beaches and backwaters and has a significant coastline along the Arabian Sea. It is not surrounded by districts on all sides.
Palakkad shares borders with both Tamil Nadu and Karnataka.
This statement is incorrect. Palakkad shares a border with Tamil Nadu to the east through the Palakkad Gap, but it does not share a border with Karnataka. The Kerala districts that share borders with Karnataka are Kasaragod, Kannur, Wayanad, and Kozhikode.