A popular dual-purpose cattle breed native to Tamil Nadu is:

Kangayam
Gir
Tharparkar
Sahiwal

The correct answer is Kangayam.

Kangayam cattle are a dual-purpose breed of cattle native to the Kangayam region of Tamil Nadu, India. They are known for their hardiness, strength, and docility. Kangayam cattle are used for both milk and meat production. They are also used as draft animals.

Gir cattle are a breed of cattle native to Gujarat, India. They are known for their large size, milk production, and docility. Gir cattle are also used as draft animals.

Tharparkar cattle are a breed of cattle native to the Thar Desert of India and Pakistan. They are known for their hardiness, drought tolerance, and milk production. Tharparkar cattle are also used as draft animals.

Sahiwal cattle are a breed of cattle native to the Punjab region of Pakistan. They are known for their large size, milk production, and docility. Sahiwal cattle are also used as draft animals.

Kangayam cattle are the only breed of cattle native to Tamil Nadu. They are also the only breed of cattle that is specifically adapted to the climate and terrain of Tamil Nadu. Kangayam cattle are therefore the best choice for farmers in Tamil Nadu who are looking for a dual-purpose breed of cattle that is both hardy and productive.