A major National Park in Kerala known for its tiger population is:

Periyar
Eravikulam
Silent Valley
Mathikettan Shola

The correct answer is A) Periyar.

Periyar National Park is a national park in the Western Ghats mountain range of Kerala, India. It is one of the most popular tourist destinations in Kerala and is known for its tiger population. The park is also home to a variety of other wildlife, including elephants, leopards, deer, and monkeys.

Eravikulam National Park is a national park in the Idukki district of Kerala, India. It is located in the Western Ghats mountain range and is known for its high altitude grasslands and its population of Nilgiri tahr, a type of wild goat.

Silent Valley National Park is a national park in the Palakkad district of Kerala, India. It is located in the Western Ghats mountain range and is known for its dense forests and its population of endangered species, including the lion-tailed macaque and the Nilgiri tahr.

Mathikettan Shola National Park is a national park in the Idukki district of Kerala, India. It is located in the Western Ghats mountain range and is known for its shola forests, a type of tropical montane forest. The park is also home to a variety of wildlife, including elephants, tigers, leopards, and deer.