Which caste is majority in Tamil nadu?

No caste is majority.
By population order (I added all subcastes into single caste),
mutharaiyar(its 29 subcastes)~19%

Vanniars form ~20%

nadar~6%

Kongu Vellalar Gounders form ~8%.

Thevars form ~7%.

Chettiar (excluding Kannada/Telugu origin), Muthaliars, Pillai (tot ~10%).

Scheduled Castes like Paraiyyar, Pallar, Sakkiliar, others together ~18%.

Tamil Brahmins ~3%

~7% is formed by other minor Tamil castes

~4% by non-Tamil origin people like Chettairs (Kannada/Telugu), Naidus/Reddies (Telugu), Nairs (Mallu), Kannadigas and North-Indians.