Which of the following statements is correct about Chaghtai Turks?

a- Chagtai Turks traced descent from the eldest son of Genghiz Khan.

b- The Mughals were Chaghtai Turks by origin, Turkish was their mother tongue. 

Both statements are correct.

Mughal court chronicles were written in Persian. Under the Sultans of Delhi, it flourished as a language of the court and of literary writings, alongside north Indian languages, especially Hindavi and its regional variants. As the Mughals were Chaghtai Turks by origin, Turkish was their mother tongue. Their first ruler Babur wrote poetry and his memoirs in this language.

Chagtai Turks traced descent from the eldest son of Genghiz Khan.