Correct option is A
The correct option is (a) B, C and E only.
A. (Incorrect): The beginning of historiography in Persian was not prompted by the "rise of Arab-speaking intelligentsia." Instead, it was prompted by the Persian Renaissance (under dynasties like the Samanids in Khurasan) where local elites sought to revive Persian as a literary language, distinct from the dominant Arabic tradition, though they adopted Arabic historical forms.
B. (Correct): Abu Said Gardēzī (author of Zayn al-Akhbar) and Abul Fazal Baihaqi (author of Tarikh-i Baihaqi) were associated with the Ghaznavid court. Their works established the stylistic norms (focus on the Sultan's actions and courtly virtues) that later Indo-Persian historians of the Delhi Sultanate followed.
C. (Correct): Fakhr-i-Mudabbir (Fakhr-ud-Din Mubarak Shah) is considered one of the pioneers of this tradition in India. He dedicated his work to Qutb ud-Din Aibak, marking the start of history writing under the Delhi Sultanate.
Additional Knowledge
A. Beginning of historiography in Persian, was prompted by the rise of Arab-speaking intelligentsia, in the eastern lands of Islamic world. This statement is not entirely accurate; Persian historiography arose due to a variety of factors, and the rise of Arab-speaking intelligentsia was a parallel development, not the direct prompt for Persian historiography.
D. His two literary works are Shajarā-i-Ansab and Chachnama. The two works attributed to Fakhr-i-Mudabbir are Adab al-harb wa-l-shaja'a (or Shajarā-i-Ansab) and Bahr al-ansab. The Chachnama was originally written in Arabic and later translated into Persian by Ali Kufi in the 13th century, it was not one of Fakhr-i-Mudabbir's original works.