Rajiv Ranjan Prasad Sinha was the first elected Chairman of the Bihar Legislative Council — option 2.

The setting. The Government of India Act, 1935 gave provincial autonomy and provided bicameral legislatures in six of the eleven provinces, Bihar among them. Elections were held under the Act in 1937, and the two chambers — the Bihar Legislative Assembly and the Bihar Legislative Council — began functioning from that year, with the Council presided over by a Chairman elected by its own members.

Why the Council survives in Bihar. Under Article 169, a Legislative Council may be created or abolished by Parliament, but only on a resolution of the state Assembly passed by a special majority. Bihar is one of the few states that still has one, with Uttar Pradesh, Maharashtra, Karnataka, Andhra Pradesh and Telangana. Its members are elected in part by the members of the Assembly, in part by local authorities, in part by graduates and by teachers, with a share nominated by the Governor for distinction in literature, science, art, the cooperative movement or social service.

Why option 3 is a trap. Rajendra Prasad is the name most associated with Bihar in this period, and he was President of the Constituent Assembly from 1946 and first President of India from 1950 — but he did not hold this provincial office. A candidate reaching for the most famous name will pick him.

What the Council does. As a second chamber it can delay but not block ordinary legislation, has no effective power over money bills, and its main value is as a revising chamber and as a route into the legislature for those who have not fought a general election.

Hence, the answer is Rajiv Ranjan Sinha.