Who headed the second 'backward caste commission'? 

The correct answer is option 4 i.e B.P Mandal.

B P Mandal:

• The Mandal Commission was formed in the year 1979.
• The commission was chaired by the B. P. Mandal.
• It was the second backward caste commission
• The commission was formed to determine the criteria for defining India’s “socially and educationally backward classes” and to recommend steps to be taken for the advancement of those classes.

The Kaka Kalelkar Commission:

• It was set up in 1953.
• The commission was set up under the chairmanship of Kaka Kalelkar
• It was the first to identify backward classes other than the Scheduled Castes and Scheduled Tribes at the national level. 

Fazal Ali Commission:

• In December 1953, the Government of India appointed a 3 member States Reorganisation Commission under the chairmanship of Fazl Ali to examine the question of the creation of states on a linguistic basis. 
• The commission accepted language as the basis of the reorganization of states, but rejected the theory of ‘one language–one state’.