Their resignations came in the wake of the agitation by the students of FTII demanding removal of small screen actor Gajendra Chauhan as chairman of the institute.
Pledged her support to the agitation by the students, Joshi told PTI, "There is no point in continuing as member of the FTII Society if the students with whom I wanted to interact as future prospects of the film industry, are unhappy."
Asked if she would reconsider her decision on request from authorities concerned, she said, "I am firm on my stand supporting the students' demands".
"I do not want to see the students of this premier institute joining the film industry unsatisfactorily with half-baked knowledge," Joshi said.
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Barua, who is an alumnus of the FTII, said he had shown his reservations of not being a part of the institute for a long time.
"I had conveyed my resignation to the director of FTII through a mail. I had been showing my unwillingness for a long time due to the protest. I don't want to be in it anymore," he told PTI.
"I have always been assisting government on the matter of FTII. I shall continue to do so. It's my duty to assist because I am emotionally attached to it," Barua said.
The nomination of Barua, Joshi and other members to the FTII society was announced by the Information and Broadcasting ministry last month.
The agitation, which has received the support of many leading personalities of Indian cinema, entered the 25th day today with students boycotting the academic work after failure of their talks with Information and Broadcasting Minister Arun Jaitley in New Delhi last week.
While welcoming the ministry's assurance of upgrading the institute, the FTII Students' Association has declared that the strike will continue till removal of Chauhan, who they allege lacks vision and stature to head FTII, and reconstitution of the FTII Society is accepted.