The notices were issued by Justices V M Kanade and Shalini Phansalkar-Joshi, who heard the public interest litigation (PIL) filed by Supreme Court lawyer Vineet Dhanda.
The Union Ministries of Information and Broadcasting and Home are respondents in the petition, which has prayed that the Centre may be directed to end the ongoing crisis at Film and Television Institute of India (FTII).
The PIL also prayed for a direction to the Centre to make transparent policies for the appointment of heads/chairpersons of such institutions in future.
Jayprakash Dhanda, lawyer for the petitioner, said there is resentment among students over the appointment of TV actor Gajendra Chauhan as the institute's chairman.
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He said the students are demanding that a more experienced and talented person from the industry may be appointed as the head of FTII so that they can benefit from his teaching.
However, the judges said that they would consider this only after the petitioner had served all the respondents and after all the parties were heard in the matter.
The petition was posted for further hearing after two weeks.
The students have been boycotting classes since June 12 opposing appointment of Chauhan, who they claim lacks credentials to head FTII.
The I&B Ministry has, however, cold-shouldered their main demand for cancellation of Chauhan's appointment while keeping the dialogue channel open to resolve the prolonged deadlock that has brought academic activity on the campus to a standstill.