IIT Kharagpur had suspended Kumar for "misconduct" in May 2011, the same year the Supreme Court had lauded him as an "unsung hero" for his efforts to reform the IIT Joint Entrance Examination (JEE), which has since been re-christened as JEE Advanced.
The institute set up a probe panel that found him guilty.
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In 2014, the IIT decided to compulsorily retire him.
Kumar, who alleged that the panel was biased, had moved the Delhi High Court and obtained a stay on the IIT's decision. He had also appealed to the then president requesting that the order be quashed.
While he had resigned in 2014, the institution had not accepted his resignation saying the matter was sub-judice.
"(Former) President and Visitor of IIT Kharagpur has set aside the penalty of compulsory retirement on professor Rajeev Kumar...The institute accepts his technical resignation in view of the HRD (Human Resource Development) communication following the presidential order," an official memorandum said.
Following the high court's stay order, Kumar had taken lien for two years and joined Jawaharlal Nehru University (JNU) in 2015. However, he was relieved from JNU in June to allow him to re-join IIT Kharagpur.
The professor has appealed to the JNU vice-chancellor to reinstate him as his penalty has been quashed and resignation accepted.
JNU Vice-Chancellor M Jagdeesh Kumar, when contacted, did not comment on the issue.
Days before he demitted office last month, Mukherjee had ordered setting aside of the penalty imposed on Kumar.
The HRD ministry had last week an issued order to the IIT Kharagpur director to comply with the former president's order.
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