Justices K K Sasidharan and G R Swaminathan of the Madurai bench gave the direction on a petition, which claimed that no girl student in the state had benefited under the National Scheme of Incentive to Girls for Secondary Education, after 2009.
Rejecting the petitioner's claim, the Centre's counsel said it was wrong to say that funds were not given under the scheme to the students in Tamil Nadu.
Earlier, the petitioner submitted that no girl student in the state had received the incentives after 2008-09.
Recording the submissions, the judges said the state's principal secretary of School Education should send a fresh proposal to the Union human resource development ministry and social justice and empowerment ministry, which should be considered and funds sanctioned.
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Disposing off the petition, the judges refused to concur with the contention of the Centre's counsel that many students would have completed their education and it might not be possible to trace them.
The Centre had launched the scheme in 2008-09 in a bid to reduce the dropout rate among the Adidravidar and tribal girl students and promote the enrollment of girls in the age group of 14-18 in educational institutions.
Under the scheme, an amount of Rs 3,000 is deposited in the bank accounts of the eligible girl students, which can be withdrawn after they turn 18 and clear their Class 10 board exam.