A bench of justices Badar Durrez Ahmed and Siddharth Mridul said "we will think of some names" and listed the matter for hearing on February 19.
During the hearing, Delhi government submitted a list of three names to the bench for setting up the panel. However, advocate Khagesh Jha said several parents have complained against one of the persons in the list due to the manner in which he runs his own institution.
Meanwhile, the association representing the private unaided schools said their participation in the panel is not required as it is the government which is obligated under the Right to Education (RTE) Act to provide free books and uniforms to children belonging to economically weaker section (EWS) and disabled group.
To this, the court said the burden of providing the free books and uniform would be on the government.
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The court on February 5 had asked the government and the private schools to submit names of experts from the field of education also having administrative experience, who could be made part of the committee.
Delhi government had earlier told the court that it favoured bringing uniformity in uniforms and study material provided to EWS kids vis-a-vis other students.