The petitions included those filed by Congress MLA Lakshminarayanan and the three nominated legislators.
In their petitions, the three nominated MLAs -- V Saminathan, K G Shankar and S Selvaganapathi, challenged the notice issued by the Puducherry assembly secretary refusing them permission to attend House proceedings.
The Assembly secretary had said that according to the speaker's decision, their nominations were not valid.
The Puducherry Assembly speaker had rejected nomination of three BJP members to the House by the Centre. He had said their nomination was void as it was in contravention of the constitutional provisions and made by an "incompetent authority".
The first bench comprising Chief Justice Indira Banerjee and Justice M Sundar reserved orders on the petitions, after hearing arguments from both sides.
The three nominated MLAs were sworn in as members of the Puducherry Assembly by Lt Governor Kiran Bedi in July.