The court also asked several questions to the Shinde camp on various issues.
Maharashtra Chief Minister Eknath Shinde's faction on Tuesday claimed their right to the Shiv Sena party and said that a legislature party is integral and organically connected to the political party.
Senior Advocate NK Kaul, appearing for Shinde faction, told a five-judge constitution bench that rival leaders had no faith in the ministry any longer.
Five-judge Constitution bench of Chief Justice DY Chandrachud, Justices MR Shah, Krishna Murari, Hima Kohli and PS Narasimha was dealing with the issue related to Maharashtra political crisis.
Justice Narasimha, who was part of the bench, asked the Shinde camp to show that they have a political majority and not a legislative majority.
Senior Advocate NK Kaul, replied to the court that he would address this issue on Wednesday.
The court also asked several questions to the Shinde camp on various issues, legal aspects on various judgements and sought to know how to separate defection and floor test.
CJI Chandrachud also remarked that if the antecedent reason for a floor test is based on a violation of the tenth schedule, then holding a floor test at that stage will defeat the whole basis and purpose of the tenth schedule. The court also sought to know if they are legitimizing a defection which is otherwise not permissible under the tenth schedule.
Advocate replied that their case is not a case of split under the tenth schedule, they are talking about a rival faction within a party which is dissent and the essence of democracy within a party and they claim that their camp is the Shiv Sena.
During the hearing, the court noted that the problem which necessitated the floor test is an alleged defection and said the problem arises because the trust vote is so intrinsically connected with the disqualification proceedings.
Senior Advocate Kaul said that this is a case of internal dissent and the Shinde group is the faction that represents Shiv Sena, which can be decided by the Election Commission of India. As far as floor test is concerned, it is only related to the issue of whether the Chief Minister has the confidence, Kaul said.
The court also noted that the head of the political party did not inform the Governor that they were withdrawing from the alliance of Maha Vikas Aghadi (MVA).
Kaul replied that 34 out of 55 have written to the Governor saying they had no faith in this government.
As the hearing remained inconclusive on Tuesday, the matter was adjourned for Wednesday.
Uddhav Thackeray faction had earlier submitted that the opposite camp has no defence under the tenth schedule.
A five-judge Constitution bench was hearing a batch of petitions filed by rival factions Uddhav Thackeray and Chief Minister Eknath Shinde in relation to the Maharashtra political crisis.
The Supreme Court's Constitution bench has earlier said it would decide later on referring the cases related to the Maharashtra political crisis to a larger seven-judge bench for reconsideration of a 2016 Nabam Rebia judgment on powers of Assembly Speakers to deal with disqualification pleas.
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