A bench of justices Gita Mittal and P S Teji will pass the order on the pleas, which the CBI has sought dismissal of on the ground that it was an attempt to delay the proceedings.
Kumar and others have alleged in their applications that Justice Teji should not hear the matter as he had heard the case as a trial court judge earlier.
Kumar was acquitted by a trial court in 2013 in the case pertaining to the killing of five Sikhs by a mob in Delhi Cantonment's Raj Nagar area during the 1984 riots.
Former MLA Mahender Yadav, who was handed a three-year jail term in the matter and is currently on bail, had also alleged that "Justice Teji was exercising keen interest in the matter" and should recuse himself from hearing these appeals.
Besides Kumar and Yadav, convict Kishan Khokkar, who was sentenced to three-year in jail and is on bail, has also filed a similar application.
While acquitting Kumar, the trial court had held five accused guilty and awarded them varying jail terms for being part of the mob that killed the Sikhs.
CBI had moved the high court challenging the acquittal of Kumar in a case relating to the killing of Kehar Singh, Gurpreet Singh, Raghuvender Singh, Narender Pal Singh and Kuldeep Singh, all belonging to the same family, by a mob during the riots.
Besides CBI, the victims' family members Jagdish and Nirpreet Kaur had also challenged the trial court verdict.
The case against Kumar, a former Lok Sabha MP from Outer Delhi, and others was registered in 2005 on a recommendation by Justice G T Nanavati Commission. CBI had filed two charge sheets against him and other accused in January 2010.
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