The CBI recently submitted its final report before the fast-track court dealing with "criminal cases arising from paper leaks as well as the use of other unfair means in public examinations".
The plea sought the court's permission as the accused wanted to "demonstrate their bona fides" and assist the agency to conduct a "fair and transparent investigation."
The three accused moved an application seeking permission for a polygraph (lie-detector) test and Brain Electrical Activation Profile (BEAP) examination, also known as brain mapping.
Raj Thackeray also asked who would apologise to student protesters who were assaulted and faced police firing and pellet guns while protesting in Delhi.
