However, the TDP hit back at the opposition party after its ally, the BJP, threw its weight behind the ruling party.
Narayana holds the charge of Municipal Administration department, wehereas Rao, who is his close relative, is the HRD Minister.
BJP Floor Leader P Vishnu Kumar Raju said it was a "simple logic" that the purported leak could have made no difference in a matter of just five minutes.
Chief Minister N Chandrababu Naidu said the government would take action against the guilty but he wanted the YSRC to specify if the purported leak was a whistleblower's act or a case of a sting operation.
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"The ball is in your court. You first tell if it was a whistleblower or a sting operator (referring to a reporter of a newspaper of YSRC ) who brought out the leak. I will spare none," the Chief Minister told the Leader of Opposition Y S Jaganmohan Reddy.
Jagan, however, stuck to his demand that the government should order a CBI enquiry, saying that minister P Narayana's educational institution was involved in the whole affair.
Amid the noisy scenes, Speaker Kodela Sivaprasada Rao left it to the House to decide whether a CBI inquiry or a judicial probe be ordered.
Earlier, the day began on a stormy note with the YSRC MLAs storming the Speaker's podium, demanding immediate action against the ministers.
The minister Rao clarified that the government itself had detected the leak and also identified Narayana educational institution as the source.
"We have already initiated disciplinary action against some officials," he said.
"The leaks happened not just in one place but at three-four places, and everywhere the source was Narayana institute. While small employees are being punished, the guilty ministers are being let off. So, a CBI inquiry is inevitable to nail the minister," Jagan said.
Amid the heated arguments, BJP floor leader Vishnu Kumar Raju intervened to say that any leak with "just five minutes" for the examination could have made no difference as spelling out answers for many descriptive questions was not possible in such a short time.