The youth, who identified himself as BHU's B.A. II year student Ashutosh Singh, started started shouting "Modi ji, please listen to the voice of the students community" as soon as the Prime Minister finished his speech and was getting off the stage.
He was immediately whisked away by the police personnel present there.
The commotion apparently did not catch sight of the Prime Minister or other dignitaries accompanying him as the visitors' gallery was a few hundred metres away from the stage.
The policemen who whisked away the youth said he would be "released soon without being booked for any serious crime."
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The students' union in BHU was banned about a decade ago after the varsity campus was rocked by violence. The union has thereafter been replaced by a Students' Council, which has office-bearers elected by "representatives" from each class.
Ashutosh, who was sitting in the Visitors' Gallery, said he had wished to submit a memorandum to the Prime Minister with the demand that the BHU students' union be restored but permission for the same was not granted by the varsity authorities.
Outside, a number of BSP supporters were chased away by police from the Lanka Chauraha, a few hundred metres from the BHU premises, where they were shouting slogans in protest against the visit of the Prime Minister.
Modi's visit came at a time when political temperatures are running high over the issues of Rohith's suicide and JNU student leader Kanhaiya Kumar being sent to jail on charges of sedition.