Gandhi, who asked students to refer to him as Rahul, said the law must apply to everybody and not be applied selectively. He said this in response to a question on his brother-in-law Robert Vadra, who is being probed in connection with a money laundering case related to purchase of assets abroad and a land case in Rajasthan's Bikaner district.
"Law should apply to everybody equally. Prime Minister Narendra Modi has his name in government documents which say that he is directly responsible for negotiating parallelly with Dassault on Rafale deal. Investigate everybody," he said. "I will be the first person to say it... Investigate Robert Vadra but also investigate Prime Minister Narendra Modi."
Gandhi, who asked the students to challenge him and "make him uncomfortable", also questioned whether the prime minister could stand in a large audience and answer people's questions.
"How many times have you seen the PM of India standing here like this, being open to any question from anybody? Why doesn't the PM have the guts to come and stand in front of 3000 women and be questioned by them?" Gandhi asked.
He said the UPA defeat in 2014 taught him several lessons. "I learn from Modi. I don't hate him. Do you hate the person who teaches you?" Gandhi asked to students and got a big "No" as the answer. "The biggest teachers are the people who attack. The more you are attacked, the more you give love and affection back."
Gandhi told the students that the economic growth is directly related to the mood of the nation and one cannot expect it to happen in a negative and fearful atmosphere. "You cannot have a negative atmosphere in the country and expect economic growth. The economic growth is directly related to the mood of the country. We will move the country to a place where people feel empowered and happy."
On bringing peace back in Jammu and Kashmir, he said the first step was to build the bridge to the people there. It was built between 2004 and 2014 during the UPA government.
"When we came to power in 2004, policies of the Vajpayee government had set fire in Jammu and Kashmir. We decided to fight terrorism strategically. Firstly, we isolated Pakistan all over the world and then we engaged with the population of Jammu and Kashmir," Gandhi said.
As a result, terror attacks came down drastically and power was given to the people by holding elections.
"The moment Mr. Modi came to power, he made a mistake of forming alliance with the PDP. Today, his policies are actually setting fire to Jammu and Kashmir. His policies are pushing people away and allowing Pakistan to carry out terrorism in India."
To a question on the status of women in the country, he said the situation was better in south India than in north India.
"South India is significantly better than North India in the way women are treated. Tamil Nadu is one of the leaders in how it treats its women. However, there is still a lot of improvement required in Tamil Nadu as well," Gandhi said.
He said the UPA will reserve 33 per cent government jobs for women and pass the Women's Reservation Bill giving 33 per cent of seats in the Lok Sabha if it wins 2019 elections.
"Women should be at the same level as men. Frankly, I don't see enough women in leadership positions. We are going to pass the Women's Reservation Bill in the Parliament and we are going to reserve 33 per cent of government jobs to women."
Gandhi also called his party's minimum income guarantee scheme a revolutionary idea.
(With inputs from agencies)