The Minister for Textiles and Information and Broadcasting also said people have respect, "grudgingly or ungrudgingly," for those who had come from the humblest of the backgrounds and made a mark with their contribution.
The Rajya Sabha MP from Gujarat recalled Modi's childhood days of selling tea in a railway station in that state, referring to his humble background.
She was addressing students of Vels University at a "Sankalp se Siddhi" programme near here.
"The fact that our democracy gives wings to such dreams brings hope to so many people across the nation is one thing we all as Indians can be extremely proud of," she said.
Irani said that as a woman she was proud Lok Sabha Speaker Sumitra Mahajan was a woman.
The country's President was from the "marginalised community," she added.
The minister recalled that Modi was born in a village "which barely had electricity" and he had "resolved" to ensure that the benefits people deserve did not go to middlemen. He "leverages" technology, she added.
On the various initiatives of the three-year-old NDA government, Irani said the 'Jandhan Scheme' was launched with the aim of ensuring every poor person had a bank account.
So far, close to 300 million people have new bank accounts under this scheme and it was almost equal to the population of the U.S., she said.
These 300 million-odd people managed to open bank accounts with the cooperation of banks, Central and state governments, she added.
The Mudra scheme, where loans ranging between Rs 50,000-Rs 10 lakh were given without collateral for entrepreneurs to start a business, had covered about 80 million beneficiaries, she said.
Even 20-30 years back, only the rich could afford to start a business, Irani said.
Such things were "possible when government and people come together," the minister added.
Hailing the sacrifices of freedom fighters on the occasion of the 75th year of Quit India movement, she urged the students to contribute towards a prosperous India.
Later, the students took the 'Sankalp Se Siddhi' pledge, vowing to make India free from menaces like corruption, casteism and communalism.
Irani asked BJP State President Tamilisai Sounderrajan, also present at the event, to administer the pledge to the students in Tamil and the latter followed suit.
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