The pent-up hopes and frustrations of India’s young people found a release in a protest movement that gathered steam this past week in the capital, New Delhi.

A crowd of thousands was mobilized by a call by the leaders of a youth movement to reform India’s troubled education system and to push for the resignation of the country’s education minister, Dharmendra Pradhan, whom they blamed for a botched college-entrance exam that left millions in the lurch.

On Saturday, Mr. Pradhan submitted his resignation to Mr. Modi, handing the protesters a major win. But it wasn’t immediately clear that the protesters would call it a day given that their grievances have grown since a violent crackdown by police on Monday. The beating of demonstrators fueled people’s anger and the spirit of the protests has become more inclusive, attracting activists and academics, curious teenagers, blue-collar parents and children from affluent homes, established celebrities and newly minted influencers, atheists, farmers, religious leaders, and even a man wearing a Spiderman mask.

The movement may continue to pose one of the most substantial challenges in years to the leadership of India’s prime minister, Narendra Modi. The anger is hard for him to ignore, with young people accounting for 40 percent of India’s population.

Here are some of their voices:

AMAL HAYAT, 20

Amal Hayat, 20, a student of electrical and computer engineering at Delhi’s Jamia Millia Islamia University, is the kind of young person whose ambitions are essential to Mr. Modi’s vision of a “Vikshit Bharat,” or developed India, by 2047.

She is the first woman in her family to go to college — a point of pride — and said she chose engineering because she had a head for math and wanted to pursue a career in artificial intelligence. “Solving problems gives me peace,” she said.

She joined the protests not because of a person, or a political party or movement. “It’s about the issues, the students, it’s about the future of the country,” she said.

And, for her, it’s about fairness. She walked around the protest grounds on Thursday afternoon, holding a large sheet of paper on which she had scrawled in black ink: “Sticks for students, garlands for rapists.”

Ms. Hayat, 20, said she was making a point about impunity. She contrasted the batons used by security forces to hit protesters as they marched toward Parliament on Monday, to the treatment of some Indian politicians who continue to enjoy the perks of public life even as they face criminal cases against them for serious charges, including rape.

“So what kind of justice is this?” she asked.

ANSHU GUDIYA, 13

Anshu Gudiya, an eighth-grader who lives in Faridabad, a city in the greater Delhi area, said she came to the protests to see what the fuss was all about, even if it meant taking a day off from school.

Her father works in a hotel in Delhi, and her mother is a tailor. Her parents allowed her to go by herself, she said, because the scandal that ignited the protest movement — the botched college exam — “also affects my future.”

Science is her favorite subject at school, Anshu said, and she wants to study machine learning and artificial intelligence, two subjects that require government-administered exams to get into top public engineering schools. She has not thought about her future beyond that, but hopes someday to “work at Google.”

Anshu said it took her more than three hours, after multiple train changes and a ride on a rented bike, to reach the protest site, next to the 18th-century Jantar Mantar observatory. She came prepared for Delhi’s merciless sun, with a head scarf and sunscreen.

She had first heard about the protests and the group behind them, the Cockroach Janta Party, on Instagram. “I also wanted to see the protest for myself,” and to understand how people conduct demonstrations against the government, said Anshu.

CHANDAN KUMAR, 28

Chandan Kumar, 28, is a delivery driver, not a student, but the protest movement’s demands resonated with him.

Like millions of India’s young people, he was forced to choose between pursuing school and finding a job. He said he dropped out of high school after his mother fell ill, and the family needed extra income to cover her medical costs. He found work in construction, and eventually gave up his dreams of going back to school.

At one point, he said he learned how to use Excel and interviewed for data entry jobs, but could not type fast enough. In 2018, he found a job as a delivery agent for a popular online food platform. “When a person is left with no options, they have to do whatever comes their way,” Mr. Kumar said.

The work is “decent enough,” Mr. Kumar said, as he sat on his motorbike, taking a break from delivering food that customers had ordered for the protesters, from pizza to vegetable curry.

Mr. Kumar said he supported the protesters’ demand that the education minister resign. He was hopeful that the education system would be fixed so that his child can have a better future. “Compared to where I am, my child will reach a place that is a hundred times better.”

ZAFAR HABIB

Zafar Habib’s future doesn’t directly rest on the outcome of the protest movement. The son of a math professor and an activist mother, Mr. Habib, 22, is a history graduate from a private university, and is headed to Oxford University for further studies.

But although he said he had not faced the same educational challenges, he joined the protests out of solidarity and a sense that the outpouring of anger is a significant moment for the country.

People who had grown up seeing little other than “bigotry, fear-mongering and hatred” under Mr. Modi’s Hindu nationalist government, which has been in power since 2014, were getting the chance to “express a love for each other,” he said. It resonated with him as a Muslim, Mr. Habib said, adding that he had suffered taunts as a child because of his last name.

People were helping each other, handing out free food and water, and joining hands to be heard, he said. The humanity he has witnessed made Mr. Habib hopeful that once people go back to their daily lives, “we will carry this kindness forward.”

The student protests that have gripped India sent thousands of young people into the streets on Friday, where some were beaten by the police, as the government sought to buy time in negotiations with the movement’s leaders without conceding to their central demand.

In Mumbai and New Delhi, thousands of demonstrators turned out again to vent their anger over a botched medical school entrance examination that affected millions of young people, and a wider sense of frustration about a lack of jobs and opportunity. In Kolkata, police used batons to disperse crowds of thousands, according to local media reports, and there were demonstrations in Chennai, Hyderabad, Pune and Jaipur, as protests reached cities across India on Friday.

The youth-led protest movement is posing one of the most substantial challenges in years to the leadership of India’s prime minister, Narendra Modi. Many of the protesters are students, and others are working, but they share a sense of desperation and rage about education and employment prospects. Their anger is hard for Mr. Modi to ignore, with young people accounting for 40 percent of India’s population.

The self-described Cockroach Janta Party, which derived its name from an insult, is the driving force behind the protests. The group said on Friday that it would press for demonstrations nationally until Dharmendra Pradhan, India’s education minister, stepped down, a demand it has framed as nonnegotiable.

The group holds Mr. Pradhan directly accountable for the leak of the exams, which led to canceled results. But he is a key operative in Mr. Modi’s ruling Bharatiya Janata Party, credited with helping the party come to power in some recent state elections.

After talks with government ministers on Friday, Ashutosh Ranka, a spokesman for the protesters, said in a social media statement that the government had agreed “in principle” to compensate families affected by the suicides of students and would take “no legal action against protesters.” According to the C.J.P., at least 21 students have died by suicide since the exam leak, unable to handle the stress.

The government has requested more time to respond to the demand for the removal of the education minister, and another round of discussions is planned for Saturday.

Saurav Das, another spokesman for the protesters, said that, once they had achieved their main goal, the resignation of Mr. Pradhan, the group would also ask the government to consider its far more sweeping agenda for change, including judicial reforms, gender quotas for Parliament and punishments for politicians who switch political parties after being elected.

The prospect of an organized, student-led opposition to Mr. Modi, an acutely image-conscious leader, has added a new challenge to his recent days in office. He is also managing economic difficulties caused by the war in Iran and recently led his party to power in a series of state elections.

Some of the students’ fury is turning directly on him, but his response so far does not appear to have satisfied them. On Thursday, he posted on social media that “Nothing is more important than the welfare and future of our youth!” He has promised fast-track tribunals to punish those responsible for the exam leak. Even that acknowledgment was rare for Mr. Modi, a strongman leader, who must balance the need to placate the students with a desire to make sure that his political party does not look weak.

The protests in New Delhi and elsewhere have been going on for more than a month. But the protesters’ call to march to Parliament on July 20, its first day in session, has given the movement momentum. Thousands of people gathered in the capital for the march, and many have remained camped out at the protest site for days despite the authorities’ calls to disperse.

Anupreeta Das, Alex Travelli and Mujib Mashal contributed reporting.