NEW DELHI — Moulshri Mohan was an excellent student at one of the top private high schools in New Delhi. When she applied to colleges, she received scholarship offers of $20,000 from Dartmouth and $15,000 from Smith. Her pile of acceptance letters would have made any ambitious teenager smile: Cornell, Bryn Mawr, Duke, Wesleyan, Barnard and the University of Virginia.

But because of her 93.5 percent cumulative score on her final high school examinations, which are the sole criteria for admission to most colleges here, Ms. Mohan was rejected by the top colleges at Delhi University, better known as D.U., her family’s first choice and one of India’s top schools.

“Daughter now enrolled at Dartmouth!” her mother, Madhavi Chandra, wrote, updating her Facebook page. “Strange swings this admission season has shown us. Can’t get into DU, can make it to the Ivies.”

Ms. Mohan, 18, is now one of a surging number of Indian students attending American colleges and universities, as competition in India has grown formidable, even for the best students. With about half of India’s 1.2 billion people under the age of 25, and with the ranks of the middle class swelling, the country’s handful of highly selective universities are overwhelmed.