For cheap tickets to India there are many options from almost anywhere in the world. There are internet sites advertising the lowest prices or they will match them. One of these is makemytrip.com. They will match any fare that is posted from the US to India. But to find out exactly what their prices are would mean you will have to decide on a date for your trip. The lowest price they offer is $399, these are from New York to either Mumbai or Ahmedabad.
Then there is 4lowfare.com. This site has a special, just in time for the fiesta season. There are limited seats available but fares are starting at $349 excluding taxes. This is an important thing to remember, most low prices do not include the taxes that are associated with the fare.
Another discount fare site is primetravels.com. They are currently taking reservations for passengers from New York to Delhi at $370 plus taxes
Most other sites make offers of low prices like Yatra.com, but they come up short. A flight from New York to Mumbai is at $781 on Kuwait Airlines. The plane and airlines is top notch but the price is not necessarily cheap and there is a stopover in Kuwaiti City.
All of the above examples are for round trip tickets purchased online from their respective sites. If you need a visa to travel to India or at any possible stopover in Europe, then that additional cost is not included. All prices are subject to change without prior notice. But there are many options for cheap tickets to India for under $400 plus taxes.