My passport will expire in 2018 and I want F1 VISA till 2021.?
No, not all. The existing current passport valid upto 2018 will be sufficient for you to apply for your US F1 visa. They will determine the duration of the F1 visa, which will have no bearing on your passport expiring in 2018. While you are in US, six months prior to expiry of your passport, you can apply to nearest Indian Consul in US to get the passport extended. Even after issue of new passport, carry old and new passports, as your US visa would be available in your old passport,