E-mails being sent to the potential supervisors

[tuba]

I am going to apply to the phd programs in the US. However, I have a small budget and I can make one or two applications. Do you think it would be inappropriate to send e-mails (my CV, SOP and research proposal attached) to the professors to learn my chances of getting admitted?

[fuzzylogician]

What field are you in? It's hard to give an answer that fits your needs without knowing that. I started writing a "if you're in X kind of field, Y is a good course of action" type reply but there are too many if's and most of what I would write would not be useful to you. So, at least tell us if you're in a field where you have to have an advisor lined up before applying or if you apply to the department as a whole and pick a lab/advisor later. 

In the meanwhile, you should also look into fee waivers, so you could perhaps apply to more than just a couple of schools.