I applied through college or university. The process took 1 day. I interviewed at US Navy (Washington, DC) in Sep 2012
Interview
Two technical interviews asking for your response on basic Calculus and Physics problems, followed by one interview by a four star admiral to ensure you'd be a good fit for the nuclear program.
Interview questions [1]
Question 1
Why would you be a good submarine officer? You weren't an engineering major in college. Can you handle the rigor of Nuclear Power School?
Math, Physics, thermofluids topics were asked by 2 different interviewers. They tended to care much more about thought process than the ultimate correct answers to the problems. Ended with the admiral interview; very direct and simple behavior questions.
Three technical interviews in Calculus/Physics, one personal with the admiral. Technical interview process was relatively straightforward and are straight from the practice problems your recruiter gives you. Definitely concentrate on optimization calculus problems and how to derive the volumes of shapes.
I applied in-person. The process took 3 months. I interviewed at US Navy (Washington, DC)
Interview
3 Rounds of interviews.
2 - Technical in nature, can be asked about any technical subject studied while at University. Calculus and Physics are fair game to all candidates. If you do not perform well on 1, you may receive 3rd technical interview.
1 - Interview with NAVSEA08 - Will be more of a personality interview, could reflect on past failures/obstacles, why you want to do the job, where you think you may struggle, and why you are a good candidate
Interview questions [1]
Question 1
The questions for technical interviews are derived from the NUPOC study guide materials.
These questions are random in nature, but you will generally have to demonstrate your knowledge on Physics and Calculus at a minimum and then often will answer questions concerning your major field of study.