Conceptual physics problems with solutions for IIT and GRE prep

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Dani708
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Physics forum users,
Thanks in advance for your help and discussion!

I am looking for conceptual problems in introductory physics which include solutions -- for self study. It should cover all the material for the IIT or GRE exams, but should emphasize forming connections, analysis and applying principles cumulatively -- in addition to questions that are specific only to the topic of one chapter/section.

An example of conceptual questions is the "questions" at end of chapters in the Halliday, D. & Resnick, R. text -- this text includes at end of chapter first a "questions" section, followed by a "problems" section, but I did not find solutions on the Internet/in-print to the former.
--But even if I found a solution-set against which I can check my work, maybe the Halliday, D. & Resnick, R. text is not the right thing given my goal that I mentioned.
Maybe at the other extreme would be "Thinking Physics" by Epstein, L., which I read about but haven't seen -- maybe that would be useful but would not suffice for forming an understanding.

I also want to find some experimental guidebook that would supplement this study.
To that end, background about myself:
I have background in math at the level of the GRE (math) subject test and some topics more advanced than that.

However, I have very little knowledge of any kind in physics. Only basic one-particle-mass dynamics, say.

That said, engineering subjects such as stability of (physical, man-made) structures and practical design, or modelling related problems as a boundary-value problem are what interest me.
Dan
 
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So that you don't get the wrong impression -- I do not believe my mentioned endeavour to be equivalent in any way to a degree in physics. Probably the scope I am presently concerned with concentrates on the common core studied in engineering or physics degrees, but with the emphasis I described. I mentioned the GRE subject test because the physics 1 - 3 texts are recommended in preparing for it on the Internet, but maybe in reality this exam requires more specialization.