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Is there any good reference for conceptual problems for students which learn nuclear physics first time? I am not searching problems that involve difficult calculations. Quite the converse, they should be computational rather simple but conceptually difficult.

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Try looking at the nuclear physics questions in the Physics GRE test. These are multiple choice questions that are supposed to be answered in a few minutes each. At this link:
You will find a few nuclear physics questions such as these ones from the 8677 test:

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