How can any of these compounds give same SN1 & SN2 product?

[TeethWhitener]

But is there a general rule so as to decide which factor dominates under what conditions?

It's not a matter of one factor dominating over another (at least not for this question). Rearrangements will happen, and stereochemical effects will happen. I unfortunately didn't think of rearrangements when I initially answered your question, but Ygggdrasil did, and his answer was therefore on the money. If you consider only rearrangements, then c will be the correct answer. If you consider rearrangements and stereochemistry, c is still correct, assuming that you start with a racemic mixture of c. If you assume that you start with one enantiomer of c, then there is no correct answer (S_N1 and S_N2 give different compunds in every case).

 

[baldbrain]

It's not a matter of one factor dominating over another (at least not for this question). Rearrangements will happen, and stereochemical effects will happen. I unfortunately didn't think of rearrangements when I initially answered your question, but Ygggdrasil did, and his answer was therefore on the money. If you consider only rearrangements, then c will be the correct answer. If you consider rearrangements and stereochemistry, c is still correct, assuming that you start with a racemic mixture of c. If you assume that you start with one enantiomer of c, then there is no correct answer (S_N1 and S_N2 give different compunds in every case).

Oh. Yes, that last bit was very helpful thanks to @Ygggdrasil .
All my concepts are quite clear, but I still **** up during exams (probably due to haste). I also solve a lot of problems, I can get them quicker when there's no time limit.
Sometimes, the opposite happens. I get the good problems, and **** up the easy ones. Can you give me some advice regarding this?