Reaction 1:
As Dan has said,it's a tert-butanol so you should know tert-butanol would undergo which kind of mechanism pathway.
Consider the following factors:
1. High T favours elimination. Is T high?
2. Strong base favour SN2/E2. Is there a strong base?
3. Bulky base favour elimination. Is there a bulky base?
4. Weak nucleophile favour SN1/E1 while strong nucleophile favour SN2/E2. Is the nucleophile in this case strong or weak?
5. Polar aprotic solvent favours SN2/E2 while polar protic solvent favours SN1/E1. Is the solvent polar aprotic or polar protic?
Yup, that should lead you to your answer.
Reaction 2:
If you think E2 is possible then take a look at the carbon adjacent to the C-Br. For E2 to occur, the C-H adjacent to the C-Br must be anti-periplanar or syn-coplanar in rigid molecules.
But is there any H attached to the carbon adjacent to the C-Br? That would help reduce your choices.
If you want to understand better, try drawing the envelope-conformation of the cyclopentane, that would help in determining whether nucleophilic substitution is feasible if its not clear.