A1) True.
B1) False.  BFS may find a solution with low depth but high cost.
A2) True.
B2) False.  Graph search with an admissible heuristic may find suboptimal
paths to the goal before the optimal path, and thus when the optimal path is
found it will be trown out as the goal node has already been stored by graph
search.
A3) False.
B3) False. Space complexity is not polynomial and time complexity >= space
complexity
A4) False.
B4) True.