Here actually u have to go through the circuit diagram and through options.Basically it is asking the first 2 input sequence which would result in transition to state 11 which is 00 initially..
So if we take input = 0 initially..Hence x = 0 initially..
Now if u just go through the circuit we will get Ja = 1 and Ka = Qb = 0
Hence next state of A flip flop which is a JK flip flop = 1
Similarly Jb = 0 and Kb = 1
Hence next state of B flip flop will be 0..
Hence after 1st cycle we get Qa Qb = 1 0
Hence these inputs along with x = 0 once again (if we go with option A) , on applying similar to the procedure as above will lead us to have Qa Qb = 1 1
The key thing is minimum input is being asked..Hence always preferable to start with 00 i.e. in first cycle we applied x = 0 then in 2nd cycle we have applied x = 0 here as well..
Hence A) is the correct answer