GATE Computer Science (CS) 2019 Solved Papers

L={a2+3k or b10+12k} for k≥0
=a2(a3)* or b10(b12)*
The pumping length is p, than for any string w∈L with |w|≥p must have a repetition i.e. such a string must be breakable into w=xyz such that |y|≥0 and y can be pumped indefinitely, which is same as saying xyz∈L⇒ xy*z∈L
The minimum pumping length in this language is clearly 11, since b10 is a string which has no repetition number, so upto 10 no number can serve as a pumping length. Minimum pumping length is 11. Any number at or above minimum pumping length can serve as a pumping length. The only number at or above 11 , in the choice given is 24 .