GATE Computer Science (CS) 2019 Solved Papers

$\mathit{L}=\{\mathit{a}2+3\mathit{k}$ or $\mathit{b}10+12\mathit{k}\}$ for $\mathit{k}\ge 0$
$=\mathit{a}2{\left(\mathit{a}3\right)}^{*}$ or $\mathit{b}10{\left(\mathit{b}12\right)}^{*}$
The pumping length is $\mathit{p}$, than for any string $\mathit{w}\in \mathit{L}$ with $\left|\mathit{w}\right|\ge \mathit{p}$ must have a repetition i.e. such a string must be breakable into $\mathit{w}=\mathit{x}\mathit{y}\mathit{z}$ such that $\left|\mathit{y}\right|\ge 0$ and $\mathit{y}$ can be pumped indefinitely, which is same as saying $\mathit{x}\mathit{y}\mathit{z}\in \mathit{L}\Rightarrow$ $\mathit{x}{\mathit{y}}^{*}\mathit{z}\in \mathit{L}$
The minimum pumping length in this language is clearly 11, since $\mathit{b}10$ 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 .