The degree of dissociation (α) of a weak acid HA in 0.1 M solution is 0.006. The value
of 'α' for HA in 0.005 M solution is 27x10^-x . X is

K_a =Cα² Since dissociation constant of acid,K is constant, α depends upon concentration.
${\mathrm{\alpha }}^2\propto \frac{1}{\mathrm{c}}\text{ or }\mathrm{\alpha }\propto \frac{1}{\sqrt{\mathrm{c}}}\text{ or }\frac{{\mathrm{\alpha }}_2}{{\mathrm{\alpha }}_1}=\sqrt{\frac{{\mathrm{c}}_1}{{\mathrm{c}}_2}}$Substituting the values, $\frac{{\mathrm{\alpha }}_2}{0.006}=\sqrt{\frac{0.1}{0.05}}=\sqrt{20}$The degree of dissociation in 0.05M solution is $=0.027=27\times {10}^{-3}$