In silicon, for the effective mass for density of states calculation, electron mass (1.08) is more than hole mass (0.81). Whereas, the effective mass for conductivity calculation, hole mass (0.386) is more than electron mass (0.26). Why is it so?
This is because the band structure need not be isotropic so the "effective mass" models work in different ways for conductivity and density of states. Specifically, conductivity is inversely proportional to effective mass and in silicon the conduction band minimum is not at the Gamma point so it is highly anisotropic - so the effective mass is different in different $k$-directions. Adding conductive contributions in different directions yields different results than how the different directions combine for the density of states.
Note that in Gallium Arsenide there is a single isotropic conduction band at the Gamma point, so conductive effective mass and density of states effective mass are the same for electrons in that semiconductor.
This reference should make it very clear: https://ecee.colorado.edu/~bart/book/effmass.htm