$${\rm I}.\,\,\,\,$$ The elastic critical stress in compression increases with decrease in slenderness ratio

$${\rm II}.\,\,\,\,$$ The effective length depends on the boundary conditions at its ends

$${\rm III}.\,\,\,\,$$ The elastic critical stress in compression is independent of the slenderness ratio

$${\rm IV}.\,\,\,\,$$ The ratio of the effective length to its radius of gyration is called as slenderness ratio

The TRUE statements are

$${\rm I}.\,\,\,\,$$ Effective length of a battened column is usually increased to account for the additional load on battens due to the lateral expansion of columns.

$${\rm II}.\,\,\,\,$$ As per $$IS:$$ $$800$$-$$1984,$$ permissible stress in bending compression depends on both Euler buckling stress and the yield stress of steel.

$${\rm III}.\,\,\,\,$$ As per $$IS:$$ $$800$$-$$1984,$$ the effective length of a column effectively held in position at both ends but not restrained against rotation, is taken to be greater than that in the ideal end conditions.

The TRUE statements are