Consider the following statements

$${\rm I}.\,\,\,\,$$ 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

In the design of welded tension members, consider the following statements:

$${\rm I}.\,\,\,\,\,\,\,\,\,$$ The entire cross-sectional area of the connected leg is assumed to contribute to the effective area in case of angles.
$${\rm II}.\,\,\,\,\,\,\,\,\,$$ Two angles back-to-back and tack-welded as per code requirements may be assumed to be behave as a $$T$$-section
$${\rm III}.\,\,\,\,\,\,\,\,\,$$ A check on slenderness ratio may be necessary in some cases.

The TRUE statements are

The buckling load $$P = {P_{cr}}$$ for the column $$AB$$ in figure, as $${K_T}$$ approaches infinity, becomes $$\alpha {{{\pi ^2}E{\rm I}} \over {{L^2}}}$$

Where $$\alpha $$ is equal to

Consider a propped cantilever $$ABC$$ under two loads of magnitude $$P$$ each as shown in figure below. Flexural rigidity of the beam is $$EI$$.

The reaction at $$C$$ is