In a two stage wire drawing operation, the fractional reduction (ratio of change in cross sectional area to initial cross sectional area ) in the first stage is $$0.4.$$ The fractional reduction in the second stage is $$0.3.$$ The overall fractional reduction is

In a slab rolling operation, the maximum thickness reduction $$\left( {\Delta {h_{\max }}} \right)$$ is given by $$\Delta {h_{\max }} = {\mu ^2}R,$$ where $$R$$ is the radius of the roll and $$\mu $$ is the coefficient of friction between the roll and the sheet. If $$\mu = 0.1,$$ the maximum angle subtended by the deformation zone at the center of the roll (bit angle in degrees) is ____________

In a rolling operation using rolls of diameter $$500mm,$$ if a thick plate cannot be reduced to less than $$20mm$$ in one pass, the coefficient of friction between the roll and the plate is ____________.

A mild steel plate has to be rolled in one pass such that the final plate thickness is $$2/{3^{rd}}$$ of the initial thickness, with the entrance speed of $$10m/min$$ and roll diameter of $$500mm.$$ If the plate widens by $$2\% $$ during rolling, the exit velocity (in $$m/min$$) is ____________