An experimental setup is planned to determine the taper of work piece as shown in the figure. If the two precision rollers have radii $$8mm$$ and $$5mm$$ and the total thickness of slip gauges inserted between the rollers is $$15.54mm,$$ the taper angle $$'\theta '$$ is

The following data are given for calculating limits of dimensions and tolerances for a hole: Tolerance unit $$'i'$$ (microns) $$=0.45$$ $${\left( D \right)^{1/3}} + 0.001D.$$ The unit of $$D$$ is $$mm.$$ Diameter step is $$18-30.$$ If the fundamental deviation for hole $$H$$ is zero and $${\rm I}T8 = 26i$$ the maximum and minimum limits of dimension for a $$25{H_8}$$ hole (in $$mm$$) are

Tolerance on the dimension $$'x'$$ in the two component assembly shown below is (all dimensions are in $$mm$$)

A tool with side cutting edge angle of $$30$$ degrees and end cutting edge angle $$10deg$$ is used for fine turning with a feed of $$1mm/rev$$. Neglecting nose radius of the tool, the maximum (peak to valley) height of the surface roughness produced will be