In a $$CAD$$ package, mirror image of a $$2D$$ points $$P(5, 10)$$ is to be obtained about a line which passes through the origin and makes an angle of $${45^ \circ }$$ counterclockwise with the $$X$$-axis. The coordinates of the transformed points will be

In a rolling process, the state of stress of the material undergoing deformation is

Circular blanks of $$10mm$$ diameter are punched from an aluminium sheet of $$2$$ $$mm$$ thickness. The shear strength of aluminium is $$80$$ $$MPa.$$ The minimum punching force required in $$kN$$ is

Cylindrical pins of $${25^{\matrix{ { + 0.020} \cr { + 0.010} \cr } }}\,\,mm$$ diameter are electroplated in a shop. Thickness of the plating is $$30 \pm 0.2$$ micron. Neglecting gage tolerances, the size of the $$GO$$ gage in $$mm$$ to inspect the plated components is