A firm is required to procure three items $$(P, Q$$ and $$R).$$ The prices quoted for these items (in Rs.) by suppliers $${S_1},{S_2},$$ and $${S_3}$$ are given in table. The management policy requires that each item has to be supplied by only one supplier and one supplier supply only one item. The minimum total cost (in Rs.) of procurement to the firm is:

A cylindrical shafts is subjected to an alternating stress of $$100MPa.$$ Fatigue strength to sustain $$1000$$ cycles is $$490MPa.$$ If the corrected endurance strength is $$70MPa,$$ estimated shaft life will be

A $$60mm$$ long and $$6mm$$ thick fillet weld carries a steady load of $$15kN$$ along the weld. The shear strength of the weld material is equal to $$200MPa.$$ The factor of safety is

Twenty degree full depth involute profiled $$19$$-tooth pinion and $$37$$-tooth gear are in mesh. If the module is $$5mm,$$ the center distance between the gear pair will be