The too life equation for $$HSS$$ tool is $$V{T^{0.14}}\,\,{f^{0.7}}\,\,{d^{0.4}} = $$ Constant. The tool life $$(T)$$ of $$30$$ $$min$$ is obtained using the following cutting conditions $$=45$$ $$m/min,$$ $$f=0.35mm,$$ $$d=2.0$$ $$mm.$$ If speed $$(V),$$ feed $$(f)$$ and depth of cut $$(D)$$ are increased individually by $$25\% ,$$ the tool life (in $$min$$) is

Match the following

The figure below represents a triangle $$PQR$$ with initial coordinates of the vertices as $$P(1,3),$$ $$Q(4,5)$$ and $$R(5,3.5).$$ The triangle is rotated in the $$X-Y$$ plane about the vertex $$P$$ by angle in clockwise direction. If sin $$\theta = 0.6$$ and cos $$\theta = 0.8$$, the new coordinates of the vertex $$Q$$ are

A hypothetical engineering stress-strain curve shown in the figure has three straight lines PQ, QR, RS with coordinates P(0,0), Q(0.2,100), R(0.6,140) and S(0.8,130). 'Q' is the yield point, 'R' is the UTS point and 'S' the fracture point.

The tougness of the material (in MJ/m³) is __________.