In a structural member under fatigue loading, the minimum and maximum stresses developed at the critical point are $$50$$ $$MPa$$ and $$150$$ $$MPa,$$ respectively. The endurance, yield, and the ultimate strengths of the material are $$200$$ $$MPa,$$ $$300$$ $$MPa$$ and $$400$$ $$MPa,$$ respectively. The factor of safety using modified Goodman criterion is

The welding process which uses a blanket of fusible granular flux is

The value of true strain produced in compressing a cylinder to half its original length is

Gray cast iron blocks of size $$100\,\,mm \times 50\,\,mm \times 10\,\,mm$$ with a central spherical cavity of diameter $$4$$ mm are sand cast. The shrinkage allowance for the pattern is $$3\% $$. The ratio of the volume of the pattern to volume of the casting is ___________________