The shape factor for a casting in the form of an annular cylinder of outside diameter $$30$$ $$cm,$$ inside diameter $$20$$ $$cm$$ and height $$30$$ $$cm$$ (correction factor $$k=1.0$$) will be

A cast steel slab of dimension $$30 \times 20 \times 5\,\,cm$$ is poured horizontally using a side riser. The riser is cylindrical in shape with diameter and height, both equal to $$D.$$ The freezing ratio of the moulds is

The eigen values of the matrix $$M$$ given are $$15, 3, $$ and $$0.$$
$$M = \left[ {\matrix{ 8 & { - 6} & 2 \cr { - 6} & 7 & { - 4} \cr 2 & { - 4} & 3 \cr } } \right],$$ the value of the determinant of a matrix is

Which one of the following is Not associated with vector calculus?