A solid cylinder of diameter $$D$$ and height equal to $$D,$$ and a solid cube of side $$L$$ are being sand cast by using the same material. Assuming there is no super-heat in both the cases, the ratio of solidification times of the cylinder to the solidification time of the cube is

Hot chamber die casting is NOT suited for

The value of the determinant $$\left| {\matrix{ 1 & 3 & 2 \cr 4 & 1 & 1 \cr 2 & 1 & 3 \cr } } \right|$$ is

During the numerical solution of a first order differential equation using the Euler (also known as Euler Cauchy) method with step size $$h,$$ the local truncation error is of the order of