In a sheet metal of $$2$$ $$mm$$ thickness a hole of $$10$$ $$mm$$ diameter needs to be punched. The yield strength in tension of the sheet material is $$100$$ $$MPa$$ and its ultimate shear strength is $$80$$ $$MPa.$$ The force required to punch the hole (in $$kN$$) is ______________

Match the following part programming codes with their respective functions

Two optically flat plates of glass are kept at a small angle $$\theta $$ as shown in the figure. Monochromatic light is incident vertically.

If the wavelength of light used to get a fringe spacing of $$1$$ $$mm$$ is $$450$$ $$nm,$$ the wavelength of light (in $$nm$$) to get a fringe spacing of $$1.5$$ $$mm$$ is ________________________.

A point $$P\left( {1,\,\,\,3,\,\,\, - 5} \right)$$ is translated by $$2\widehat i + 3\widehat j - 4\widehat k$$ and then rotated counter clockwise by $${90^ \circ }$$ about the $$z$$-axis. The new position of the point is