Using the Simpson's $$1/{3^{rd}}$$ rule, the value of $$\,\int {ydx} \,\,$$ computed, for the data given below, is

If the equation $$sin(x)$$ $$\, = {x^2}$$ is solved by Newton Raphson's method with the initial guess of $$x=1,$$ then the value of $$x$$ after $$2$$ iterations would be _________.

Brazing and soldering are

In an arc welding operation carried out with a power source maintained at $$40$$ volts and $$400$$ amperes, the consumable electrode melts and just fills the gap between the metal plates to be butt-welded. The heat transfer efficiency for the process is $$0.8,$$ melting efficiency is $$0.3$$ and the heat required to melt the electrode is $$20$$ $$J/m{m^3}$$. If the travel speed of the electrode is $$4$$ $$mm/s$$, the cross-sectional area, in $$m{m^2}$$, of the weld joint is ________________.