In sand casting of hallow part of lead, a cylindrical core of diameter $$120mm$$ and height $$180mm$$ is placed inside the mould cavity. The densities of core material and lead are $$1600kg/{m^3}$$ and $$11300kg/{m^3}$$ respectively. The net force (in $$N$$) that tends to lift the core during pouring of molten metal will be

The inverse of matrix $$\left[ {\matrix{ 0 & 1 & 0 \cr 1 & 0 & 0 \cr 0 & 0 & 1 \cr } } \right]$$ is

The value of the integral $$\,\,\int\limits_{ - \pi /2}^{\pi /2} {\left( {x\,\cos \,x} \right)dx\,\,} $$ is

The value of the expansion $$\mathop {Lim}\limits_{x \to 0} \left[ {{{\sin \left( x \right)} \over {{e^x}X}}} \right]\,\,$$ is