The maximum reduction per pass during wire drawing of an aluminium alloy ignoring friction and redundant work is $$77\% $$. The strain hardening exponent of the material is ______________.

Open die forging of a cylinder made of a rigid perfectly plastic material with yield strength of $$200$$ $$MPa$$ having a height of $$25$$ $$mm$$ and diameter of $$25$$ $$mm$$ is being carried out. The cylinder is subjected to a true compressive strain of $$3.6$$ during the process. Assuming frictionless and homogeneous deformation, the energy expended, in $$kJ$$ is __________________.

A surface is prepared specially for an application with the profile as shown in the figure.

The theoretical $${R_a}$$ value for this surface, in $$\mu m,$$ is _______________.

During the measurement of internal taper of a part using standard balls of diameter $$15$$ $$mm$$ and $$20$$ $$mm$$, the large ball is found to protrude by $$5$$ $$mm$$ $$\left( {{h_1}} \right)$$ and the top of small ball is found to be $$35$$ $$mm$$ $$\left( {{h_2}} \right)$$ below the top face of the gauge. The taper angle, in degree, is ________________.