The total emissive power of a surface is $$500$$ $$W/{m^2}$$ at a temperature $${T_1}$$ and $$1200$$ $$W/{m^2}$$ at a temperature $${T_2}$$, where the temperatures are in Kelvin. Assuming the emissivity of the surface to be constant, the ratio of the temperatures $${{{T_1}} \over {{T_2}}}$$ is

A balanced counter-flow heat exchanger has a surface area of $$20\,\,{m^2}$$ and overall heat transfer coefficient of $$20$$ $$W/{m^2}$$-$$K$$. Air $$\left( {{C_p} = 1000J/kg - K} \right)$$ entering at $$0.4$$ $$kg/s$$ and $$280$$ $$K$$ is to preheated by the air leaving the system at $$0.4$$ $$kg/s$$ and $$300$$ $$K.$$ The outlet temperature (in $$K$$) of the preheated air is

Annual demand of a product is $$50,000$$ units and the ordering cost is Rs. $$7,000$$ per order. Considering the basic economic order quantity model, the economic order quantity is $$10,000$$ units. When the annual inventory cost is minimized, the annual inventory holding cost (in Rs.) is ___________

A project consists of $$7$$ activities. The network along with the time durations (in days) for various activities is shown in the figure.

The minimum time (in days) for completion of the project is _____________