For a current carrying wire of $$20$$ $$mm$$ diameter and having $$k=0.5W/mK$$ is exposed to air $$\left( {h = 20W/{m^2}K} \right),$$ maximum heat dissiption occurs when thickness of insulation is

Match List - $${\rm I}$$ with List - $${\rm II}$$ and select the correct answer using the code given below the Lists:

List - $${\rm I}$$
$$A.$$ Grashof number
$$B.$$ Schmid number
$$C.$$ Weber number
$$D.$$ Fourier number

List - $${\rm II}$$
$$1.$$ Mass diffusion
$$2.$$ Transient heat conduction
$$3.$$ Free convection
$$4.$$ Forced convection
$$5.$$ Surface tension
$$6.$$ Radiation

In an assembly line for assembling toys, five workers are assigned tasks which take times of $$10, 8, 6, 9$$ and $$10$$ minutes respectively. The balance delay for the line is

If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means that