The geometric mean radius of a conductor, having four equal strands with each strand of radius r, as shown in the figure below, is

The valid positive, negative and zero sequence impedances (in p.u.), respectively, for a 220 kV, fully transported three-phase transmission line, from the given choices are

The fuel cost functions in rupees/hour for two 600 MW thermal power plants are given by

Plant 1 : C₁ = 350 + 6P₁ + 0.004P$$_1^2$$

Plant 2 : C₂ = 450 + aP₂ + 0.003P$$_2^2$$

where P₁ and P₂ are power generated by plant 1 and plant 2, respectively, in MW and a is constant. The incremental cost of power ($$\lambda$$) is 8 rupees per MWh. The two thermal power plants together meet a total power demand of 550 MW. The optimal generation of plant 1 and plant 2 in MW, respectively, are