The inverse of the matrix $$X = \left[ {\matrix{ 2 & 0 & 0 \cr 0 & 3 & 0 \cr 0 & 0 & 4 \cr } } \right]$$ is

For an L.P.P. the objective function is Z = 4x + 3y, and the feasible region determined by a set of constraints (linear inequations) is shown in the graph.

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Which one of the following statements is true?

In a residential society comprising of 100 houses, there were 60 children between the ages of 10-15 years. They were inspired by their teachers to start composting to ensure that biodegradable waste is recycled. For this purpose, instead of each child doing it for only his/her house, children convinced the Residents Welfare Association to do it as a society initiative. For this they identified a square area in the local park. Local authorities charged amount of Rs.50 per square metre for space so that there is no misuse of the space and Resident Welfare Association takes it seriously. Association hired a labourer for digging out 250 m³ and he charged Rs.400 $$\times$$ (depth)². Association will like to have minimum cost.

Let side of square plot is x m and its depth is h metres, then cost c for the pit is

In a residential society comprising of 100 houses, there were 60 children between the ages of 10-15 years. They were inspired by their teachers to start composting to ensure that biodegradable waste is recycled. For this purpose, instead of each child doing it for only his/her house, children convinced the Residents Welfare Association to do it as a society initiative. For this they identified a square area in the local park. Local authorities charged amount of Rs.50 per square metre for space so that there is no misuse of the space and Resident Welfare Association takes it seriously. Association hired a labourer for digging out 250 m³ and he charged Rs.400 $$\times$$ (depth)². Association will like to have minimum cost.

Value of h (in m) for which $${{dc} \over {dh}} = 0$$ is