The corner points of the feasible region determined by a set of constraints (linear inequalities) are P(0, 5), Q(3, 5), R(5, 0) and S(4, 1) and the objective function is Z = ax + 2by where a, b > 0. The condition on a and b such that the maximum Z occurs at Q and S is

If curves y² = 4x and xy = c cut at right angles, then the value of c is

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?