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none of these.. (d) is the correct answer

The sign of is Case-1: For evaluating the sign of the determinant, it can be either Positive or negative is considered. i.e., for any values of a, b, or c But the determinant you can get is 3abc – (a³ + b³ + c³) Differentiating partially w.r.t a, we can get 3bc – 3a² = 0 Hence bc - a² = 0, bc = a² So, in order to remove imaginary roots, we must consider b,c as positive values only as they do exist for positive values. Similarly, a must be +ve. So the answer is 3. But the conclusion is only for positive values of a, b and c