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JEE Advanced 2016 Paper 1 Mathematics Question 50

The total number of distinct \(x \in \mathbb{R}\) for which \(\left| \begin{array}{ccc} x & x^2 & 1+x^3 \\ 2x & 4x^2 & 1+8x^3 \\ 3x & 9x^2 & 1+27x^3 \end{array} \right| = 10 \), is