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JEE Main 2015 Mathematics question

MathematicsDeterminantsJEE Main 2015

The least value of the product (such that , and are real numbers) for which the determinant is non-negative is

Answer: (3)

Solution

Expand the determinant along the first row: . The condition reads . We want the smallest attainable value of subject to this. By symmetry, look for the extremum on the diagonal : the constraint becomes $

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Question ID VK-115302