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JEE Main 2024 Mathematics question

MathematicsDeterminantsJEE Main 2024

Consider the matrices : , and . Let the set of all m, for which the system of equations AX = B has a negative solution (i.e., x < 0 and y < 0), be the interval (a, b). Then is equal to .

Answer: 450

Solution

2x − 5y = 20 and 3x + my = m give y = (2m − 60)/(2m + 15) and x = 25m/(2m + 15). y < 0 needs m ∈ (−15/2, 30), and x < 0

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Question ID VK-016474