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JEE Main 2024 Mathematics question

MathematicsStraight LinesJEE Main 2024

Let for any three distinct consecutive terms a, b, c of an A.P., the lines ax + by + c = 0 be concurrent at the point P and Q(α, β) be a point such that the system of equations. x + y + z = 6, 2x + 5y + αz = β and x + 2y + 3z = 4, has infinitely many solutions. Then (PQ)² is equal to .

Answer: 113

Solution

Since a − 2b + c = 0, the lines ax + by + c = 0 all pass through P(1, −2). For infinitely many solutions the coefficient determinant [[1,1,1],[2,5,α],[1,2,3]] =

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Question ID VK-016834