JEE Main 2024 Mathematics question
If the sum of squares of all real values of α, for which the lines 2x – y + 3 = 0, 6x + 3y + 1 = 0 and αx + 2y – 2 = 0 do not form a triangle is p. then the greatest integer less than or equal to p is .
Answer: 32
Solution
Three lines fail to form a triangle if two are parallel or all three are concurrent. Lines 1 and 3 are parallel when 2/α = −1/2, α = −4; lines 2 and 3 are parallel
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