JEE Main202624 January 2026Evening ShiftMathematicsFunctionsActual

Let f be a function such that 3 f(x)+2 f ( m 19 x )=5 x, x 0 , where m= _ i=1 ⁹(i)² . Then f(5)-f(2) is equal to

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Correct answer

A. 18

Step-by-step solution

m = _ i=1 ⁹ i^2 = 9 10 19 6 = 285 , so m 19 = 15 . The equation becomes 3f(x) + 2f ( 15 x ) = 5x ...(i) Replace x by 15 x : 3f ( 15 x ) + 2f(x) = 75 x ...(ii) From 3 (i) - 2 (ii) : 5f(x) = 15x - 150 x , so f(x) = 3x - 30 x . f(5) = 15 - 6 = 9 , f(2) = 6 - 15 = -9 . f(5) - f(2) = 9 - (-9) = 18 .

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