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JEE Main202523 Jan 2025Evening ShiftMathematicsLimitsActual

_ x (2 x^2-3 x+5 )(3 x-1)^ x 2 (3 x^2+5 x+4 ) (3 x+2)^x is equal to :

Options

  1. A2 3 e
  2. B2 e 3
  3. C2 3 e
  4. D2 e 3

Correct answer

C. 2 3 e

Step-by-step solution

aligned & _ x (2 x^2-3 x+5 )(3 x-1)^ x / 2 (3 x^2+5 x+4 ) (3 x+2)^x & = _ x x^2 (2- 3 x + 5 x^2 )(3 x)^ x 2 x^2 (3+ 5 x + 4 x^2 )(3 x)^ x 2 (1- 1 3 x )^ x 2 (1+ 2 3 x )^ x 2 & _ x (1- 1 3 x )^ x 2 =e^ _ x (1- 1 3 x -1 ) x 2 =e^ -1 6 & _ x (1+ 2 3 x )=e^ _ x (1+ 2 3 x -1 ) x 2 & =e^ 1 3 aligned So, 2 3 e^ -1 6 e^ 1 3 = 2 3 1 e^ 1 3 + 1 6 = 2 3 e

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