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JEE Main202529 Jan 2025Evening ShiftMathematicsFunctionsActual

If the domain of the function ₅ (18 x-x^2-77 ) is ( , ) and the domain of the function _ (x-1) ( 2 x^2+3 x-2 x^2-3 x-4 ) is ( , ) , then ^2+ ^2+ ^2 is equal to :

Options

  1. A195
  2. B179
  3. C186
  4. D174

Correct answer

C. 186

Step-by-step solution

aligned & f₁(x)= ₅ (18 x-x^2-77 ) & 18 x-x^2-77>0 & x^2-18 x+77 1, x-1 1, 2 x^2+3 x-2 x^2-3 x-4 >0 & x>1, x 2, (2 x-1)(x+2) (x-4)(x+1) >0 aligned aligned & x (4, ) & =4 & ^2+ ^2+ ^2=49+121+16 & =186 aligned

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