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AP EAMCET202421 May 2024Morning ShiftMathematicsApplication of DerivativesActual

If a number is drawn at random from the set 1,3,5,7 , , 59 , then the probability that it lies in the interval in which the function f(x)=x^3-16 x^2+20 x-5 is strictly decreasing, is

Options

  1. A1 5
  2. B1 3
  3. C1 2
  4. D1 6

Correct answer

D. 1 6

Step-by-step solution

aligned & f(x)=x^3-16 x^2+20 x-5 & f^ (x)=3 x^2-32 x+20=(3 x-2)(x-10) & f^ (x) 0 & x ( 2 3 , 0 ) x can take values 1,3,5,7,9 & n( ~S )=30, n( E )=5 & Required probability = n( E ) n( ~S ) = 5 30 = 1 6 aligned

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