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MHT CET20227 Aug 2022Evening ShiftMathematicsApplication of DerivativesActual

The rate of disintegration of a radio active element at time t is proportional to its mass at that time. Then the time during which the original mass of 6 gm will disintegrate into its mass of 3 gm is proportional to

Options

  1. A4
  2. B3
  3. C5
  4. D2

Correct answer

D. 2

Step-by-step solution

aligned & d(m) d t m & d m d t =-k m & d m m =- k d t & _e m=-k t+c & m=e^ -k t+c =e^c e^ -k t & at t=0, m=6 e^c=6 & i.e., m=6 e^ -k t aligned at t=t, m=3 Hence 3=6 e^ -k t aligned & 1 2 =e^ -k t & ( 1 2 )=-k t & - 2=-k t & . t= 2 k [Propotional to 2 ] aligned

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