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MHT CET202210 Aug 2022Morning ShiftMathematicsDifferential EquationsActual

An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half the quantity of ice melts in 20 minutes. x₀ is the initial quantity of ice. If after 40 minutes the amount of ice left is k x₀ x , then k is

Options

  1. A1 8
  2. B1 2
  3. C1 3
  4. D1 4

Correct answer

D. 1 4

Step-by-step solution

aligned & d x ~d t =-k x & d x x =-k d t & _e x=-k t+c & x=e^ -k t+c =e^c e^ -k t & at t=0, x^ -k =x₀ & e^c=x₀ & x=x₀ e^ -k t aligned

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