2. Solved Papers
  3. JEE Main & Advanced

JEE Main & Advanced AIEEE Solved Paper-2011

  • question_answer
    Let I be the purchase value of an equipment and                                                                                                       \[V(t)\]  be the value after it has been used for t years. The value                                                                                                       \[V(t)\]  depreciates at a rate given by differential equation                                                                            \[\frac{dV(t)}{dt}=-k(T-t)\], where \[k>0\] is a constant and T is the total life in years of the equipment. Then the scrap value \[V(T)\] of the equipment is.   AIEEE  Solved  Paper-2011

    A) \[{{e}^{-kT}}\]                   

    B) \[{{T}^{2}}-\frac{I}{k}\]

    C) \[I-\frac{k{{T}^{2}}}{2}\]                  

    D) \[I-\frac{k{{\left( T-t \right)}^{\left. 2 \right|}}}{2}\]

    Correct Answer: C

    Solution :

                 \[\int\limits_{I}^{V(T)}{dV(t)=\int\limits_{t=0}^{T}{-k(T-t)dt}}\] \[\Rightarrow \,\,V(T)-I=k\left[ \frac{{{(T-t)}^{2}}}{2} \right]_{0}^{T}\] \[\Rightarrow \,\,\,V(T)-I=-k\left[ \frac{{{T}^{2}}}{2} \right]\] \[\Rightarrow \,\,\,V(T)=I-\frac{k{{T}^{2}}}{2}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner