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JEE Main & Advanced JEE Main Paper (Held On 19 May 2012)

  • question_answer
    The weight W of a certain stock of fish is given by W=nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as \[n=2{{t}^{2}}+3\]and \[w={{t}^{2}}-t+2,\]then the rate of change of W with respect to t at t = 1 is     JEE Main  Online Paper (Held On 19  May  2012)

    A) 1                             

    B)                        8

    C)                        13        

    D)                        5

    Correct Answer: C

    Solution :

                    Let \[W=nw\]\[\Rightarrow \]\[\frac{dW}{dt}=n\frac{dw}{dt}+w.\frac{dn}{dt}\] Given :\[w={{t}^{2}}-t+2\]and\[n=2{{t}^{2}}+3\] \[\Rightarrow \]\[\frac{dw}{dt}=2r-1\]and\[\frac{dn}{dt}=4t\] \[\therefore \]Equation (1) \[\Rightarrow \]\[\frac{dw}{dt}=(2{{t}^{2}}+3)(2r-1)+({{t}^{2}}-t+2)(4t)\] Thus,\[{{\left. \frac{dw}{dt} \right|}_{t=1}}=(2+3)(2-1)+(2)(4)\] \[=5(1)+8=13\]                                


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