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JEE Main & Advanced JEE Main Paper (Held On 12 May 2012)

  • question_answer
    Consider a rectangle whose length is increasing at the uniform rate of 2 m/sec, breadth is decreasing at the uniform rate of 3 m/sec and the area is decreasing at the uniform rate of it \[5\,{{m}^{2}}/\sec .\] If after some time the breadth of the rectangle is 2 m then the length of the rectangle is     JEE Main Online Paper (Held On 12 May 2012)

    A) 2m                                         

    B)                        4m

    C)                        1m                                         

    D)                        3m

    Correct Answer: D

    Solution :

                    Let A be the area, b be the breadth and \[\ell \] be the length of the rectangle. Given: \[\frac{dA}{dt}=-5,\frac{d\ell }{dt}=2m,\frac{db}{dt}=-3\] We know,\[A=\ell \times b\] \[\Rightarrow \]\[\frac{dA}{dt}=\ell .\frac{db}{dt}+b.\frac{d\ell }{dt}=-3\ell +2b\] \[\Rightarrow \]\[-5=-3\ell +2b.\]When b = 2, we have \[-5=-3\ell +4\Rightarrow \ell =\frac{9}{3}=3m\]


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