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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2012

  • question_answer
        The speed v of a particle moving along a straight line is given by\[a+b{{v}^{2}}={{x}^{2}}\](where X, is its distance from the origin). The acceleration of the particle is

    A)  \[bx\]                                  

    B)  \[\frac{x}{a}\]

    C)  \[\frac{x}{b}\]                                 

    D)  \[\frac{x}{ab}\]

    Correct Answer: C

    Solution :

                    Let \[I=\int{\frac{2x\,dx}{({{x}^{2}}+1)({{x}^{2}}+2)}}\] Put         \[{{x}^{2}}=t\] \[\Rightarrow \]               \[2xdx=dt\] \[\therefore \]  \[I=\int{\frac{dt}{(t+1)(t+2)}}\]                 \[=\int{\left( \frac{1}{t+1}-\frac{1}{t+2} \right)}dt\](By partial fraction) \[I=\log |t+1|-\log |t+2|+c\] \[\Rightarrow \]               \[I=\log |{{x}^{2}}+1|-\log |{{x}^{2}}+2|+c\]\[(\because t={{x}^{2}})\]


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