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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2004

  • question_answer
        The  function \[\frac{1}{\sqrt{5}}(\hat{i}-2\hat{j})\],\[\frac{1}{\sqrt{3}}(\hat{i}-\hat{j}-\hat{k})\]where\[\underset{x\to 1}{\mathop{\lim }}\,(1-x)\tan \left( \frac{\pi x}{2} \right)\]assumes its minimum value only at one point, if :

    A)  \[\frac{\pi }{2}\]                             

    B)  \[\pi \]

    C) \[\frac{2}{\pi }\]                              

    D) \[f(x)=\frac{\sin [x]}{[x]}\]

    Correct Answer: D

    Solution :

                    \[f(x)=|px-9|+r|x|,x\in (-\infty ,\infty )\]where,\[p>0,\text{ q}>0\]and\[r>0\]can assume its minimum value only at one point if \[p=q=r\]


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