JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2014

  • question_answer
    If   the    roots    of   the    equation \[=\underset{x\to \infty }{\mathop{\lim }}\,\frac{2+1/x}{1+2/x}={{e}^{-2}}\] are real and less than 3,then

    A) \[[-1,\infty )-\{0\}\]

    B) \[\text{x}=0\]

    C) \[\therefore \]

    D) \[Rf'(0)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(0+h)-f(0)}{h}\]

    Correct Answer: A

    Solution :

                     Given equation is \[\upsilon /\text{1}0\]. If roots are real, then \[f\] \[1.11f\]               \[1.22f\] \[f\]       \[1.27f\] \[\text{1}.0\text{1}\times \text{1}{{0}^{\text{5}}}\text{ N}/{{\text{m}}^{\text{2}}}\]                \[\text{9}.\text{13}\times \text{1}{{0}^{\text{4}}}\text{ N}/{{\text{m}}^{\text{2}}}\] Also roots are less than 3, hence \[\text{9}.\text{13}\times \text{1}{{0}^{\text{3}}}\text{N}/{{\text{m}}^{\text{2}}}\] \[\text{18}.\text{26 N}/{{\text{m}}^{\text{2}}}\]              \[\text{2}.\text{25}\times \text{1}{{0}^{\text{3}}}\text{min}\] \[\text{3}.\text{97}\times \text{1}{{0}^{\text{3}}}\text{min}\]  \[9.13\times {{10}^{3}}N/{{m}^{2}}\] \[\text{5}.\text{25}\times \text{1}{{0}^{\text{3}}}\text{min}\]  \[\left[ \text{FL}{{\text{T}}^{-\text{2}}} \right]\] Either \[\left[ \text{F}{{\text{L}}^{\text{2}}}{{T}^{-\text{2}}} \right]\] or \[\left[ \text{F}{{\text{L}}^{-\text{1}}}{{\text{T}}^{\text{2}}} \right]\] Hence, only \[\left[ {{\text{F}}^{2}}\text{L}{{\text{T}}^{\text{-2}}} \right]\] satisfy.


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