JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2015

  • question_answer
    If \[y=f\left( \frac{2x+3}{3-2x} \right)\]and\[f(x)=\sin (\log x)\], then the angle between\[\frac{dy}{dx}\] and \[\frac{12}{9-4{{x}^{2}}}\cos \left\{ \log \left( \frac{2x+3}{3-2x} \right) \right\}\]is

    A) \[\frac{12}{9-4{{x}^{2}}}\cos \left\{ \log \left( \frac{2x+3}{2x-3} \right) \right\}\]                              

    B) \[\frac{12}{4{{x}^{2}}-9}\cos \left\{ \log \left( \frac{2x+3}{3-2x} \right) \right\}\]             

    C) \[\frac{12}{9-4{{x}^{2}}}\cos \left\{ \log \left( \frac{3-2x}{2x+3} \right) \right\}\]                              

    D) \[f(x)={{x}^{2}}{{e}^{-x}}\]

    Correct Answer: D

    Solution :

    Here,     \[KI\] \[{{C}_{6}}{{H}_{6}}+{{C}_{2}}{{H}_{5}}Cl\xrightarrow{AlC{{l}_{3}}}{{C}_{6}}{{H}_{5}}{{C}_{2}}{{H}_{5}}+HCl\]                 And        \[{{C}_{2}}{{H}_{5}}OH+HCl\xrightarrow{ZnC{{l}_{2}}}{{C}_{2}}{{H}_{5}}Cl+{{H}_{2}}O\]                                                 \[{{C}_{6}}{{H}_{5}}Cl+C{{H}_{3}}COCl\xrightarrow{AlC{{l}_{3}}}{{C}_{6}}{{H}_{5}}COCl+C{{l}_{2}}\] Let\[{{C}_{6}}{{H}_{5}}Br+Mg\xrightarrow{Ether}{{C}_{5}}{{H}_{5}}MgBr\] be the angle between \[FeSi{{O}_{3}}\]and\[MgSi{{O}_{3}}\]. Then,    \[CaSi{{O}_{3}}\] \[N{{a}_{2}}C{{O}_{3}}\xrightarrow{s{{o}_{2}}}A\xrightarrow{Na{{ & }_{2}}C{{O}_{3}}}B\xrightarrow[\Delta ]{Elemental}\]   \[C\xrightarrow{{{I}_{2}}}D\] \[\text{N}{{\text{a}}_{\text{2}}}\text{S}{{\text{O}}_{\text{3}}}\]                \[\text{N}{{\text{a}}_{\text{2}}}{{\text{S}}_{2}}{{\text{O}}_{3}}\]


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