JEE Main & Advanced Sample Paper JEE Main Sample Paper-43

  • question_answer
    If \[{{y}^{x}}-{{x}^{y}}=1,\] then the value of \[\frac{dy}{dx}\] at \[x=1\] is

    A)  \[2(1-\log \,2)\]           

    B)  \[2(1+\,\log \,2)\]

    C)  \[2-\log \,2\]                

    D)  \[2+\log \,2\]

    Correct Answer: A

    Solution :

                \[{{N}_{S}}=\left( \frac{\rho S}{\rho P} \right)\times {{N}_{P}}\] Put \[=\frac{(4.4\times {{10}^{3}})\,\times 100}{220}=2000\] we get\[{{\rho }_{S}}\] One differentiating both sides w.r.t. x, we get \[{{\rho }_{P}}\] \[-h=-u{{t}_{1}}+\frac{1}{2}gt_{1}^{2}\]          \[-h=-u{{t}_{2}}+\frac{1}{2}gt_{2}^{2}\] \[0=u({{t}_{2}}-{{t}_{1}})+\frac{1}{2}g(t_{1}^{2}-t_{2}^{2})\] \[u=\frac{1}{2}g({{t}_{1}}+{{t}_{2}})\]  \[h=\frac{g{{t}_{1}}{{t}_{2}}}{2}\]

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