2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main - Mock Test - 28

  • question_answer
    The curve \[x+y-{{\log }_{e}}(x+y)=2x+5\] has a vertical tangent at the point\[(\alpha ,\beta )\]. Then \[\alpha +\beta \] is equal to

    A) \[-1\]                  

    B)        \[1\]        

    C) \[2\]                      

    D)        \[-2\]

    Correct Answer: B

    Solution :

      [b]  \[x+y-{{\log }_{e}}(x+y)=2x+5\] \[\Rightarrow \,\,\,\,\,1+y'-\frac{1}{x+y}.\,(1+y')=2\] \[\Rightarrow \,\,(1+y')\,\,(x+y)-(1+y')=2x+2y\] \[\Rightarrow \,\,\,\,\,\,x+y+y'(x+y-1)-1=2x+2y\] \[\Rightarrow \,\,\,\,\,\,y'=\frac{x+y+1}{x+y-1}\] \[\Rightarrow \,\,\,\,\,\,\alpha +\beta =1\]           


You need to login to perform this action.
You will be redirected in 3 sec spinner