2. Sample Papers
  3. KVPY

KVPY Sample Paper KVPY Stream-SX Model Paper-4

  • question_answer
    The number of real solutions of the equation, \[{{\cot }^{-1}}(x-1)+{{\cot }^{-1}}(6-x)={{\cot }^{-1}}(x-2)\] is -

    A) 0                                 

    B) 1

    C) 2                     

    D) infinite

    Correct Answer: C

    Solution :

    [C]
    \[\because {{\cot }^{-1}}(x-1)+{{\cot }^{-1}}(6-x)={{\cot }^{-1}}(x-2)\]
    Take cot of both sides, we get
    \[\Rightarrow \left[ \frac{(x-1)\,\,(6-x)-1}{6-x+x-1} \right]=(x-2)\]
    \[\Rightarrow -\frac{{{x}^{2}}+7x-7}{5}=x-2\]
    \[{{x}^{2}}-2x-3=0\]
    \[\Rightarrow (x-3)\,\,(x+1)=0\]
    \[x=3;\,\,\,x=-\,1\]
    both satisfy the given equation


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