2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main - Mock Test - 37

  • question_answer
    If the value of the determinant \[\left| \begin{matrix}    a & 1 & 1  \\    1 & b & 1  \\    1 & 1 & c  \\ \end{matrix} \right|\]is positive, then -

    A) \[abc>1\]          

    B)        \[abc>-8\]

    C) \[abc<-8\]         

    D)        \[abc>-2\]

    Correct Answer: B

    Solution :

    [b] \[\Delta >0\] \[abc+2>3{{\left( abc \right)}^{1/3}}\] Let \[{{\left( abc \right)}^{1/3}}=x\] \[{{x}^{3}}+1>3x\] \[{{\left( x-1 \right)}^{2}}\left( x+2 \right)>0\] \[\therefore x+2>0\] \[x>-2\] \[{{\left( abc \right)}^{1/3}}>-2\] \[abc>-8\]


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