KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    Solution set of inequality \[{{\log }_{\sin \,\,e}}{{\log }_{3}}{{\log }_{0.2}}x<0\] is (where e is Napier's constant)

    A) \[\left( \frac{1}{125},\,\,\infty  \right)\]

    B) \[\left( -\,\infty ,\,\,\frac{1}{125} \right)\]

    C) \[\left( 0,\,\,\frac{1}{125} \right)\]

    D) none of these

    Correct Answer: C

    Solution :

    As sine\[\simeq \] sin 2.71 = positive value less than 1
    \[{{\log }_{\text{sine}}}{{\log }_{3}}{{\log }_{0.2}}x<0\]
    \[\Rightarrow \]\[{{\log }_{3}}{{\log }_{0.2}}x<1\]    \[\Rightarrow \]\[{{\log }_{0.2}}x>3\] \[\Rightarrow \]\[x<{{(0.2)}^{3}}\]
    \[\therefore \] solution set is \[\left( 0,\,\,\frac{1}{125} \right)\]

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