KVPY Sample Paper KVPY Stream-SX Model Paper-4

  • question_answer
    Solution set of inequality \[lo{{g}_{sin\text{ }e}}\text{ }logo\text{ }x<0\] 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 \[\sin \,e\simeq sin2.71=\] positive value less than 1
    \[{{\log }_{\sin e}}{{\log }_{3}}{{\log }_{0.2}}x<0\]
    \[\Rightarrow {{\log }_{3}}{{\log }_{0.2}}x>1\]
    \[\Rightarrow {{\log }_{0.2}}x>3\]
    \[\Rightarrow x<{{(0.2)}^{3}}\]             \[\left\{ {{(0.2)}^{3}}=0.08=\frac{1}{125} \right\}\]
    \[\therefore \] solution set is \[\left( 0,\frac{1}{125} \right)\]

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