KVPY Sample Paper KVPY Stream-SX Model Paper-15

  • question_answer
    The solution of the in-equation \[{{4}^{-x\text{ }+\text{ }0.5}}-{{7.2}^{-x}}<4,\] \[x\in R,\] is:

    A) \[(-2,\infty )\]

    B) \[(2,\infty )\]

    C) \[\left( 2,\frac{7}{2} \right)\]

    D) None of these

    Correct Answer: A

    Solution :

    Let \[{{2}^{-x}}=t\]                
    \[\therefore t>0\] ?? (i)
    \[\therefore \,\,2{{t}^{2}}-7t<4\]
    \[\Rightarrow \frac{-1}{2}<t<4\] ?? (ii)
    From (i) & (ii)
    \[0<t<4\]
    \[0<{{2}^{-x}}<4\]
    \[\Rightarrow -2<x<\infty \]
    \[\Rightarrow x\in (-2,\infty )\]


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