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JEE Main & Advanced Mathematics Equations and Inequalities Question Bank Self Evaluation Test - Linear Inequalities

  • question_answer
    If \[5\{x\}=x+[x]\] and \[[x]-\{x\}=\frac{1}{2}\] when \[\{x\}\] and \[[x]\] are fractional and integral part of x then x is

    A) \[\frac{1}{2}\]

    B) \[\frac{3}{2}\]

    C) \[\frac{5}{2}\]

    D) \[\frac{7}{2}\]

    Correct Answer: B

    Solution :

    [b] \[5\{x\}=x+[x]\,\,and\,\,[x]-\{x\}=\frac{1}{2}\] Since \[x=[x]+\{x\}\Rightarrow 4\{x\}=2[x]\] and \[[x]-\{x\}=\frac{1}{2}\] after solving \[[x]=1\] and \[\{x\}=\frac{1}{2}\therefore x=1+\frac{1}{2}=\frac{3}{2}.\]


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