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J & K CET Engineering J and K - CET Engineering Solved Paper-2004

  • question_answer
    If a, b, c are distinct positive real numbers and \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=1,\]then \[3{{({{a}^{2}}{{b}^{2}}{{c}^{2}})}^{1/3}}\] is

    A)  Less than 1                              

    B)  Equal to 1

    C)  Greater than 1

    D)  any real number

    Correct Answer: A

    Solution :

    Using \[AM>GM\] \[\therefore \] \[\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{3}>{{({{a}^{2}}{{b}^{2}}{{c}^{2}})}^{1/3}}\] \[\Rightarrow \]                      \[3{{({{a}^{2}}{{b}^{2}}{{c}^{2}})}^{1/3}}<1\]


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