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Which among 2^{1/2},3^{1/3},4^{1/4},6^{1/6}\: and\: 12^{1/12}  is the largest?

  • Option 1)

    5\tfrac{1}{2}

  • Option 2)

    3^{1/3}

  • Option 3)

    4^{1/4}

  • Option 4)

    6^{1/6}

  • Option 5)

    2^{1/2}

            21/2, 31/3, 41/4, 61/6 and 121/12 26, 34, 43, 62 and 12                 34 is largest

If x = -0.5, then which of the following has the smallest value?

  • Option 1)

    2^{1/x}

  • Option 2)

    \frac{1}{x}

  • Option 3)

    \frac{1}{x^{2}}

     

  • Option 4)

    1

  • Option 5)

    2^{x}

            

Let x, y and z be distinct integers, that are odd and positive. Which one of the following statements cannot be true?

  • Option 1)

    (x – y)2 y is even

  • Option 2)

    (x – y)2 z is even

  • Option 3)

    (x + y + z)2 (x + y) is even      

  • Option 4)

    (x – y)(y + z)(x + y – z) Cannot be even

  • Option 5)

    xyz2 is odd`          

D option is false as sum or difference of two numbers will become even number

 

Which amongst the following is neither the greatest, nor the smallest:

 

  • Option 1)

     

    ^{5}\sqrt{220}

     

  • Option 2)

     

    \sqrt[3]{15}

     

     

  • Option 3)

     

    \sqrt[6]{220}

     

  • Option 4)

     

    None of these

     

  • Option 5)

     

    \sqrt{6}
     

     

The following option is neither the greatest nor the smallest:             
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