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NTSE Sample Paper NTSE SAT Practice Test-17

  • question_answer
    Let there be n numbers (where n > 1) of which one is \[\left( 1-\frac{1}{n} \right)\]and the rest are 1. The mean of n numbers is

    A) 1                                 

    B) \[n-\frac{1}{n}\]

    C) \[1-\frac{1}{{{n}^{2}}}\]        

    D) \[n-\frac{1}{{{n}^{2}}}\]

    Correct Answer: C

    Solution :

    [c] Sum of the n numbers \[=\left( 1-\frac{1}{n} \right)+(1+1+...........+\overline{n-1}\,\,\,times)\] \[=\frac{n-1}{n}+(n-1)=(n-1)\left( 1+\frac{1}{n} \right)=\frac{{{n}^{2}}-1}{n}\] Mean (Average) \[=\frac{{{n}^{2}}-1}{n}.\frac{1}{n}=\frac{{{n}^{2}}-1}{{{n}^{2}}}\] \[=1-\frac{1}{{{n}^{2}}}\]     


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