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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2001

  • question_answer
    If \[{{\,}^{n}}{{P}_{4}}=24{{\,}^{n}}{{C}_{5}},\]then the value of \[n:\]

    A)  10                                         

    B)  15

    C)  9                                            

    D)  5

    Correct Answer: C

    Solution :

    \[{{\,}^{n}}{{P}_{4}}=24\,{{\,}^{n}}{{C}_{5}}\Rightarrow \frac{n!}{n-4!}=\frac{24\,n!}{5!n-5!}\] \[\Rightarrow \]\[\frac{n!}{(n-4)n-5!}=\frac{24n!}{5!n-5!}\] \[\Rightarrow \]\[\frac{1}{n-4}=\frac{24}{5.4.3.2}\Rightarrow \frac{1}{n-4}=\frac{1}{5}\] \[\Rightarrow \]\[n-4=5\Rightarrow n=9\]


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