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BCECE Engineering BCECE Engineering Solved Paper-2013

  • question_answer
    If \[{{\,}^{n}}{{C}_{r-1}}=10,{{\,}^{n}}{{C}_{r}}=45\] and \[{{\,}^{n}}{{C}_{r+1}}=120,\] then r equals to

    A)  1                       

    B)  2                            

    C)  3                     

    D)  4

    Correct Answer: B

    Solution :

    Using \[\frac{{{\,}^{n}}{{C}_{r}}}{^{n}{{C}_{r-1}}}=\frac{n-r+1}{r},\] \[\frac{{{\,}^{n}}{{C}_{r}}}{^{n}{{C}_{r-1}}}=\frac{45}{10}\]and \[\frac{{{\,}^{n}}{{C}_{r+1}}}{^{n}{{C}_{r}}}=\frac{120}{45}\] \[\Rightarrow \]               \[\frac{n-r+1}{r}=\frac{9}{2}\] and        \[\frac{n-r}{r+1}=\frac{8}{3}\] \[\Rightarrow \]               \[\frac{8}{3}(r+1)+1=\frac{9}{2}r\] \[\Rightarrow \]               \[16r+16+6=27r\] \[\Rightarrow \]               \[11r=22\] \[\therefore \]  \[r=2\]


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