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KVPY Sample Paper KVPY Stream-SX Model Paper-20

  • question_answer
    If  \[^{n}{{C}_{4}}{{,}^{n}}{{C}_{5}}\]and\[^{n}{{C}_{6}}\]are in A.P., then n can be :

    A) 9

    B) 14 

    C) 11

    D) 12

    Correct Answer: B

    Solution :

    \[{{2.}^{n}}{{C}_{5}}{{-}^{n}}{{C}_{4}}{{+}^{n}}{{C}_{6}}\]
    \[2.\frac{\left| \!{\nderline {\,   n \,}} \right. }{\left| \!{\nderline {\,   5\left| \!{\nderline {\,   n-5 \,}} \right.  \,}} \right. }=\frac{\left| \!{\nderline {\,   n \,}} \right. }{\left| \!{\nderline {\,   4\left| \!{\nderline {\,   n-4 \,}} \right.  \,}} \right. }+\frac{\left| \!{\nderline {\,   n \,}} \right. }{\left| \!{\nderline {\,   6\left| \!{\nderline {\,   n-6 \,}} \right.  \,}} \right. }\]
    \[\frac{2}{5}.\frac{1}{n-5}=\frac{1}{(n-4)(n-5)}+\frac{1}{30}\]
    \[n=14\]satisfying equation.


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