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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2005

  • question_answer
    If\[{{\,}^{n}}{{C}_{12}}={{\,}^{n}}{{C}_{6}}\], then \[^{n}{{C}_{2}}=\]

    A)  72                                         

    B)  153

    C)  306                                       

    D)  2556

    Correct Answer: B

    Solution :

    Given that                 \[^{n}{{C}_{12}}={{\,}^{n}}{{C}_{6}}\] or            \[^{n}{{C}_{n}}={{\,}^{n}}{{C}_{6}}\] \[\Rightarrow \]               \[n-12=6\,\,\,\,\,\Rightarrow \,\,\,\,\,n=18\] \[\therefore \]  \[^{n}{{C}_{2}}={{\,}^{18}}{{C}_{2}}=\frac{18\times 17}{2\times 1}\]                                 \[=153\]


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