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  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main Sample Paper-1

  • question_answer
    In a football championship, there were played 153 matches. Every two teams played one match with each other. The number of teams participating in the championship is

    A)  14                                         

    B)  22

    C)  18                                         

    D)  None of these

    Correct Answer: C

    Solution :

    If n is the number of teams, then \[^{n}{{C}_{2}}=153\Rightarrow \frac{n!}{2!(n-2)!}=153\] \[\Rightarrow \]\[n(n-1)=153\times 2\] \[\Rightarrow \]\[{{n}^{2}}-n-306=0\] \[\Rightarrow \]\[(n-18)(n+17)=0\] \[\Rightarrow \]\[n=18,-17\] \[\therefore \]                  n = 18                    \[(n\ne -17)\]


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