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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 9

  • question_answer
    In a meeting, there are six ministers, all speak exactly two languages. \[{{M}_{1}}\] speaks only \[{{L}_{1}}\] and \[{{L}_{2}},{{M}_{2}}\] speaks only \[{{L}_{2}}\] and \[{{L}_{3}},\]\[{{M}_{3}}\] speaks only \[{{L}_{3}}\] and \[{{L}_{4}},\,\,{{M}_{4}}\] speaks only \[{{L}_{4}}\] and \[{{L}_{2}},\]\[{{M}_{5}}\] speaks only \[{{L}_{4}}\] and \[{{L}_{1}},\]\[{{M}_{6}}\] speaks only \[{{L}_{1}}\] and \[{{L}_{3}}\]. If two ministers are chosen at random, then the probability that they speak a common language is

    A) \[1/2\]                   

    B) \[2/3\]                  

    C) \[4/5\]    

    D) \[5/6\]

    Correct Answer: C

    Solution :

     [c]
      \[{{M}_{1}}\] \[{{M}_{2}}\] \[{{M}_{3}}\] \[{{M}_{4}}\] \[{{M}_{5}}\] \[{{M}_{6}}\]
    \[{{L}_{1}}\] √       √ √
    \[{{L}_{2}}\] √ √   √    
    \[{{L}_{3}}\]   √ √     √
    \[{{L}_{4}}\]     √ √ √  
    Required probability \[=\frac{^{4}{{C}_{1}}{{\times }^{3}}{{C}_{2}}}{^{6}{{C}_{2}}}=\frac{4}{5}\]            


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