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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 19

  • question_answer
    Let r, s, t be different prime numbers and a, b, c be positive integers. If LCM of a, b, c is \[{{r}^{2}}{{s}^{4}}{{t}^{2}}\]and HCF of a, b, c is \[r{{s}^{2}}t,\] then the number of ordered triplets (a, b, c) is  

    A) \[{{6}^{2}}\]                      

    B)        \[{{6}^{6}}\]                     

    C) \[216\]                  

    D)        \[432\]

    Correct Answer: D

    Solution :

    [d]
    a b c No. of ways
    r r \[{{r}^{2}}\] 3
    r \[{{r}^{2}}\] \[{{r}^{2}}\] 3
    t t \[{{t}^{2}}\] 3
    t \[{{t}^{2}}\] \[{{t}^{2}}\] 3
    \[{{s}^{2}}\] \[{{s}^{2}}\] \[{{s}^{4}}\] 3
    \[{{s}^{2}}\] \[{{s}^{3}}\] \[{{s}^{4}}\] 6
    \[{{s}^{2}}\] \[{{s}^{4}}\] \[{{s}^{4}}\] 3
    Total number of ways \[=6\times 6\times 12=432\]


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