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JEE Main & Advanced JEE Main Paper (Held on 10-4-2019 Morning)

  • question_answer
    The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated, is : [JEE Main 10-4-2019 Morning]

    A) 36                               

    B) 60

    C) 48                               

    D) 72

    Correct Answer: B

    Solution :

    Sum of given digits 0, 1, 2, 5, 7, 9 is 24. Let the six digit number be abcdef and to be divisible by 11 so \[|(a+c+e)-(b+d+f)|\]is multiple of 11. Hence only possibility is \[a+c+e=12=b+d+f\] Case-I \[\left\{ a,c,e \right\}=\left\{ 9,2,1 \right\}\And \left\{ b,d,f \right\}=\]\[\left\{ 7,5,0 \right\}\] So, Number of numbers \[=3!\times 3!=36\] Case-II \[\left\{ a,c,e \right\}=\left\{ 7,5,0 \right\}\]and \[\left\{ b,d,f \right\}=\left\{ 9,2,1 \right\}\] So, Number of numbers \[2\times 2!\times 3!=24\] Total = 60


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