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JEE Main & Advanced Mathematics Sets Question Bank Self Evaluation Test - Sets

  • question_answer
    Let\[A=\{x|x\le 9,x\in N\}\]. Let \[B=\{a,b,c\}\] be the subset of A where \[\left( a+b+c \right)\] is a multiple of 3. What is the largest possible number of subsets like B?

    A) 12

    B) 21

    C) 27

    D) 30

    Correct Answer: D

    Solution :

    [d]Given \[A=\{x:x\le 9,x\in N\}=\{1,2,3,4,5,6,7,8,9\}\] Total possible multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27 But 3 and 27 are not possible because 3 and 27 cannot be express as such that \[a+b+c\]multiple of 3
    \[6\to 1+2+3\]
    \[9\to 2+3+4,5+3+1,6+2+1\]
    \[12\to 9+2+1,8+3+1,7+1+4,7+2+3\]
    \[6+4+2,\text{ }6+5+1,\text{ }5+4+3\]
    \[15\to 9+4+2,9+5+1,8+6+1,8+5+2,\]
    \[8+4+3,7+6+2,7+5+3,6+5+4\]
    \[18\to 9+8+1,9+7+2,9+6+3,\]
    \[9+5+4,8+7+3,8+6+4,7+6+5\]
    \[21\to 9+8+4,9+7+5,8+7+6\]
    \[24\to 9+8+7\]
    Hence, total largest possible subsets are 30.


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