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JEE Main & Advanced Mathematics Functions Question Bank Self Evaluation Test - Relation and Functions-II

  • question_answer
    Let \[f:\{x,y,z\}\to \{1,2,3\}\] be a one-one mapping such that only one of the following three statements is true and remaining two are false: \[f(x)\ne 2,f(y)=2,f(z)\ne 1\], then

    A) \[f(x)>f(y)>f(z)\]

    B) \[f(x)<f(y)<f(z)\]

    C) \[f(y)<f(x)<f(z)\]

    D) \[f(y)<f(z)<f(x)\]

    Correct Answer: C

    Solution :

    [c] Let \[f(x)\ne 2\] be true and \[f(y)=2,f(z)\ne 1\] are False \[\Rightarrow f(x)\ne 2,f(y)\ne 2,f(z)=1\] \[\Rightarrow f(x)=3,f(y)=3,f(z)=1\] but then function is many one, similarly to other cases.


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