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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 35

  • question_answer
    The relation R denned on the set N of natural numbers by \[x\,Ry\Leftrightarrow 2{{x}^{2}}-3xy+{{y}^{2}}=0\] is

    A) Symmetric but not reflexive                         

    B) Only symmetric

    C) Not symmetric but reflexive  

    D) Equivalence

    Correct Answer: C

    Solution :

      [c] (i) \[x\,\,R\,\,x\Leftrightarrow 2{{x}^{2}}-3x.x+{{x}^{2}}=0;\,\,\forall x\in N,\] So, R is reflexive. (ii) For  \[x=1,\] \[y=2;\] \[2{{x}^{2}}-3xy+{{y}^{2}}=0\] \[\therefore \,\,1\,R\,\,2\]but \[2\times {{2}^{2}}-3\times 2\times 1+{{1}^{2}}=3\ne 0.\]. So, 2 is not R-related to 1. So, R is not symmetric.                    


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