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JEE Main & Advanced Sample Paper JEE Main Sample Paper-14

  • question_answer
    Let \[f:N\times N\] satisfying \[f(0)=0,\] \[f(1)=1,\] \[f(n)=f(n-1)+f(n-2),\,n\ge 2,\] then which of the following is true?

    A)  \[fof\,\,(2)=2\]               

    B)  \[fof\,\,(2)=1\]

    C)  \[f({{S}_{n}})\] is divisible by 9

    D)  \[fof\,(5)=1\]

    Correct Answer: B

    Solution :

     Given relation \[f(n)=f(n-1)+f(n-2)\] \[f(2)=f(1)+f(0)=1+0=1\] \[f(3)=f(2)+f(1)=1+1=2\] \[f(4)=f(3)+f(2)=2+1=3\] \[f(5)=f(4)+f(3)=3+2=5\] \[\therefore \]  \[fof(1)=f\{f(1)\}=f(1)=1\] \[fof(2)=f\{f(2)\}=f(1)=1\]


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