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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2005

  • question_answer
    Let\[{{D}_{70}}=\{1,2,5,7,10,14,35,70\}\]. Define\[+,\]\[.,\] and\[,,\]by\[a+b=1\,cm(a,b),a.b-\gcd (a,b)\]and \[a=\frac{70}{a}\]for all\[a,b\in {{D}_{70}}\].The value of\[(2+7)\]\[(14.10)\]is:

    A)  7                                            

    B)  14

    C)  35                         

    D)         5

    E)  1

    Correct Answer: A

    Solution :

    \[(2+7)=1cm\text{ (}2,7)=14\] and \[(14-10)=gcd\text{ (}14,10)=2\] \[\therefore \]  \[(14.10)=\frac{70}{2}=35\] \[\therefore \]  \[(2+7)(14.10)\]                 \[=14.35=\gcd (14,35)=7\]


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