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KVPY Sample Paper KVPY Stream-SX Model Paper-1

  • question_answer
    The number of ordered pair (a, b), where \[a,b\in \{1,2,3,...,50\}\] such that \[{{6}^{a}}+{{9}^{b}}\] is multiple of \[5\] is

    A) 1260                

    B) 2500    

    C) 625                              

    D) 500

    Correct Answer: A

    Solution :

    [a]
    \[{{6}^{a}}+{{9}^{b}}={{(5+1)}^{a}}+{{(10-1)}^{b}}\]
    \[=5\lambda +(1){}^\circ +10\mu +{{(-1)}^{b}}\]
    \[=5\,(\lambda +24)+{{(1)}^{a}}+{{(-1)}^{b}}\]
    is divisible by 5 if b is odd.
    \[\therefore \] Total number of ordered pair \[(a,b)\]
                \[=50\times 25=1250\]


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