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KVPY Sample Paper KVPY Stream-SX Model Paper-26

  • question_answer
    When \[1!+2!+3!+4!+....2020!\] is divided by 35, then remainder will be

    A) 31

    B) 32

    C) 33

    D) 34

    Correct Answer: C

    Solution :

    \[1!+2!+3!+4!+5!+6!+7!+8!.......+2020!\]
    \[1+2+6+24+120+720+35k\][\[\therefore 7!\,\] onward are divisible by 35]
    \[\Rightarrow \,\,\,\,873+35k\] \[\Rightarrow \,\,\,\,840+33+35k\] \[\Rightarrow \,\,\,\,35\times 24+35k+33\] \[\Rightarrow 35\left( 24+k \right)+33\]
    \[\therefore \]Remainder = 33


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