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KVPY Sample Paper KVPY Stream-SX Model Paper-2

  • question_answer
    Sum of all the digits used in writing all the numbers from 1 to 1000 is:

    A) 12741              

    B) 13946

    C) 4996                            

    D) 13501

    Correct Answer: D

    Solution :

    \[S=0+1+2+3+......+998+999\]
    \[S=999+998+.......\text{ }+1+0\]
    \[2S=999+999+....(1000\,\,\text{times})\]
    (sum of the digits being 27 in each case)
    \[=1000\times 27\]\[\Rightarrow \]\[S=13501\]


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