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Eduncle posted an MCQ
May 28, 2023 • 22:32 pm 0 points
  • CSIR NET
  • Mathematical Sciences

Let S be the set of all integers from 100 to 999 which are neither divisible by 3 or nor divisible by 5.The number of elements in S is

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    Eduncle Best Answer

    S = {n :100 ≤ n ≤ 999 such that 3∤n and 5∤n}

    We know total number of integer from 'n' consecutive integers which are divisible by 'K' is given by nK , where [ ] denotes greatest integer function.

    Total number in elements in S

    = (Total numbers of integers from 100 to 999)- {total numbers of integers from 100 to 999 which are divisible by 3 } + (Total number of integers from 100 to 999.

    which are divisible by 5)- (Total number of integers from 100 to 999 which are divisible by 15).}

                    = 900 – 9003+9005-90015

                = 900 – 300-180+60 = 420+60=480

                    ⇒ So, option (1) is correct.

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