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JEE Main & Advanced Mathematics Functions Question Bank Critical Thinking

  • question_answer
    For a real number \[x,\ [x]\] denotes the integral part of x. The value of  \[\left[ \frac{1}{2} \right]+\left[ \frac{1}{2}+\frac{1}{100} \right]+\left[ \frac{1}{2}+\frac{2}{100} \right]+....+\left[ \frac{1}{2}+\frac{99}{100} \right]\] is [IIT Screening 1994]           

    A) 49

    B) 50

    C) 48

    D) 51

    Correct Answer: B

    Solution :

    Q [x] denotes the integral part of x. Hence, after term \[\left[ \frac{1}{2}+\frac{50}{100} \right]\,,\] each term will be one. Hence the sum of given series will be 50.


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