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JEE MATHEMATICS MCQ: FUNCTIONS

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If [x][x] denotes the greatest integer ≤x\le x, then
[23]+[23+199]+[23+299]+...+[23+9899]\left[ {\frac{2}{3}} \right] + \left[ {\frac{2}{3} + \frac{1}{{99}}} \right] + \left[ {\frac{2}{3} + \frac{2}{{99}}} \right] + ... + \left[ {\frac{2}{3} + \frac{{98}}{{99}}} \right] is equal to
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Correct option: C
66
Option C is correct. The value inside the greatest integer function becomes greater than or equal to 1 when r >= 33. Therefore, the sum is equal to the number of terms where r >= 33, which is 98 - 33 + 1 = 66.

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