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JEE Main 2018

JEE Main 2018 Mathematics question on Limits Continuity and Differentiability

For each t∈Rt \in \mathbf{R}, let [t][t] be the greatest integer less than or equal to tt. Then,
lim⁡x→0+x([1x]+[2x]+…+[15x])\lim_{x \to 0^+} x\left(\left[\frac{1}{x}\right] + \left[\frac{2}{x}\right] + \ldots + \left[\frac{15}{x}\right]\right)
  1. A.
    is equal to 0
  2. B.
    is equal to 15
  3. C.
    is equal to 120
  4. D.
    does not exist (in R\mathbf{R})
Show answer

Correct option: C

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