JEE Main 25 July 2021 Shift 1 Solved Paper

Section: Mathematics

Question : 74 of 90

Marks: +1, -0

Let f:[0,∞)→[0,∞) be defined as
f(x)=

∫

[y]dy
where [x] is the greatest integer less than or equal to x. Which of the following is true?

[25 Jul 2021 Shift 1]

f is continuous at every point in [0,∞) and differentiable except at the integer points.
f is both continuous and differentiable except at the integer points in [0,∞).
f is continuous everywhere except at the integer points in [0,∞).
f is differentiable at every point in [0,∞).

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