MathsJEE Main 22 Jan 2026, Shift 2·Q18·MCQ·Moderate

Sets, Relations & Functions · Greatest integer function

Let

f(x) = [x]^2 - [x + 3] - 3

,

x \in \mathbb{R}

where

[\,\bullet\,]

is the greatest integer function. Then

(1) $f(x) > 0$ only for $x \in [4, \infty)$
(2) $f(x) < 0$ only for $x \in [-1, 3)$
(3) $\displaystyle\int_0^2 f(x)\,dx = -6$
(4) $f(x) = 0$ for finitely many values of $x$ .

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