JEE Main 2026 · 2 Apr · Shift 2 · Mathematics Q25

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MathematicsInteger+4 / -1Question 25 of 75

The number of points in the interval $[2,4]$ , at which the function $f(x)=\left[x^2-x-\dfrac12\right]$ , where $[\cdot]$ denotes the greatest integer function, is discontinuous, is ________.

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Answer and worked solution

Official answer: 10

Where it jumps. $g(x)=x^2-x-\frac12$ increases on $[2,4]$ from 1.5 to 11.5. $[g]$ is discontinuous exactly where $g$ crosses an integer: $g=2,3,\dots,11$ .

Count 10 points (none at the endpoints).

Answer: 10

Topics:Continuity

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JEE Main 2026 · 2 Apr · Shift 2, Mathematics question 25