JEE Main 2025 — Continuity and Differentiability Question with Solution
JEE Main 2025 (24 Jan Shift 2)
Question
Let denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function , is not continuous and not differentiable. Then is equal to :
Choose an option
Show full solutionCorrect option: B
Correct answer
B8
Step-by-step explanation
$\begin{aligned}
& f(x)=[x]+|x-2|,-2 < x < 3 \\
& \therefore f(x)=\left\{\begin{array}{l}
-x,-2 < x < -1 \\
1-x,-1 \leq x < 0 \\
2-x, 0 \leq x < 1 \\
3-x, 1 \leq x < 2 \\
x, 2 \leq x < 3
\end{array}\right.
\end{aligned}$
It is clearly discontinues at 4 points and nondifferentiable at 4 points.
It is clearly discontinues at 4 points and nondifferentiable at 4 points.
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This is a previous-year question from JEE Main 2025, covering the Continuity and Differentiability chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.