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JEE Main 24-Jan-2025 Paper - Shift 2 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 24-Jan-2025 Paper - Shift 24 Marks
MCQ
Let $[\mathrm{x}]$ denote the gereatest integer function, and let m and n respectively be the numbers of the points, where the function $f(x)=[x]+|x-2|$, $-2<x<3$, is not continuous and not differentiable.
  • A
    6
  • B
    9
  • ✓
    8
  • D
    7
✓

Answer

Correct option: C.
8
(C)
Sol. $\mathrm{f}(\mathrm{x})=[\mathrm{x}]+|\mathrm{x}-2| \quad-2<\mathrm{x}<3$
$f(x)=\left\{\begin{array}{cc}-x, & -2<x<-1 \\ -x+1, & -1 \leq x<0 \\ -x+2, & 0 \leq x<1 \\ -x+3, & 1 \leq x<2 \\ x, & 2 \leq x<3\end{array}\right.$
So $f(x)$ is not continuous at 4 points and not differentiable at 4 point
So $m+n=4+4=8$

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