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JEE Main 202524 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
24 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Continuity and Differentiability

JEE Main 2025 · 24 January · Evening Shift · Mathematics · Continuity and Differentiability

Let [x] denote the greatest integer function, and let m and n...

Let [x][x] denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function f(x)=[x]+∣x−2∣,−2<x<3f(x)=[x]+|x-2|,-2 \lt x \lt 3, is not continuous and not differentiable. Then m+n\mathrm{m}+\mathrm{n} is equal to :Let [x] denote the greatest integer function, and let m and n respectively be the numbers of the points, where the

Options

  1. A6
  2. B8
  3. C9
  4. D7

Correct answer

B. 8

Step-by-step solution

f(x)=[x]+∣x−2∣,−2<x<3∴f(x)={−x,−2<x<−11−x,−1≤x<02−x,0≤x<13−x,1≤x<2x,2≤x<3\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}Let [x] denote the greatest integer function, and let m and n respectively be the numbers of the points, where the
It is clearly discontinues at 4 points and nondifferentiable at 4 points. ∴m+n=8\therefore \quad m+n=8
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