Let denote the greatest integer function and , . Let be the number of points in , where is not continuous and be the number of points in where is not differentiable. Then, is equal to:

3 Explanation: Solution 1. Function ka Analysis: Hume intervals ke hisaab se function ko simplify karna hoga: Case I: (Yahan ) Case II: (Yahan ) Case III: (Yahan ) 2. Resulting Function: 3. Points of Non-continuity ( ) aur Non-differentiability ( ): Continuity: , lekin . Isliye par discontinuous hai. Differentiability: ke andar ek smooth line hai, jo har jagah differentiable hai. 4. Final Calculation: Correct Option: (2)

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let $[x]$ denote the greatest integer function and $f(x) = \max \{1 + x + [x], 2 + x, x + 2[x]\}$ , $0 \leq x \leq 2$ . Let $m$ be the number of points in $[0, 2]$ , where $f$ is not continuous and $n$ be the number of points in $(0, 2)$ where $f$ is not differentiable. Then, $(m + n)^2$ is equal to:

JEE 2023 — Mathematics PYQ

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