Question 17 - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at August 14, 2026 by Teachoo

Question 17 - The function 𝑓: 𝑅 → 𝑍 defined by f(x)=[x]; where - CBSE Class 12 Sample Paper for 2025 Boards

part 2 - Question 17 - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

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Question 17 The function 𝑓:𝑅→𝑍 defined by 𝑓(𝑥)=[𝑥]; where [⋅] denotes the greatest integer function, is (A) Continuous at 𝒙=𝟐.𝟓 but not differentiable at 𝒙=𝟐.𝟓 (B) Not Continuous at 𝒙=𝟐.𝟓 but differentiable at 𝒙=𝟐.𝟓 (C) Not Continuous at 𝒙=𝟐.𝟓 and not differentiable at 𝒙=𝟐.𝟓 (D) Continuous as well as differentiable at 𝒙=𝟐.𝟓Let’s draw the graph We note that At integer points, [x] is not continuous At non integer points, [x] is continuous and differentiable Therefore, [x] is continuous and differentiable both at x = 2.5 So, the correct answer is (D)

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