
CBSE Class 12 Sample Paper for 2025 Boards
CBSE Class 12 Sample Paper for 2025 Boards
Last updated at Dec. 13, 2024 by Teachoo
Question 17 The function π:π βπ defined by π(π₯)=[π₯]; where [β ] denotes the greatest integer function, is (A) Continuous at π=π.π but not differentiable at π=π.π (B) Not Continuous at π=π.π but differentiable at π=π.π (C) Not Continuous at π=π.π and not differentiable at π=π.π (D) Continuous as well as differentiable at π=π.πLetβs 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)