Maths Functions, Limits, Continuity and Differentiability NTA Abhiyas Question - Continuity and Differentiability Single Correct MCQ
Published on: August 12, 2026

The function f (x) = {x} sin ( [x] ) , where [.] denotes the greatest integer function and {.} is the fractional part function, is discontinuous at

A
all x
B
all integer points
C
no x
D
x which is not an integer

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Text Solution

Verified by Experts
The correct answer is:
C

no x

f(x) = {x} S in( [x])

= {x} sin (integral multiple of )

=0

Hence, f (x) is continuous for all x.

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