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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Continuity and Differentiability

NTA Abhyas 2020 · Mathematics · Continuity and Differentiability

The number of discontinuity of the greatest integer function f (x)...

The number of discontinuity of the greatest integer function f(x)=[x],x∈(−72,100)f \left(x\right) = \left[x\right], x \in \left(- \dfrac{7}{2},100\right) is equal to

Options

  1. A104
  2. B102
  3. C101
  4. D103

Correct answer

D. 103

Step-by-step solution

Given, f(x)=[x],x∈(−3.5,100)f \left(x\right) = \left[x\right], x \in \left(-3.5, 100\right)

As we know greatest integer is discontinuous on integer values.

In given interval, the integer values are

(−3,−2,−1,0,…,99)( - 3, - 2, - 1, 0, \ldots , 99 )

∴Totalnumbersofintegersare103.∴ Total numbers of integers are 103.
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