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JEE Main 202126 AugustEvening Shift
Exam
JEE Main
Year
2021
Date
26 August
Shift
Evening Shift
Subject
Mathematics
Chapter
Continuity and Differentiability

JEE Main 2021 · 26 August · Evening Shift · Mathematics · Continuity and Differentiability

Let [ t ] denote the greatest integer less than or equal to t . Let...

Let [t][ t ] denote the greatest integer less than or equal to t.t .
Let f(x)=x−[x],g(x)=1−x+[x],f ( x ) = x - [ x ] , g ( x ) = 1 - x + [ x ] , and h(x)=minf(x),g(x),x∈[−2,2].h ( x ) = min { f ( x ) , g ( x ) } , x \in [ - 2, 2 ] . Then hh is :Let [ t ] denote the greatest integer less than or equal to t . Let f ( x ) = x - [ x ] , g ( x ) = 1 - x + [ x ] , and

Options

  1. Acontinuous in [−2,2][ - 2, 2 ] but not differentiable at more than four points in (−2,2)( - 2, 2 )
  2. BContinous in [−2,2][ - 2, 2 ] but not differentiable at exactly three poionts in (−2,2)( - 2, 2 )
  3. Cnot continuous at exactly four points in [−2,2][ - 2, 2 ]
  4. Dnot continuous at exactly three points in [−2,2][ - 2, 2 ]

Correct answer

A. continuous in [−2,2][ - 2, 2 ] but not differentiable at more than four points in (−2,2)( - 2, 2 )

Step-by-step solution

f(x)=x−[x]=xf ( x ) = x - [ x ] = { x }

g(x)=1−x+[x]=1−xg ( x ) = 1 - x + [ x ] = 1 - { x }

Now, Graph of min f(x),g(x){ f ( x ) , g ( x ) }

Let [ t ] denote the greatest integer less than or equal to t . Let f ( x ) = x - [ x ] , g ( x ) = 1 - x + [ x ] , and

Clearly graph is continuous in [−2,2][ - 2, 2 ] but non differentiable at 77 points (i.e. greater than 44) in (−2,2)( - 2, 2 )

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