jee-main 2023 Q73

jee-main · India · session2_15apr_shift1 Integration by Substitution Substitution to Evaluate a Definite Integral (Numerical Answer)

Let $[ x ]$ denote the greatest integer function and $f ( x ) = \max \{ 1 + x + [ x ] , 2 + x , x + 2 [ x ] \} , 0 \leq x \leq 2$, where $m$ is the number of points in $( 0,2 )$ where $f$ is not continuous and $n$ be the number of points in $( 0,2 )$, where $f$ is not differentiable. Then $( m + n ) ^ { 2 } + 2$ is equal to
(1) 2
(2) 11
(3) 6
(4) 3

Let $[ x ]$ denote the greatest integer function and $f ( x ) = \max \{ 1 + x + [ x ] , 2 + x , x + 2 [ x ] \} , 0 \leq x \leq 2$, where $m$ is the number of points in $( 0,2 )$ where $f$ is not continuous and $n$ be the number of points in $( 0,2 )$, where $f$ is not differentiable. Then $( m + n ) ^ { 2 } + 2$ is equal to\\
(1) 2\\
(2) 11\\
(3) 6\\
(4) 3

Paper Questions

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