QJEEM20Mab59e: JEE Main 2020 Mathematics - Class 12 JEEM20Mab59e Solution: Let , for -10< x < 10, where [t] denotes the greatest integer…

$x \in ( - 10,10)$

$\Rightarrow$ ${x \over 2} \in ( - 5,5) \to 9$ integers

check continuity at x = 0

$$\begin{array}{ccc}f& (0)=& 0\\ f& (0^{+})=& 0\\ f& (0^{-})=& 0\end{array}\}continuousatx=0$$

function will be discontinuous when

${x \over 2} = \pm 4, \pm 3, \pm 2, \pm 1$

For example checking continuity at x = 4

$$\begin{array}{ccc}f& (4)=& 4\\ f& (4^{+})=& 4\\ f& (4^{-})=& 3\end{array}\}discontinuousatx=4$$

$\therefore$ 8 points of discontinuity.