JEE 2023 — Mathematics PYQ

• Function Analysis: $f(x)=|[x]|+\sqrt{\{x\}}$, jahan $\{x\}$ fractional part function hai.

• Discontinuity Points: Hum jante hain ki $[x]$ aur $\{x\}$ dono integers par discontinuous hote hain.

• Interval $(-2,1)$: Is interval ke andar integers hain: $x=-1$ aur $x=0$.

• Checking $x=-1$: Left hand limit aur Right hand limit check karne par values alag aati hain.

• Checking $x=0$: Yahan bhi jump discontinuity milti hai.

• Dono points ($x=-1,0$) par function discontinuous hai.

Ans: $2$