Graph of |x|

Q. $\text{If}f\left(x\right)=2x-1,\text{then the number of positive solution(s)}\text{of the equation}|f\left(x\right)|=|f(|x|-1)|\text{is/are}$

1. $1$
2. $2$
3. $4$
4. $8$

Q.

How many integers satisfy the condition $|x|\le -5$

Q.

How many integers satisfy the condition $|x|\ge 2$ and $|x|\le 6$

Q. How many integers satisfy the condition $|x|\le 3$? ___

Q. The number of points of intersection of the graphs of $(x-1{)}^2+y^2-9=0$ and $|y|=|\ln (|x|-1)|$ is -

1. $4$ when $x\in (0,\infty )$
2. $2$ when $x\in (2,\infty )$
3. $2$ when $x\in (-2,0)$
4. $3$ when $x<0$

Q. The equation $2\sin x=|x|+a$ has no solution for $a\in$

1. $(\frac{3\sqrt{3}-\pi }{3},\infty )$
2. $(\frac{3\sqrt{3}+\pi }{3},\infty )$
3. $(-\infty ,\frac{3\sqrt{3}-\pi }{3})$
4. $(-\infty ,\frac{3\sqrt{3}+\pi }{3})$

Q.

How many integers satisfy the condition $|x|\le 3$?

Q. The function $f\left(x\right)=min\{|x|,|x-2|,2-|x-1|\}$ is non-differentiable at $x$ equals

1. $-0.5$
2. $0$
3. $2$
4. $2.5$