Solve the following inequality: $\frac{|x-1|}{x+2} < 1$.

If $\frac{x^{2}-1}{x^{2}+1} \geq 0,$ then $x \in$

Let $a$ $(a < 0, a \notin I)$ be a constant and $t$ be a parameter. Then the set of values of $t$ for which the function $f(x) = \left( \frac{|[t]+1|+a}{|[t]+1|+1-a} \right)x$ is a decreasing function of $x$ (where $[.]$ denotes the greatest integer function) is:

The solution set of the constraints $|x-y| \leqslant 1, x, y \geqslant 0$ is

The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is $180 \ cm$,then:

The region represented by the inequation $x-y \leq -1, x-y \geq 0, x \geq 0, y \geq 0$ is $.....$