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

Find the solution set of the inequality: $4x + 3 \geq 2x + 17$ and $3x - 5 < -2$.

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 number of elements in the set $S = \{x \in \mathbb{Z} : x^2 - 7x + 6 \leq 0 \text{ and } x^2 - 3x > 0\}$ is

The region represented by the inequations $2x + 3y \leqslant 18$,$x + y \geqslant 10$,$x \geqslant 0$,$y \geqslant 0$ is

The marks obtained by a student of Class $XI$ in first and second terminal examination are $62$ and $48$,respectively. Find the minimum marks he should get in the annual examination to have an average of at least $60$ marks.